544 lines
436 KiB
Python
544 lines
436 KiB
Python
from sympy.polys.rings import ring
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from sympy.polys.fields import field
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from sympy.polys.domains import ZZ, QQ
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from sympy.polys.solvers import solve_lin_sys
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# Expected times on 3.4 GHz i7:
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# In [1]: %timeit time_solve_lin_sys_189x49()
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# 1 loops, best of 3: 864 ms per loop
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# In [2]: %timeit time_solve_lin_sys_165x165()
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# 1 loops, best of 3: 1.83 s per loop
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# In [3]: %timeit time_solve_lin_sys_10x8()
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# 1 loops, best of 3: 2.31 s per loop
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# Benchmark R_165: shows how fast are arithmetics in QQ.
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R_165, uk_0, uk_1, uk_2, uk_3, uk_4, uk_5, uk_6, uk_7, uk_8, uk_9, uk_10, uk_11, uk_12, uk_13, uk_14, uk_15, uk_16, uk_17, uk_18, uk_19, uk_20, uk_21, uk_22, uk_23, uk_24, uk_25, uk_26, uk_27, uk_28, uk_29, uk_30, uk_31, uk_32, uk_33, uk_34, uk_35, uk_36, uk_37, uk_38, uk_39, uk_40, uk_41, uk_42, uk_43, uk_44, uk_45, uk_46, uk_47, uk_48, uk_49, uk_50, uk_51, uk_52, uk_53, uk_54, uk_55, uk_56, uk_57, uk_58, uk_59, uk_60, uk_61, uk_62, uk_63, uk_64, uk_65, uk_66, uk_67, uk_68, uk_69, uk_70, uk_71, uk_72, uk_73, uk_74, uk_75, uk_76, uk_77, uk_78, uk_79, uk_80, uk_81, uk_82, uk_83, uk_84, uk_85, uk_86, uk_87, uk_88, uk_89, uk_90, uk_91, uk_92, uk_93, uk_94, uk_95, uk_96, uk_97, uk_98, uk_99, uk_100, uk_101, uk_102, uk_103, uk_104, uk_105, uk_106, uk_107, uk_108, uk_109, uk_110, uk_111, uk_112, uk_113, uk_114, uk_115, uk_116, uk_117, uk_118, uk_119, uk_120, uk_121, uk_122, uk_123, uk_124, uk_125, uk_126, uk_127, uk_128, uk_129, uk_130, uk_131, uk_132, uk_133, uk_134, uk_135, uk_136, uk_137, uk_138, uk_139, uk_140, uk_141, uk_142, uk_143, uk_144, uk_145, uk_146, uk_147, uk_148, uk_149, uk_150, uk_151, uk_152, uk_153, uk_154, uk_155, uk_156, uk_157, uk_158, uk_159, uk_160, uk_161, uk_162, uk_163, uk_164 = ring("uk_:165", QQ)
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def eqs_165x165():
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return [
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 411400*uk_100 + 1683000*uk_101 + 166375*uk_103 + 680625*uk_104 + 2784375*uk_106 + 729*uk_109 + 456471*uk_11 + 4131*uk_110 + 11016*uk_111 + 4455*uk_112 + 18225*uk_113 + 23409*uk_115 + 62424*uk_116 + 25245*uk_117 + 103275*uk_118 + 2586669*uk_12 + 166464*uk_120 + 67320*uk_121 + 275400*uk_122 + 27225*uk_124 + 111375*uk_125 + 455625*uk_127 + 6897784*uk_13 + 132651*uk_130 + 353736*uk_131 + 143055*uk_132 + 585225*uk_133 + 943296*uk_135 + 381480*uk_136 + 1560600*uk_137 + 154275*uk_139 + 2789545*uk_14 + 631125*uk_140 + 2581875*uk_142 + 2515456*uk_145 + 1017280*uk_146 + 4161600*uk_147 + 411400*uk_149 + 11411775*uk_15 + 1683000*uk_150 + 6885000*uk_152 + 166375*uk_155 + 680625*uk_156 + 2784375*uk_158 + 11390625*uk_161 + 3025*uk_17 + 495*uk_18 + 2805*uk_19 + 55*uk_2 + 7480*uk_20 + 3025*uk_21 + 12375*uk_22 + 81*uk_24 + 459*uk_25 + 1224*uk_26 + 495*uk_27 + 2025*uk_28 + 9*uk_3 + 2601*uk_30 + 6936*uk_31 + 2805*uk_32 + 11475*uk_33 + 18496*uk_35 + 7480*uk_36 + 30600*uk_37 + 3025*uk_39 + 51*uk_4 + 12375*uk_40 + 50625*uk_42 + 130470415844959*uk_45 + 141482932855*uk_46 + 23151752649*uk_47 + 131193265011*uk_48 + 349848706696*uk_49 + 136*uk_5 + 141482932855*uk_50 + 578793816225*uk_51 + 153424975*uk_53 + 25105905*uk_54 + 142266795*uk_55 + 379378120*uk_56 + 153424975*uk_57 + 627647625*uk_58 + 55*uk_6 + 4108239*uk_60 + 23280021*uk_61 + 62080056*uk_62 + 25105905*uk_63 + 102705975*uk_64 + 131920119*uk_66 + 351786984*uk_67 + 142266795*uk_68 + 582000525*uk_69 + 225*uk_7 + 938098624*uk_71 + 379378120*uk_72 + 1552001400*uk_73 + 153424975*uk_75 + 627647625*uk_76 + 2567649375*uk_78 + 166375*uk_81 + 27225*uk_82 + 154275*uk_83 + 411400*uk_84 + 166375*uk_85 + 680625*uk_86 + 4455*uk_88 + 25245*uk_89 + 2572416961*uk_9 + 67320*uk_90 + 27225*uk_91 + 111375*uk_92 + 143055*uk_94 + 381480*uk_95 + 154275*uk_96 + 631125*uk_97 + 1017280*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 413820*uk_100 + 1633500*uk_101 + 65340*uk_102 + 178695*uk_103 + 705375*uk_104 + 28215*uk_105 + 2784375*uk_106 + 111375*uk_107 + 4455*uk_108 + 97336*uk_109 + 2333074*uk_11 + 19044*uk_110 + 279312*uk_111 + 120612*uk_112 + 476100*uk_113 + 19044*uk_114 + 3726*uk_115 + 54648*uk_116 + 23598*uk_117 + 93150*uk_118 + 3726*uk_119 + 456471*uk_12 + 801504*uk_120 + 346104*uk_121 + 1366200*uk_122 + 54648*uk_123 + 149454*uk_124 + 589950*uk_125 + 23598*uk_126 + 2328750*uk_127 + 93150*uk_128 + 3726*uk_129 + 6694908*uk_13 + 729*uk_130 + 10692*uk_131 + 4617*uk_132 + 18225*uk_133 + 729*uk_134 + 156816*uk_135 + 67716*uk_136 + 267300*uk_137 + 10692*uk_138 + 29241*uk_139 + 2890983*uk_14 + 115425*uk_140 + 4617*uk_141 + 455625*uk_142 + 18225*uk_143 + 729*uk_144 + 2299968*uk_145 + 993168*uk_146 + 3920400*uk_147 + 156816*uk_148 + 428868*uk_149 + 11411775*uk_15 + 1692900*uk_150 + 67716*uk_151 + 6682500*uk_152 + 267300*uk_153 + 10692*uk_154 + 185193*uk_155 + 731025*uk_156 + 29241*uk_157 + 2885625*uk_158 + 115425*uk_159 + 456471*uk_16 + 4617*uk_160 + 11390625*uk_161 + 455625*uk_162 + 18225*uk_163 + 729*uk_164 + 3025*uk_17 + 2530*uk_18 + 495*uk_19 + 55*uk_2 + 7260*uk_20 + 3135*uk_21 + 12375*uk_22 + 495*uk_23 + 2116*uk_24 + 414*uk_25 + 6072*uk_26 + 2622*uk_27 + 10350*uk_28 + 414*uk_29 + 46*uk_3 + 81*uk_30 + 1188*uk_31 + 513*uk_32 + 2025*uk_33 + 81*uk_34 + 17424*uk_35 + 7524*uk_36 + 29700*uk_37 + 1188*uk_38 + 3249*uk_39 + 9*uk_4 + 12825*uk_40 + 513*uk_41 + 50625*uk_42 + 2025*uk_43 + 81*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 118331180206*uk_47 + 23151752649*uk_48 + 339559038852*uk_49 + 132*uk_5 + 146627766777*uk_50 + 578793816225*uk_51 + 23151752649*uk_52 + 153424975*uk_53 + 128319070*uk_54 + 25105905*uk_55 + 368219940*uk_56 + 159004065*uk_57 + 627647625*uk_58 + 25105905*uk_59 + 57*uk_6 + 107321404*uk_60 + 20997666*uk_61 + 307965768*uk_62 + 132985218*uk_63 + 524941650*uk_64 + 20997666*uk_65 + 4108239*uk_66 + 60254172*uk_67 + 26018847*uk_68 + 102705975*uk_69 + 225*uk_7 + 4108239*uk_70 + 883727856*uk_71 + 381609756*uk_72 + 1506354300*uk_73 + 60254172*uk_74 + 164786031*uk_75 + 650471175*uk_76 + 26018847*uk_77 + 2567649375*uk_78 + 102705975*uk_79 + 9*uk_8 + 4108239*uk_80 + 166375*uk_81 + 139150*uk_82 + 27225*uk_83 + 399300*uk_84 + 172425*uk_85 + 680625*uk_86 + 27225*uk_87 + 116380*uk_88 + 22770*uk_89 + 2572416961*uk_9 + 333960*uk_90 + 144210*uk_91 + 569250*uk_92 + 22770*uk_93 + 4455*uk_94 + 65340*uk_95 + 28215*uk_96 + 111375*uk_97 + 4455*uk_98 + 958320*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 402380*uk_100 + 1534500*uk_101 + 313720*uk_102 + 191455*uk_103 + 730125*uk_104 + 149270*uk_105 + 2784375*uk_106 + 569250*uk_107 + 116380*uk_108 + 912673*uk_109 + 4919743*uk_11 + 432814*uk_110 + 1166716*uk_111 + 555131*uk_112 + 2117025*uk_113 + 432814*uk_114 + 205252*uk_115 + 553288*uk_116 + 263258*uk_117 + 1003950*uk_118 + 205252*uk_119 + 2333074*uk_12 + 1491472*uk_120 + 709652*uk_121 + 2706300*uk_122 + 553288*uk_123 + 337657*uk_124 + 1287675*uk_125 + 263258*uk_126 + 4910625*uk_127 + 1003950*uk_128 + 205252*uk_129 + 6289156*uk_13 + 97336*uk_130 + 262384*uk_131 + 124844*uk_132 + 476100*uk_133 + 97336*uk_134 + 707296*uk_135 + 336536*uk_136 + 1283400*uk_137 + 262384*uk_138 + 160126*uk_139 + 2992421*uk_14 + 610650*uk_140 + 124844*uk_141 + 2328750*uk_142 + 476100*uk_143 + 97336*uk_144 + 1906624*uk_145 + 907184*uk_146 + 3459600*uk_147 + 707296*uk_148 + 431644*uk_149 + 11411775*uk_15 + 1646100*uk_150 + 336536*uk_151 + 6277500*uk_152 + 1283400*uk_153 + 262384*uk_154 + 205379*uk_155 + 783225*uk_156 + 160126*uk_157 + 2986875*uk_158 + 610650*uk_159 + 2333074*uk_16 + 124844*uk_160 + 11390625*uk_161 + 2328750*uk_162 + 476100*uk_163 + 97336*uk_164 + 3025*uk_17 + 5335*uk_18 + 2530*uk_19 + 55*uk_2 + 6820*uk_20 + 3245*uk_21 + 12375*uk_22 + 2530*uk_23 + 9409*uk_24 + 4462*uk_25 + 12028*uk_26 + 5723*uk_27 + 21825*uk_28 + 4462*uk_29 + 97*uk_3 + 2116*uk_30 + 5704*uk_31 + 2714*uk_32 + 10350*uk_33 + 2116*uk_34 + 15376*uk_35 + 7316*uk_36 + 27900*uk_37 + 5704*uk_38 + 3481*uk_39 + 46*uk_4 + 13275*uk_40 + 2714*uk_41 + 50625*uk_42 + 10350*uk_43 + 2116*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 249524445217*uk_47 + 118331180206*uk_48 + 318979703164*uk_49 + 124*uk_5 + 151772600699*uk_50 + 578793816225*uk_51 + 118331180206*uk_52 + 153424975*uk_53 + 270585865*uk_54 + 128319070*uk_55 + 345903580*uk_56 + 164583155*uk_57 + 627647625*uk_58 + 128319070*uk_59 + 59*uk_6 + 477215071*uk_60 + 226308178*uk_61 + 610048132*uk_62 + 290264837*uk_63 + 1106942175*uk_64 + 226308178*uk_65 + 107321404*uk_66 + 289301176*uk_67 + 137651366*uk_68 + 524941650*uk_69 + 225*uk_7 + 107321404*uk_70 + 779855344*uk_71 + 371060204*uk_72 + 1415060100*uk_73 + 289301176*uk_74 + 176552839*uk_75 + 673294725*uk_76 + 137651366*uk_77 + 2567649375*uk_78 + 524941650*uk_79 + 46*uk_8 + 107321404*uk_80 + 166375*uk_81 + 293425*uk_82 + 139150*uk_83 + 375100*uk_84 + 178475*uk_85 + 680625*uk_86 + 139150*uk_87 + 517495*uk_88 + 245410*uk_89 + 2572416961*uk_9 + 661540*uk_90 + 314765*uk_91 + 1200375*uk_92 + 245410*uk_93 + 116380*uk_94 + 313720*uk_95 + 149270*uk_96 + 569250*uk_97 + 116380*uk_98 + 845680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 389180*uk_100 + 1435500*uk_101 + 618860*uk_102 + 204655*uk_103 + 754875*uk_104 + 325435*uk_105 + 2784375*uk_106 + 1200375*uk_107 + 517495*uk_108 + 3375000*uk_109 + 7607850*uk_11 + 2182500*uk_110 + 2610000*uk_111 + 1372500*uk_112 + 5062500*uk_113 + 2182500*uk_114 + 1411350*uk_115 + 1687800*uk_116 + 887550*uk_117 + 3273750*uk_118 + 1411350*uk_119 + 4919743*uk_12 + 2018400*uk_120 + 1061400*uk_121 + 3915000*uk_122 + 1687800*uk_123 + 558150*uk_124 + 2058750*uk_125 + 887550*uk_126 + 7593750*uk_127 + 3273750*uk_128 + 1411350*uk_129 + 5883404*uk_13 + 912673*uk_130 + 1091444*uk_131 + 573949*uk_132 + 2117025*uk_133 + 912673*uk_134 + 1305232*uk_135 + 686372*uk_136 + 2531700*uk_137 + 1091444*uk_138 + 360937*uk_139 + 3093859*uk_14 + 1331325*uk_140 + 573949*uk_141 + 4910625*uk_142 + 2117025*uk_143 + 912673*uk_144 + 1560896*uk_145 + 820816*uk_146 + 3027600*uk_147 + 1305232*uk_148 + 431636*uk_149 + 11411775*uk_15 + 1592100*uk_150 + 686372*uk_151 + 5872500*uk_152 + 2531700*uk_153 + 1091444*uk_154 + 226981*uk_155 + 837225*uk_156 + 360937*uk_157 + 3088125*uk_158 + 1331325*uk_159 + 4919743*uk_16 + 573949*uk_160 + 11390625*uk_161 + 4910625*uk_162 + 2117025*uk_163 + 912673*uk_164 + 3025*uk_17 + 8250*uk_18 + 5335*uk_19 + 55*uk_2 + 6380*uk_20 + 3355*uk_21 + 12375*uk_22 + 5335*uk_23 + 22500*uk_24 + 14550*uk_25 + 17400*uk_26 + 9150*uk_27 + 33750*uk_28 + 14550*uk_29 + 150*uk_3 + 9409*uk_30 + 11252*uk_31 + 5917*uk_32 + 21825*uk_33 + 9409*uk_34 + 13456*uk_35 + 7076*uk_36 + 26100*uk_37 + 11252*uk_38 + 3721*uk_39 + 97*uk_4 + 13725*uk_40 + 5917*uk_41 + 50625*uk_42 + 21825*uk_43 + 9409*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 385862544150*uk_47 + 249524445217*uk_48 + 298400367476*uk_49 + 116*uk_5 + 156917434621*uk_50 + 578793816225*uk_51 + 249524445217*uk_52 + 153424975*uk_53 + 418431750*uk_54 + 270585865*uk_55 + 323587220*uk_56 + 170162245*uk_57 + 627647625*uk_58 + 270585865*uk_59 + 61*uk_6 + 1141177500*uk_60 + 737961450*uk_61 + 882510600*uk_62 + 464078850*uk_63 + 1711766250*uk_64 + 737961450*uk_65 + 477215071*uk_66 + 570690188*uk_67 + 300104323*uk_68 + 1106942175*uk_69 + 225*uk_7 + 477215071*uk_70 + 682474864*uk_71 + 358887644*uk_72 + 1323765900*uk_73 + 570690188*uk_74 + 188725399*uk_75 + 696118275*uk_76 + 300104323*uk_77 + 2567649375*uk_78 + 1106942175*uk_79 + 97*uk_8 + 477215071*uk_80 + 166375*uk_81 + 453750*uk_82 + 293425*uk_83 + 350900*uk_84 + 184525*uk_85 + 680625*uk_86 + 293425*uk_87 + 1237500*uk_88 + 800250*uk_89 + 2572416961*uk_9 + 957000*uk_90 + 503250*uk_91 + 1856250*uk_92 + 800250*uk_93 + 517495*uk_94 + 618860*uk_95 + 325435*uk_96 + 1200375*uk_97 + 517495*uk_98 + 740080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 374220*uk_100 + 1336500*uk_101 + 891000*uk_102 + 218295*uk_103 + 779625*uk_104 + 519750*uk_105 + 2784375*uk_106 + 1856250*uk_107 + 1237500*uk_108 + 7189057*uk_109 + 9788767*uk_11 + 5587350*uk_110 + 4022892*uk_111 + 2346687*uk_112 + 8381025*uk_113 + 5587350*uk_114 + 4342500*uk_115 + 3126600*uk_116 + 1823850*uk_117 + 6513750*uk_118 + 4342500*uk_119 + 7607850*uk_12 + 2251152*uk_120 + 1313172*uk_121 + 4689900*uk_122 + 3126600*uk_123 + 766017*uk_124 + 2735775*uk_125 + 1823850*uk_126 + 9770625*uk_127 + 6513750*uk_128 + 4342500*uk_129 + 5477652*uk_13 + 3375000*uk_130 + 2430000*uk_131 + 1417500*uk_132 + 5062500*uk_133 + 3375000*uk_134 + 1749600*uk_135 + 1020600*uk_136 + 3645000*uk_137 + 2430000*uk_138 + 595350*uk_139 + 3195297*uk_14 + 2126250*uk_140 + 1417500*uk_141 + 7593750*uk_142 + 5062500*uk_143 + 3375000*uk_144 + 1259712*uk_145 + 734832*uk_146 + 2624400*uk_147 + 1749600*uk_148 + 428652*uk_149 + 11411775*uk_15 + 1530900*uk_150 + 1020600*uk_151 + 5467500*uk_152 + 3645000*uk_153 + 2430000*uk_154 + 250047*uk_155 + 893025*uk_156 + 595350*uk_157 + 3189375*uk_158 + 2126250*uk_159 + 7607850*uk_16 + 1417500*uk_160 + 11390625*uk_161 + 7593750*uk_162 + 5062500*uk_163 + 3375000*uk_164 + 3025*uk_17 + 10615*uk_18 + 8250*uk_19 + 55*uk_2 + 5940*uk_20 + 3465*uk_21 + 12375*uk_22 + 8250*uk_23 + 37249*uk_24 + 28950*uk_25 + 20844*uk_26 + 12159*uk_27 + 43425*uk_28 + 28950*uk_29 + 193*uk_3 + 22500*uk_30 + 16200*uk_31 + 9450*uk_32 + 33750*uk_33 + 22500*uk_34 + 11664*uk_35 + 6804*uk_36 + 24300*uk_37 + 16200*uk_38 + 3969*uk_39 + 150*uk_4 + 14175*uk_40 + 9450*uk_41 + 50625*uk_42 + 33750*uk_43 + 22500*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 496476473473*uk_47 + 385862544150*uk_48 + 277821031788*uk_49 + 108*uk_5 + 162062268543*uk_50 + 578793816225*uk_51 + 385862544150*uk_52 + 153424975*uk_53 + 538382185*uk_54 + 418431750*uk_55 + 301270860*uk_56 + 175741335*uk_57 + 627647625*uk_58 + 418431750*uk_59 + 63*uk_6 + 1889232031*uk_60 + 1468315050*uk_61 + 1057186836*uk_62 + 616692321*uk_63 + 2202472575*uk_64 + 1468315050*uk_65 + 1141177500*uk_66 + 821647800*uk_67 + 479294550*uk_68 + 1711766250*uk_69 + 225*uk_7 + 1141177500*uk_70 + 591586416*uk_71 + 345092076*uk_72 + 1232471700*uk_73 + 821647800*uk_74 + 201303711*uk_75 + 718941825*uk_76 + 479294550*uk_77 + 2567649375*uk_78 + 1711766250*uk_79 + 150*uk_8 + 1141177500*uk_80 + 166375*uk_81 + 583825*uk_82 + 453750*uk_83 + 326700*uk_84 + 190575*uk_85 + 680625*uk_86 + 453750*uk_87 + 2048695*uk_88 + 1592250*uk_89 + 2572416961*uk_9 + 1146420*uk_90 + 668745*uk_91 + 2388375*uk_92 + 1592250*uk_93 + 1237500*uk_94 + 891000*uk_95 + 519750*uk_96 + 1856250*uk_97 + 1237500*uk_98 + 641520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 339020*uk_100 + 1138500*uk_101 + 1082840*uk_102 + 246895*uk_103 + 829125*uk_104 + 788590*uk_105 + 2784375*uk_106 + 2648250*uk_107 + 2518780*uk_108 + 8120601*uk_109 + 10194519*uk_11 + 8645814*uk_110 + 3716892*uk_111 + 2706867*uk_112 + 9090225*uk_113 + 8645814*uk_114 + 9204996*uk_115 + 3957288*uk_116 + 2881938*uk_117 + 9678150*uk_118 + 9204996*uk_119 + 10853866*uk_12 + 1701264*uk_120 + 1238964*uk_121 + 4160700*uk_122 + 3957288*uk_123 + 902289*uk_124 + 3030075*uk_125 + 2881938*uk_126 + 10175625*uk_127 + 9678150*uk_128 + 9204996*uk_129 + 4666148*uk_13 + 9800344*uk_130 + 4213232*uk_131 + 3068332*uk_132 + 10304100*uk_133 + 9800344*uk_134 + 1811296*uk_135 + 1319096*uk_136 + 4429800*uk_137 + 4213232*uk_138 + 960646*uk_139 + 3398173*uk_14 + 3226050*uk_140 + 3068332*uk_141 + 10833750*uk_142 + 10304100*uk_143 + 9800344*uk_144 + 778688*uk_145 + 567088*uk_146 + 1904400*uk_147 + 1811296*uk_148 + 412988*uk_149 + 11411775*uk_15 + 1386900*uk_150 + 1319096*uk_151 + 4657500*uk_152 + 4429800*uk_153 + 4213232*uk_154 + 300763*uk_155 + 1010025*uk_156 + 960646*uk_157 + 3391875*uk_158 + 3226050*uk_159 + 10853866*uk_16 + 3068332*uk_160 + 11390625*uk_161 + 10833750*uk_162 + 10304100*uk_163 + 9800344*uk_164 + 3025*uk_17 + 11055*uk_18 + 11770*uk_19 + 55*uk_2 + 5060*uk_20 + 3685*uk_21 + 12375*uk_22 + 11770*uk_23 + 40401*uk_24 + 43014*uk_25 + 18492*uk_26 + 13467*uk_27 + 45225*uk_28 + 43014*uk_29 + 201*uk_3 + 45796*uk_30 + 19688*uk_31 + 14338*uk_32 + 48150*uk_33 + 45796*uk_34 + 8464*uk_35 + 6164*uk_36 + 20700*uk_37 + 19688*uk_38 + 4489*uk_39 + 214*uk_4 + 15075*uk_40 + 14338*uk_41 + 50625*uk_42 + 48150*uk_43 + 45796*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 517055809161*uk_47 + 550497229654*uk_48 + 236662360412*uk_49 + 92*uk_5 + 172351936387*uk_50 + 578793816225*uk_51 + 550497229654*uk_52 + 153424975*uk_53 + 560698545*uk_54 + 596962630*uk_55 + 256638140*uk_56 + 186899515*uk_57 + 627647625*uk_58 + 596962630*uk_59 + 67*uk_6 + 2049098319*uk_60 + 2181627066*uk_61 + 937895748*uk_62 + 683032773*uk_63 + 2293766775*uk_64 + 2181627066*uk_65 + 2322727324*uk_66 + 998555672*uk_67 + 727209022*uk_68 + 2442119850*uk_69 + 225*uk_7 + 2322727324*uk_70 + 429285616*uk_71 + 312631916*uk_72 + 1049883300*uk_73 + 998555672*uk_74 + 227677591*uk_75 + 764588925*uk_76 + 727209022*uk_77 + 2567649375*uk_78 + 2442119850*uk_79 + 214*uk_8 + 2322727324*uk_80 + 166375*uk_81 + 608025*uk_82 + 647350*uk_83 + 278300*uk_84 + 202675*uk_85 + 680625*uk_86 + 647350*uk_87 + 2222055*uk_88 + 2365770*uk_89 + 2572416961*uk_9 + 1017060*uk_90 + 740685*uk_91 + 2487375*uk_92 + 2365770*uk_93 + 2518780*uk_94 + 1082840*uk_95 + 788590*uk_96 + 2648250*uk_97 + 2518780*uk_98 + 465520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 318780*uk_100 + 1039500*uk_101 + 928620*uk_102 + 261855*uk_103 + 853875*uk_104 + 762795*uk_105 + 2784375*uk_106 + 2487375*uk_107 + 2222055*uk_108 + 2863288*uk_109 + 7202098*uk_11 + 4052964*uk_110 + 1693776*uk_111 + 1391316*uk_112 + 4536900*uk_113 + 4052964*uk_114 + 5736942*uk_115 + 2397528*uk_116 + 1969398*uk_117 + 6421950*uk_118 + 5736942*uk_119 + 10194519*uk_12 + 1001952*uk_120 + 823032*uk_121 + 2683800*uk_122 + 2397528*uk_123 + 676062*uk_124 + 2204550*uk_125 + 1969398*uk_126 + 7188750*uk_127 + 6421950*uk_128 + 5736942*uk_129 + 4260396*uk_13 + 8120601*uk_130 + 3393684*uk_131 + 2787669*uk_132 + 9090225*uk_133 + 8120601*uk_134 + 1418256*uk_135 + 1164996*uk_136 + 3798900*uk_137 + 3393684*uk_138 + 956961*uk_139 + 3499611*uk_14 + 3120525*uk_140 + 2787669*uk_141 + 10175625*uk_142 + 9090225*uk_143 + 8120601*uk_144 + 592704*uk_145 + 486864*uk_146 + 1587600*uk_147 + 1418256*uk_148 + 399924*uk_149 + 11411775*uk_15 + 1304100*uk_150 + 1164996*uk_151 + 4252500*uk_152 + 3798900*uk_153 + 3393684*uk_154 + 328509*uk_155 + 1071225*uk_156 + 956961*uk_157 + 3493125*uk_158 + 3120525*uk_159 + 10194519*uk_16 + 2787669*uk_160 + 11390625*uk_161 + 10175625*uk_162 + 9090225*uk_163 + 8120601*uk_164 + 3025*uk_17 + 7810*uk_18 + 11055*uk_19 + 55*uk_2 + 4620*uk_20 + 3795*uk_21 + 12375*uk_22 + 11055*uk_23 + 20164*uk_24 + 28542*uk_25 + 11928*uk_26 + 9798*uk_27 + 31950*uk_28 + 28542*uk_29 + 142*uk_3 + 40401*uk_30 + 16884*uk_31 + 13869*uk_32 + 45225*uk_33 + 40401*uk_34 + 7056*uk_35 + 5796*uk_36 + 18900*uk_37 + 16884*uk_38 + 4761*uk_39 + 201*uk_4 + 15525*uk_40 + 13869*uk_41 + 50625*uk_42 + 45225*uk_43 + 40401*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 365283208462*uk_47 + 517055809161*uk_48 + 216083024724*uk_49 + 84*uk_5 + 177496770309*uk_50 + 578793816225*uk_51 + 517055809161*uk_52 + 153424975*uk_53 + 396115390*uk_54 + 560698545*uk_55 + 234321780*uk_56 + 192478605*uk_57 + 627647625*uk_58 + 560698545*uk_59 + 69*uk_6 + 1022697916*uk_60 + 1447621698*uk_61 + 604976232*uk_62 + 496944762*uk_63 + 1620472050*uk_64 + 1447621698*uk_65 + 2049098319*uk_66 + 856339596*uk_67 + 703421811*uk_68 + 2293766775*uk_69 + 225*uk_7 + 2049098319*uk_70 + 357873264*uk_71 + 293967324*uk_72 + 958589100*uk_73 + 856339596*uk_74 + 241473159*uk_75 + 787412475*uk_76 + 703421811*uk_77 + 2567649375*uk_78 + 2293766775*uk_79 + 201*uk_8 + 2049098319*uk_80 + 166375*uk_81 + 429550*uk_82 + 608025*uk_83 + 254100*uk_84 + 208725*uk_85 + 680625*uk_86 + 608025*uk_87 + 1109020*uk_88 + 1569810*uk_89 + 2572416961*uk_9 + 656040*uk_90 + 538890*uk_91 + 1757250*uk_92 + 1569810*uk_93 + 2222055*uk_94 + 928620*uk_95 + 762795*uk_96 + 2487375*uk_97 + 2222055*uk_98 + 388080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 296780*uk_100 + 940500*uk_101 + 593560*uk_102 + 277255*uk_103 + 878625*uk_104 + 554510*uk_105 + 2784375*uk_106 + 1757250*uk_107 + 1109020*uk_108 + 15625*uk_109 + 1267975*uk_11 + 88750*uk_110 + 47500*uk_111 + 44375*uk_112 + 140625*uk_113 + 88750*uk_114 + 504100*uk_115 + 269800*uk_116 + 252050*uk_117 + 798750*uk_118 + 504100*uk_119 + 7202098*uk_12 + 144400*uk_120 + 134900*uk_121 + 427500*uk_122 + 269800*uk_123 + 126025*uk_124 + 399375*uk_125 + 252050*uk_126 + 1265625*uk_127 + 798750*uk_128 + 504100*uk_129 + 3854644*uk_13 + 2863288*uk_130 + 1532464*uk_131 + 1431644*uk_132 + 4536900*uk_133 + 2863288*uk_134 + 820192*uk_135 + 766232*uk_136 + 2428200*uk_137 + 1532464*uk_138 + 715822*uk_139 + 3601049*uk_14 + 2268450*uk_140 + 1431644*uk_141 + 7188750*uk_142 + 4536900*uk_143 + 2863288*uk_144 + 438976*uk_145 + 410096*uk_146 + 1299600*uk_147 + 820192*uk_148 + 383116*uk_149 + 11411775*uk_15 + 1214100*uk_150 + 766232*uk_151 + 3847500*uk_152 + 2428200*uk_153 + 1532464*uk_154 + 357911*uk_155 + 1134225*uk_156 + 715822*uk_157 + 3594375*uk_158 + 2268450*uk_159 + 7202098*uk_16 + 1431644*uk_160 + 11390625*uk_161 + 7188750*uk_162 + 4536900*uk_163 + 2863288*uk_164 + 3025*uk_17 + 1375*uk_18 + 7810*uk_19 + 55*uk_2 + 4180*uk_20 + 3905*uk_21 + 12375*uk_22 + 7810*uk_23 + 625*uk_24 + 3550*uk_25 + 1900*uk_26 + 1775*uk_27 + 5625*uk_28 + 3550*uk_29 + 25*uk_3 + 20164*uk_30 + 10792*uk_31 + 10082*uk_32 + 31950*uk_33 + 20164*uk_34 + 5776*uk_35 + 5396*uk_36 + 17100*uk_37 + 10792*uk_38 + 5041*uk_39 + 142*uk_4 + 15975*uk_40 + 10082*uk_41 + 50625*uk_42 + 31950*uk_43 + 20164*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 64310424025*uk_47 + 365283208462*uk_48 + 195503689036*uk_49 + 76*uk_5 + 182641604231*uk_50 + 578793816225*uk_51 + 365283208462*uk_52 + 153424975*uk_53 + 69738625*uk_54 + 396115390*uk_55 + 212005420*uk_56 + 198057695*uk_57 + 627647625*uk_58 + 396115390*uk_59 + 71*uk_6 + 31699375*uk_60 + 180052450*uk_61 + 96366100*uk_62 + 90026225*uk_63 + 285294375*uk_64 + 180052450*uk_65 + 1022697916*uk_66 + 547359448*uk_67 + 511348958*uk_68 + 1620472050*uk_69 + 225*uk_7 + 1022697916*uk_70 + 292952944*uk_71 + 273679724*uk_72 + 867294900*uk_73 + 547359448*uk_74 + 255674479*uk_75 + 810236025*uk_76 + 511348958*uk_77 + 2567649375*uk_78 + 1620472050*uk_79 + 142*uk_8 + 1022697916*uk_80 + 166375*uk_81 + 75625*uk_82 + 429550*uk_83 + 229900*uk_84 + 214775*uk_85 + 680625*uk_86 + 429550*uk_87 + 34375*uk_88 + 195250*uk_89 + 2572416961*uk_9 + 104500*uk_90 + 97625*uk_91 + 309375*uk_92 + 195250*uk_93 + 1109020*uk_94 + 593560*uk_95 + 554510*uk_96 + 1757250*uk_97 + 1109020*uk_98 + 317680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 321200*uk_100 + 990000*uk_101 + 110000*uk_102 + 293095*uk_103 + 903375*uk_104 + 100375*uk_105 + 2784375*uk_106 + 309375*uk_107 + 34375*uk_108 + 185193*uk_109 + 2890983*uk_11 + 81225*uk_110 + 259920*uk_111 + 237177*uk_112 + 731025*uk_113 + 81225*uk_114 + 35625*uk_115 + 114000*uk_116 + 104025*uk_117 + 320625*uk_118 + 35625*uk_119 + 1267975*uk_12 + 364800*uk_120 + 332880*uk_121 + 1026000*uk_122 + 114000*uk_123 + 303753*uk_124 + 936225*uk_125 + 104025*uk_126 + 2885625*uk_127 + 320625*uk_128 + 35625*uk_129 + 4057520*uk_13 + 15625*uk_130 + 50000*uk_131 + 45625*uk_132 + 140625*uk_133 + 15625*uk_134 + 160000*uk_135 + 146000*uk_136 + 450000*uk_137 + 50000*uk_138 + 133225*uk_139 + 3702487*uk_14 + 410625*uk_140 + 45625*uk_141 + 1265625*uk_142 + 140625*uk_143 + 15625*uk_144 + 512000*uk_145 + 467200*uk_146 + 1440000*uk_147 + 160000*uk_148 + 426320*uk_149 + 11411775*uk_15 + 1314000*uk_150 + 146000*uk_151 + 4050000*uk_152 + 450000*uk_153 + 50000*uk_154 + 389017*uk_155 + 1199025*uk_156 + 133225*uk_157 + 3695625*uk_158 + 410625*uk_159 + 1267975*uk_16 + 45625*uk_160 + 11390625*uk_161 + 1265625*uk_162 + 140625*uk_163 + 15625*uk_164 + 3025*uk_17 + 3135*uk_18 + 1375*uk_19 + 55*uk_2 + 4400*uk_20 + 4015*uk_21 + 12375*uk_22 + 1375*uk_23 + 3249*uk_24 + 1425*uk_25 + 4560*uk_26 + 4161*uk_27 + 12825*uk_28 + 1425*uk_29 + 57*uk_3 + 625*uk_30 + 2000*uk_31 + 1825*uk_32 + 5625*uk_33 + 625*uk_34 + 6400*uk_35 + 5840*uk_36 + 18000*uk_37 + 2000*uk_38 + 5329*uk_39 + 25*uk_4 + 16425*uk_40 + 1825*uk_41 + 50625*uk_42 + 5625*uk_43 + 625*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 146627766777*uk_47 + 64310424025*uk_48 + 205793356880*uk_49 + 80*uk_5 + 187786438153*uk_50 + 578793816225*uk_51 + 64310424025*uk_52 + 153424975*uk_53 + 159004065*uk_54 + 69738625*uk_55 + 223163600*uk_56 + 203636785*uk_57 + 627647625*uk_58 + 69738625*uk_59 + 73*uk_6 + 164786031*uk_60 + 72274575*uk_61 + 231278640*uk_62 + 211041759*uk_63 + 650471175*uk_64 + 72274575*uk_65 + 31699375*uk_66 + 101438000*uk_67 + 92562175*uk_68 + 285294375*uk_69 + 225*uk_7 + 31699375*uk_70 + 324601600*uk_71 + 296198960*uk_72 + 912942000*uk_73 + 101438000*uk_74 + 270281551*uk_75 + 833059575*uk_76 + 92562175*uk_77 + 2567649375*uk_78 + 285294375*uk_79 + 25*uk_8 + 31699375*uk_80 + 166375*uk_81 + 172425*uk_82 + 75625*uk_83 + 242000*uk_84 + 220825*uk_85 + 680625*uk_86 + 75625*uk_87 + 178695*uk_88 + 78375*uk_89 + 2572416961*uk_9 + 250800*uk_90 + 228855*uk_91 + 705375*uk_92 + 78375*uk_93 + 34375*uk_94 + 110000*uk_95 + 100375*uk_96 + 309375*uk_97 + 34375*uk_98 + 352000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 304920*uk_100 + 891000*uk_101 + 75240*uk_102 + 326095*uk_103 + 952875*uk_104 + 80465*uk_105 + 2784375*uk_106 + 235125*uk_107 + 19855*uk_108 + 148877*uk_109 + 2688107*uk_11 + 53371*uk_110 + 202248*uk_111 + 216293*uk_112 + 632025*uk_113 + 53371*uk_114 + 19133*uk_115 + 72504*uk_116 + 77539*uk_117 + 226575*uk_118 + 19133*uk_119 + 963661*uk_12 + 274752*uk_120 + 293832*uk_121 + 858600*uk_122 + 72504*uk_123 + 314237*uk_124 + 918225*uk_125 + 77539*uk_126 + 2683125*uk_127 + 226575*uk_128 + 19133*uk_129 + 3651768*uk_13 + 6859*uk_130 + 25992*uk_131 + 27797*uk_132 + 81225*uk_133 + 6859*uk_134 + 98496*uk_135 + 105336*uk_136 + 307800*uk_137 + 25992*uk_138 + 112651*uk_139 + 3905363*uk_14 + 329175*uk_140 + 27797*uk_141 + 961875*uk_142 + 81225*uk_143 + 6859*uk_144 + 373248*uk_145 + 399168*uk_146 + 1166400*uk_147 + 98496*uk_148 + 426888*uk_149 + 11411775*uk_15 + 1247400*uk_150 + 105336*uk_151 + 3645000*uk_152 + 307800*uk_153 + 25992*uk_154 + 456533*uk_155 + 1334025*uk_156 + 112651*uk_157 + 3898125*uk_158 + 329175*uk_159 + 963661*uk_16 + 27797*uk_160 + 11390625*uk_161 + 961875*uk_162 + 81225*uk_163 + 6859*uk_164 + 3025*uk_17 + 2915*uk_18 + 1045*uk_19 + 55*uk_2 + 3960*uk_20 + 4235*uk_21 + 12375*uk_22 + 1045*uk_23 + 2809*uk_24 + 1007*uk_25 + 3816*uk_26 + 4081*uk_27 + 11925*uk_28 + 1007*uk_29 + 53*uk_3 + 361*uk_30 + 1368*uk_31 + 1463*uk_32 + 4275*uk_33 + 361*uk_34 + 5184*uk_35 + 5544*uk_36 + 16200*uk_37 + 1368*uk_38 + 5929*uk_39 + 19*uk_4 + 17325*uk_40 + 1463*uk_41 + 50625*uk_42 + 4275*uk_43 + 361*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 136338098933*uk_47 + 48875922259*uk_48 + 185214021192*uk_49 + 72*uk_5 + 198076105997*uk_50 + 578793816225*uk_51 + 48875922259*uk_52 + 153424975*uk_53 + 147845885*uk_54 + 53001355*uk_55 + 200847240*uk_56 + 214794965*uk_57 + 627647625*uk_58 + 53001355*uk_59 + 77*uk_6 + 142469671*uk_60 + 51074033*uk_61 + 193543704*uk_62 + 206984239*uk_63 + 604824075*uk_64 + 51074033*uk_65 + 18309559*uk_66 + 69383592*uk_67 + 74201897*uk_68 + 216823725*uk_69 + 225*uk_7 + 18309559*uk_70 + 262927296*uk_71 + 281186136*uk_72 + 821647800*uk_73 + 69383592*uk_74 + 300712951*uk_75 + 878706675*uk_76 + 74201897*uk_77 + 2567649375*uk_78 + 216823725*uk_79 + 19*uk_8 + 18309559*uk_80 + 166375*uk_81 + 160325*uk_82 + 57475*uk_83 + 217800*uk_84 + 232925*uk_85 + 680625*uk_86 + 57475*uk_87 + 154495*uk_88 + 55385*uk_89 + 2572416961*uk_9 + 209880*uk_90 + 224455*uk_91 + 655875*uk_92 + 55385*uk_93 + 19855*uk_94 + 75240*uk_95 + 80465*uk_96 + 235125*uk_97 + 19855*uk_98 + 285120*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 278080*uk_100 + 792000*uk_101 + 186560*uk_102 + 343255*uk_103 + 977625*uk_104 + 230285*uk_105 + 2784375*uk_106 + 655875*uk_107 + 154495*uk_108 + uk_109 + 50719*uk_11 + 53*uk_110 + 64*uk_111 + 79*uk_112 + 225*uk_113 + 53*uk_114 + 2809*uk_115 + 3392*uk_116 + 4187*uk_117 + 11925*uk_118 + 2809*uk_119 + 2688107*uk_12 + 4096*uk_120 + 5056*uk_121 + 14400*uk_122 + 3392*uk_123 + 6241*uk_124 + 17775*uk_125 + 4187*uk_126 + 50625*uk_127 + 11925*uk_128 + 2809*uk_129 + 3246016*uk_13 + 148877*uk_130 + 179776*uk_131 + 221911*uk_132 + 632025*uk_133 + 148877*uk_134 + 217088*uk_135 + 267968*uk_136 + 763200*uk_137 + 179776*uk_138 + 330773*uk_139 + 4006801*uk_14 + 942075*uk_140 + 221911*uk_141 + 2683125*uk_142 + 632025*uk_143 + 148877*uk_144 + 262144*uk_145 + 323584*uk_146 + 921600*uk_147 + 217088*uk_148 + 399424*uk_149 + 11411775*uk_15 + 1137600*uk_150 + 267968*uk_151 + 3240000*uk_152 + 763200*uk_153 + 179776*uk_154 + 493039*uk_155 + 1404225*uk_156 + 330773*uk_157 + 3999375*uk_158 + 942075*uk_159 + 2688107*uk_16 + 221911*uk_160 + 11390625*uk_161 + 2683125*uk_162 + 632025*uk_163 + 148877*uk_164 + 3025*uk_17 + 55*uk_18 + 2915*uk_19 + 55*uk_2 + 3520*uk_20 + 4345*uk_21 + 12375*uk_22 + 2915*uk_23 + uk_24 + 53*uk_25 + 64*uk_26 + 79*uk_27 + 225*uk_28 + 53*uk_29 + uk_3 + 2809*uk_30 + 3392*uk_31 + 4187*uk_32 + 11925*uk_33 + 2809*uk_34 + 4096*uk_35 + 5056*uk_36 + 14400*uk_37 + 3392*uk_38 + 6241*uk_39 + 53*uk_4 + 17775*uk_40 + 4187*uk_41 + 50625*uk_42 + 11925*uk_43 + 2809*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 2572416961*uk_47 + 136338098933*uk_48 + 164634685504*uk_49 + 64*uk_5 + 203220939919*uk_50 + 578793816225*uk_51 + 136338098933*uk_52 + 153424975*uk_53 + 2789545*uk_54 + 147845885*uk_55 + 178530880*uk_56 + 220374055*uk_57 + 627647625*uk_58 + 147845885*uk_59 + 79*uk_6 + 50719*uk_60 + 2688107*uk_61 + 3246016*uk_62 + 4006801*uk_63 + 11411775*uk_64 + 2688107*uk_65 + 142469671*uk_66 + 172038848*uk_67 + 212360453*uk_68 + 604824075*uk_69 + 225*uk_7 + 142469671*uk_70 + 207745024*uk_71 + 256435264*uk_72 + 730353600*uk_73 + 172038848*uk_74 + 316537279*uk_75 + 901530225*uk_76 + 212360453*uk_77 + 2567649375*uk_78 + 604824075*uk_79 + 53*uk_8 + 142469671*uk_80 + 166375*uk_81 + 3025*uk_82 + 160325*uk_83 + 193600*uk_84 + 238975*uk_85 + 680625*uk_86 + 160325*uk_87 + 55*uk_88 + 2915*uk_89 + 2572416961*uk_9 + 3520*uk_90 + 4345*uk_91 + 12375*uk_92 + 2915*uk_93 + 154495*uk_94 + 186560*uk_95 + 230285*uk_96 + 655875*uk_97 + 154495*uk_98 + 225280*uk_99,
|
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 285120*uk_100 + 792000*uk_101 + 3520*uk_102 + 360855*uk_103 + 1002375*uk_104 + 4455*uk_105 + 2784375*uk_106 + 12375*uk_107 + 55*uk_108 + 2197*uk_109 + 659347*uk_11 + 169*uk_110 + 10816*uk_111 + 13689*uk_112 + 38025*uk_113 + 169*uk_114 + 13*uk_115 + 832*uk_116 + 1053*uk_117 + 2925*uk_118 + 13*uk_119 + 50719*uk_12 + 53248*uk_120 + 67392*uk_121 + 187200*uk_122 + 832*uk_123 + 85293*uk_124 + 236925*uk_125 + 1053*uk_126 + 658125*uk_127 + 2925*uk_128 + 13*uk_129 + 3246016*uk_13 + uk_130 + 64*uk_131 + 81*uk_132 + 225*uk_133 + uk_134 + 4096*uk_135 + 5184*uk_136 + 14400*uk_137 + 64*uk_138 + 6561*uk_139 + 4108239*uk_14 + 18225*uk_140 + 81*uk_141 + 50625*uk_142 + 225*uk_143 + uk_144 + 262144*uk_145 + 331776*uk_146 + 921600*uk_147 + 4096*uk_148 + 419904*uk_149 + 11411775*uk_15 + 1166400*uk_150 + 5184*uk_151 + 3240000*uk_152 + 14400*uk_153 + 64*uk_154 + 531441*uk_155 + 1476225*uk_156 + 6561*uk_157 + 4100625*uk_158 + 18225*uk_159 + 50719*uk_16 + 81*uk_160 + 11390625*uk_161 + 50625*uk_162 + 225*uk_163 + uk_164 + 3025*uk_17 + 715*uk_18 + 55*uk_19 + 55*uk_2 + 3520*uk_20 + 4455*uk_21 + 12375*uk_22 + 55*uk_23 + 169*uk_24 + 13*uk_25 + 832*uk_26 + 1053*uk_27 + 2925*uk_28 + 13*uk_29 + 13*uk_3 + uk_30 + 64*uk_31 + 81*uk_32 + 225*uk_33 + uk_34 + 4096*uk_35 + 5184*uk_36 + 14400*uk_37 + 64*uk_38 + 6561*uk_39 + uk_4 + 18225*uk_40 + 81*uk_41 + 50625*uk_42 + 225*uk_43 + uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 33441420493*uk_47 + 2572416961*uk_48 + 164634685504*uk_49 + 64*uk_5 + 208365773841*uk_50 + 578793816225*uk_51 + 2572416961*uk_52 + 153424975*uk_53 + 36264085*uk_54 + 2789545*uk_55 + 178530880*uk_56 + 225953145*uk_57 + 627647625*uk_58 + 2789545*uk_59 + 81*uk_6 + 8571511*uk_60 + 659347*uk_61 + 42198208*uk_62 + 53407107*uk_63 + 148353075*uk_64 + 659347*uk_65 + 50719*uk_66 + 3246016*uk_67 + 4108239*uk_68 + 11411775*uk_69 + 225*uk_7 + 50719*uk_70 + 207745024*uk_71 + 262927296*uk_72 + 730353600*uk_73 + 3246016*uk_74 + 332767359*uk_75 + 924353775*uk_76 + 4108239*uk_77 + 2567649375*uk_78 + 11411775*uk_79 + uk_8 + 50719*uk_80 + 166375*uk_81 + 39325*uk_82 + 3025*uk_83 + 193600*uk_84 + 245025*uk_85 + 680625*uk_86 + 3025*uk_87 + 9295*uk_88 + 715*uk_89 + 2572416961*uk_9 + 45760*uk_90 + 57915*uk_91 + 160875*uk_92 + 715*uk_93 + 55*uk_94 + 3520*uk_95 + 4455*uk_96 + 12375*uk_97 + 55*uk_98 + 225280*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 273900*uk_100 + 742500*uk_101 + 42900*uk_102 + 378895*uk_103 + 1027125*uk_104 + 59345*uk_105 + 2784375*uk_106 + 160875*uk_107 + 9295*uk_108 + 216*uk_109 + 304314*uk_11 + 468*uk_110 + 2160*uk_111 + 2988*uk_112 + 8100*uk_113 + 468*uk_114 + 1014*uk_115 + 4680*uk_116 + 6474*uk_117 + 17550*uk_118 + 1014*uk_119 + 659347*uk_12 + 21600*uk_120 + 29880*uk_121 + 81000*uk_122 + 4680*uk_123 + 41334*uk_124 + 112050*uk_125 + 6474*uk_126 + 303750*uk_127 + 17550*uk_128 + 1014*uk_129 + 3043140*uk_13 + 2197*uk_130 + 10140*uk_131 + 14027*uk_132 + 38025*uk_133 + 2197*uk_134 + 46800*uk_135 + 64740*uk_136 + 175500*uk_137 + 10140*uk_138 + 89557*uk_139 + 4209677*uk_14 + 242775*uk_140 + 14027*uk_141 + 658125*uk_142 + 38025*uk_143 + 2197*uk_144 + 216000*uk_145 + 298800*uk_146 + 810000*uk_147 + 46800*uk_148 + 413340*uk_149 + 11411775*uk_15 + 1120500*uk_150 + 64740*uk_151 + 3037500*uk_152 + 175500*uk_153 + 10140*uk_154 + 571787*uk_155 + 1550025*uk_156 + 89557*uk_157 + 4201875*uk_158 + 242775*uk_159 + 659347*uk_16 + 14027*uk_160 + 11390625*uk_161 + 658125*uk_162 + 38025*uk_163 + 2197*uk_164 + 3025*uk_17 + 330*uk_18 + 715*uk_19 + 55*uk_2 + 3300*uk_20 + 4565*uk_21 + 12375*uk_22 + 715*uk_23 + 36*uk_24 + 78*uk_25 + 360*uk_26 + 498*uk_27 + 1350*uk_28 + 78*uk_29 + 6*uk_3 + 169*uk_30 + 780*uk_31 + 1079*uk_32 + 2925*uk_33 + 169*uk_34 + 3600*uk_35 + 4980*uk_36 + 13500*uk_37 + 780*uk_38 + 6889*uk_39 + 13*uk_4 + 18675*uk_40 + 1079*uk_41 + 50625*uk_42 + 2925*uk_43 + 169*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 15434501766*uk_47 + 33441420493*uk_48 + 154345017660*uk_49 + 60*uk_5 + 213510607763*uk_50 + 578793816225*uk_51 + 33441420493*uk_52 + 153424975*uk_53 + 16737270*uk_54 + 36264085*uk_55 + 167372700*uk_56 + 231532235*uk_57 + 627647625*uk_58 + 36264085*uk_59 + 83*uk_6 + 1825884*uk_60 + 3956082*uk_61 + 18258840*uk_62 + 25258062*uk_63 + 68470650*uk_64 + 3956082*uk_65 + 8571511*uk_66 + 39560820*uk_67 + 54725801*uk_68 + 148353075*uk_69 + 225*uk_7 + 8571511*uk_70 + 182588400*uk_71 + 252580620*uk_72 + 684706500*uk_73 + 39560820*uk_74 + 349403191*uk_75 + 947177325*uk_76 + 54725801*uk_77 + 2567649375*uk_78 + 148353075*uk_79 + 13*uk_8 + 8571511*uk_80 + 166375*uk_81 + 18150*uk_82 + 39325*uk_83 + 181500*uk_84 + 251075*uk_85 + 680625*uk_86 + 39325*uk_87 + 1980*uk_88 + 4290*uk_89 + 2572416961*uk_9 + 19800*uk_90 + 27390*uk_91 + 74250*uk_92 + 4290*uk_93 + 9295*uk_94 + 42900*uk_95 + 59345*uk_96 + 160875*uk_97 + 9295*uk_98 + 198000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 280500*uk_100 + 742500*uk_101 + 19800*uk_102 + 397375*uk_103 + 1051875*uk_104 + 28050*uk_105 + 2784375*uk_106 + 74250*uk_107 + 1980*uk_108 + 205379*uk_109 + 2992421*uk_11 + 20886*uk_110 + 208860*uk_111 + 295885*uk_112 + 783225*uk_113 + 20886*uk_114 + 2124*uk_115 + 21240*uk_116 + 30090*uk_117 + 79650*uk_118 + 2124*uk_119 + 304314*uk_12 + 212400*uk_120 + 300900*uk_121 + 796500*uk_122 + 21240*uk_123 + 426275*uk_124 + 1128375*uk_125 + 30090*uk_126 + 2986875*uk_127 + 79650*uk_128 + 2124*uk_129 + 3043140*uk_13 + 216*uk_130 + 2160*uk_131 + 3060*uk_132 + 8100*uk_133 + 216*uk_134 + 21600*uk_135 + 30600*uk_136 + 81000*uk_137 + 2160*uk_138 + 43350*uk_139 + 4311115*uk_14 + 114750*uk_140 + 3060*uk_141 + 303750*uk_142 + 8100*uk_143 + 216*uk_144 + 216000*uk_145 + 306000*uk_146 + 810000*uk_147 + 21600*uk_148 + 433500*uk_149 + 11411775*uk_15 + 1147500*uk_150 + 30600*uk_151 + 3037500*uk_152 + 81000*uk_153 + 2160*uk_154 + 614125*uk_155 + 1625625*uk_156 + 43350*uk_157 + 4303125*uk_158 + 114750*uk_159 + 304314*uk_16 + 3060*uk_160 + 11390625*uk_161 + 303750*uk_162 + 8100*uk_163 + 216*uk_164 + 3025*uk_17 + 3245*uk_18 + 330*uk_19 + 55*uk_2 + 3300*uk_20 + 4675*uk_21 + 12375*uk_22 + 330*uk_23 + 3481*uk_24 + 354*uk_25 + 3540*uk_26 + 5015*uk_27 + 13275*uk_28 + 354*uk_29 + 59*uk_3 + 36*uk_30 + 360*uk_31 + 510*uk_32 + 1350*uk_33 + 36*uk_34 + 3600*uk_35 + 5100*uk_36 + 13500*uk_37 + 360*uk_38 + 7225*uk_39 + 6*uk_4 + 19125*uk_40 + 510*uk_41 + 50625*uk_42 + 1350*uk_43 + 36*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 151772600699*uk_47 + 15434501766*uk_48 + 154345017660*uk_49 + 60*uk_5 + 218655441685*uk_50 + 578793816225*uk_51 + 15434501766*uk_52 + 153424975*uk_53 + 164583155*uk_54 + 16737270*uk_55 + 167372700*uk_56 + 237111325*uk_57 + 627647625*uk_58 + 16737270*uk_59 + 85*uk_6 + 176552839*uk_60 + 17954526*uk_61 + 179545260*uk_62 + 254355785*uk_63 + 673294725*uk_64 + 17954526*uk_65 + 1825884*uk_66 + 18258840*uk_67 + 25866690*uk_68 + 68470650*uk_69 + 225*uk_7 + 1825884*uk_70 + 182588400*uk_71 + 258666900*uk_72 + 684706500*uk_73 + 18258840*uk_74 + 366444775*uk_75 + 970000875*uk_76 + 25866690*uk_77 + 2567649375*uk_78 + 68470650*uk_79 + 6*uk_8 + 1825884*uk_80 + 166375*uk_81 + 178475*uk_82 + 18150*uk_83 + 181500*uk_84 + 257125*uk_85 + 680625*uk_86 + 18150*uk_87 + 191455*uk_88 + 19470*uk_89 + 2572416961*uk_9 + 194700*uk_90 + 275825*uk_91 + 730125*uk_92 + 19470*uk_93 + 1980*uk_94 + 19800*uk_95 + 28050*uk_96 + 74250*uk_97 + 1980*uk_98 + 198000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 267960*uk_100 + 693000*uk_101 + 181720*uk_102 + 416295*uk_103 + 1076625*uk_104 + 282315*uk_105 + 2784375*uk_106 + 730125*uk_107 + 191455*uk_108 + 614125*uk_109 + 4311115*uk_11 + 426275*uk_110 + 404600*uk_111 + 628575*uk_112 + 1625625*uk_113 + 426275*uk_114 + 295885*uk_115 + 280840*uk_116 + 436305*uk_117 + 1128375*uk_118 + 295885*uk_119 + 2992421*uk_12 + 266560*uk_120 + 414120*uk_121 + 1071000*uk_122 + 280840*uk_123 + 643365*uk_124 + 1663875*uk_125 + 436305*uk_126 + 4303125*uk_127 + 1128375*uk_128 + 295885*uk_129 + 2840264*uk_13 + 205379*uk_130 + 194936*uk_131 + 302847*uk_132 + 783225*uk_133 + 205379*uk_134 + 185024*uk_135 + 287448*uk_136 + 743400*uk_137 + 194936*uk_138 + 446571*uk_139 + 4412553*uk_14 + 1154925*uk_140 + 302847*uk_141 + 2986875*uk_142 + 783225*uk_143 + 205379*uk_144 + 175616*uk_145 + 272832*uk_146 + 705600*uk_147 + 185024*uk_148 + 423864*uk_149 + 11411775*uk_15 + 1096200*uk_150 + 287448*uk_151 + 2835000*uk_152 + 743400*uk_153 + 194936*uk_154 + 658503*uk_155 + 1703025*uk_156 + 446571*uk_157 + 4404375*uk_158 + 1154925*uk_159 + 2992421*uk_16 + 302847*uk_160 + 11390625*uk_161 + 2986875*uk_162 + 783225*uk_163 + 205379*uk_164 + 3025*uk_17 + 4675*uk_18 + 3245*uk_19 + 55*uk_2 + 3080*uk_20 + 4785*uk_21 + 12375*uk_22 + 3245*uk_23 + 7225*uk_24 + 5015*uk_25 + 4760*uk_26 + 7395*uk_27 + 19125*uk_28 + 5015*uk_29 + 85*uk_3 + 3481*uk_30 + 3304*uk_31 + 5133*uk_32 + 13275*uk_33 + 3481*uk_34 + 3136*uk_35 + 4872*uk_36 + 12600*uk_37 + 3304*uk_38 + 7569*uk_39 + 59*uk_4 + 19575*uk_40 + 5133*uk_41 + 50625*uk_42 + 13275*uk_43 + 3481*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 218655441685*uk_47 + 151772600699*uk_48 + 144055349816*uk_49 + 56*uk_5 + 223800275607*uk_50 + 578793816225*uk_51 + 151772600699*uk_52 + 153424975*uk_53 + 237111325*uk_54 + 164583155*uk_55 + 156214520*uk_56 + 242690415*uk_57 + 627647625*uk_58 + 164583155*uk_59 + 87*uk_6 + 366444775*uk_60 + 254355785*uk_61 + 241422440*uk_62 + 375067005*uk_63 + 970000875*uk_64 + 254355785*uk_65 + 176552839*uk_66 + 167575576*uk_67 + 260340627*uk_68 + 673294725*uk_69 + 225*uk_7 + 176552839*uk_70 + 159054784*uk_71 + 247102968*uk_72 + 639059400*uk_73 + 167575576*uk_74 + 383892111*uk_75 + 992824425*uk_76 + 260340627*uk_77 + 2567649375*uk_78 + 673294725*uk_79 + 59*uk_8 + 176552839*uk_80 + 166375*uk_81 + 257125*uk_82 + 178475*uk_83 + 169400*uk_84 + 263175*uk_85 + 680625*uk_86 + 178475*uk_87 + 397375*uk_88 + 275825*uk_89 + 2572416961*uk_9 + 261800*uk_90 + 406725*uk_91 + 1051875*uk_92 + 275825*uk_93 + 191455*uk_94 + 181720*uk_95 + 282315*uk_96 + 730125*uk_97 + 191455*uk_98 + 172480*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 240240*uk_100 + 594000*uk_101 + 205920*uk_102 + 455455*uk_103 + 1126125*uk_104 + 390390*uk_105 + 2784375*uk_106 + 965250*uk_107 + 334620*uk_108 + 32768*uk_109 + 1623008*uk_11 + 79872*uk_110 + 49152*uk_111 + 93184*uk_112 + 230400*uk_113 + 79872*uk_114 + 194688*uk_115 + 119808*uk_116 + 227136*uk_117 + 561600*uk_118 + 194688*uk_119 + 3956082*uk_12 + 73728*uk_120 + 139776*uk_121 + 345600*uk_122 + 119808*uk_123 + 264992*uk_124 + 655200*uk_125 + 227136*uk_126 + 1620000*uk_127 + 561600*uk_128 + 194688*uk_129 + 2434512*uk_13 + 474552*uk_130 + 292032*uk_131 + 553644*uk_132 + 1368900*uk_133 + 474552*uk_134 + 179712*uk_135 + 340704*uk_136 + 842400*uk_137 + 292032*uk_138 + 645918*uk_139 + 4615429*uk_14 + 1597050*uk_140 + 553644*uk_141 + 3948750*uk_142 + 1368900*uk_143 + 474552*uk_144 + 110592*uk_145 + 209664*uk_146 + 518400*uk_147 + 179712*uk_148 + 397488*uk_149 + 11411775*uk_15 + 982800*uk_150 + 340704*uk_151 + 2430000*uk_152 + 842400*uk_153 + 292032*uk_154 + 753571*uk_155 + 1863225*uk_156 + 645918*uk_157 + 4606875*uk_158 + 1597050*uk_159 + 3956082*uk_16 + 553644*uk_160 + 11390625*uk_161 + 3948750*uk_162 + 1368900*uk_163 + 474552*uk_164 + 3025*uk_17 + 1760*uk_18 + 4290*uk_19 + 55*uk_2 + 2640*uk_20 + 5005*uk_21 + 12375*uk_22 + 4290*uk_23 + 1024*uk_24 + 2496*uk_25 + 1536*uk_26 + 2912*uk_27 + 7200*uk_28 + 2496*uk_29 + 32*uk_3 + 6084*uk_30 + 3744*uk_31 + 7098*uk_32 + 17550*uk_33 + 6084*uk_34 + 2304*uk_35 + 4368*uk_36 + 10800*uk_37 + 3744*uk_38 + 8281*uk_39 + 78*uk_4 + 20475*uk_40 + 7098*uk_41 + 50625*uk_42 + 17550*uk_43 + 6084*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 82317342752*uk_47 + 200648522958*uk_48 + 123476014128*uk_49 + 48*uk_5 + 234089943451*uk_50 + 578793816225*uk_51 + 200648522958*uk_52 + 153424975*uk_53 + 89265440*uk_54 + 217584510*uk_55 + 133898160*uk_56 + 253848595*uk_57 + 627647625*uk_58 + 217584510*uk_59 + 91*uk_6 + 51936256*uk_60 + 126594624*uk_61 + 77904384*uk_62 + 147693728*uk_63 + 365176800*uk_64 + 126594624*uk_65 + 308574396*uk_66 + 189891936*uk_67 + 360003462*uk_68 + 890118450*uk_69 + 225*uk_7 + 308574396*uk_70 + 116856576*uk_71 + 221540592*uk_72 + 547765200*uk_73 + 189891936*uk_74 + 420004039*uk_75 + 1038471525*uk_76 + 360003462*uk_77 + 2567649375*uk_78 + 890118450*uk_79 + 78*uk_8 + 308574396*uk_80 + 166375*uk_81 + 96800*uk_82 + 235950*uk_83 + 145200*uk_84 + 275275*uk_85 + 680625*uk_86 + 235950*uk_87 + 56320*uk_88 + 137280*uk_89 + 2572416961*uk_9 + 84480*uk_90 + 160160*uk_91 + 396000*uk_92 + 137280*uk_93 + 334620*uk_94 + 205920*uk_95 + 390390*uk_96 + 965250*uk_97 + 334620*uk_98 + 126720*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 245520*uk_100 + 594000*uk_101 + 84480*uk_102 + 475695*uk_103 + 1150875*uk_104 + 163680*uk_105 + 2784375*uk_106 + 396000*uk_107 + 56320*uk_108 + 39304*uk_109 + 1724446*uk_11 + 36992*uk_110 + 55488*uk_111 + 107508*uk_112 + 260100*uk_113 + 36992*uk_114 + 34816*uk_115 + 52224*uk_116 + 101184*uk_117 + 244800*uk_118 + 34816*uk_119 + 1623008*uk_12 + 78336*uk_120 + 151776*uk_121 + 367200*uk_122 + 52224*uk_123 + 294066*uk_124 + 711450*uk_125 + 101184*uk_126 + 1721250*uk_127 + 244800*uk_128 + 34816*uk_129 + 2434512*uk_13 + 32768*uk_130 + 49152*uk_131 + 95232*uk_132 + 230400*uk_133 + 32768*uk_134 + 73728*uk_135 + 142848*uk_136 + 345600*uk_137 + 49152*uk_138 + 276768*uk_139 + 4716867*uk_14 + 669600*uk_140 + 95232*uk_141 + 1620000*uk_142 + 230400*uk_143 + 32768*uk_144 + 110592*uk_145 + 214272*uk_146 + 518400*uk_147 + 73728*uk_148 + 415152*uk_149 + 11411775*uk_15 + 1004400*uk_150 + 142848*uk_151 + 2430000*uk_152 + 345600*uk_153 + 49152*uk_154 + 804357*uk_155 + 1946025*uk_156 + 276768*uk_157 + 4708125*uk_158 + 669600*uk_159 + 1623008*uk_16 + 95232*uk_160 + 11390625*uk_161 + 1620000*uk_162 + 230400*uk_163 + 32768*uk_164 + 3025*uk_17 + 1870*uk_18 + 1760*uk_19 + 55*uk_2 + 2640*uk_20 + 5115*uk_21 + 12375*uk_22 + 1760*uk_23 + 1156*uk_24 + 1088*uk_25 + 1632*uk_26 + 3162*uk_27 + 7650*uk_28 + 1088*uk_29 + 34*uk_3 + 1024*uk_30 + 1536*uk_31 + 2976*uk_32 + 7200*uk_33 + 1024*uk_34 + 2304*uk_35 + 4464*uk_36 + 10800*uk_37 + 1536*uk_38 + 8649*uk_39 + 32*uk_4 + 20925*uk_40 + 2976*uk_41 + 50625*uk_42 + 7200*uk_43 + 1024*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 87462176674*uk_47 + 82317342752*uk_48 + 123476014128*uk_49 + 48*uk_5 + 239234777373*uk_50 + 578793816225*uk_51 + 82317342752*uk_52 + 153424975*uk_53 + 94844530*uk_54 + 89265440*uk_55 + 133898160*uk_56 + 259427685*uk_57 + 627647625*uk_58 + 89265440*uk_59 + 93*uk_6 + 58631164*uk_60 + 55182272*uk_61 + 82773408*uk_62 + 160373478*uk_63 + 388000350*uk_64 + 55182272*uk_65 + 51936256*uk_66 + 77904384*uk_67 + 150939744*uk_68 + 365176800*uk_69 + 225*uk_7 + 51936256*uk_70 + 116856576*uk_71 + 226409616*uk_72 + 547765200*uk_73 + 77904384*uk_74 + 438668631*uk_75 + 1061295075*uk_76 + 150939744*uk_77 + 2567649375*uk_78 + 365176800*uk_79 + 32*uk_8 + 51936256*uk_80 + 166375*uk_81 + 102850*uk_82 + 96800*uk_83 + 145200*uk_84 + 281325*uk_85 + 680625*uk_86 + 96800*uk_87 + 63580*uk_88 + 59840*uk_89 + 2572416961*uk_9 + 89760*uk_90 + 173910*uk_91 + 420750*uk_92 + 59840*uk_93 + 56320*uk_94 + 84480*uk_95 + 163680*uk_96 + 396000*uk_97 + 56320*uk_98 + 126720*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 250800*uk_100 + 594000*uk_101 + 89760*uk_102 + 496375*uk_103 + 1175625*uk_104 + 177650*uk_105 + 2784375*uk_106 + 420750*uk_107 + 63580*uk_108 + 592704*uk_109 + 4260396*uk_11 + 239904*uk_110 + 338688*uk_111 + 670320*uk_112 + 1587600*uk_113 + 239904*uk_114 + 97104*uk_115 + 137088*uk_116 + 271320*uk_117 + 642600*uk_118 + 97104*uk_119 + 1724446*uk_12 + 193536*uk_120 + 383040*uk_121 + 907200*uk_122 + 137088*uk_123 + 758100*uk_124 + 1795500*uk_125 + 271320*uk_126 + 4252500*uk_127 + 642600*uk_128 + 97104*uk_129 + 2434512*uk_13 + 39304*uk_130 + 55488*uk_131 + 109820*uk_132 + 260100*uk_133 + 39304*uk_134 + 78336*uk_135 + 155040*uk_136 + 367200*uk_137 + 55488*uk_138 + 306850*uk_139 + 4818305*uk_14 + 726750*uk_140 + 109820*uk_141 + 1721250*uk_142 + 260100*uk_143 + 39304*uk_144 + 110592*uk_145 + 218880*uk_146 + 518400*uk_147 + 78336*uk_148 + 433200*uk_149 + 11411775*uk_15 + 1026000*uk_150 + 155040*uk_151 + 2430000*uk_152 + 367200*uk_153 + 55488*uk_154 + 857375*uk_155 + 2030625*uk_156 + 306850*uk_157 + 4809375*uk_158 + 726750*uk_159 + 1724446*uk_16 + 109820*uk_160 + 11390625*uk_161 + 1721250*uk_162 + 260100*uk_163 + 39304*uk_164 + 3025*uk_17 + 4620*uk_18 + 1870*uk_19 + 55*uk_2 + 2640*uk_20 + 5225*uk_21 + 12375*uk_22 + 1870*uk_23 + 7056*uk_24 + 2856*uk_25 + 4032*uk_26 + 7980*uk_27 + 18900*uk_28 + 2856*uk_29 + 84*uk_3 + 1156*uk_30 + 1632*uk_31 + 3230*uk_32 + 7650*uk_33 + 1156*uk_34 + 2304*uk_35 + 4560*uk_36 + 10800*uk_37 + 1632*uk_38 + 9025*uk_39 + 34*uk_4 + 21375*uk_40 + 3230*uk_41 + 50625*uk_42 + 7650*uk_43 + 1156*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 216083024724*uk_47 + 87462176674*uk_48 + 123476014128*uk_49 + 48*uk_5 + 244379611295*uk_50 + 578793816225*uk_51 + 87462176674*uk_52 + 153424975*uk_53 + 234321780*uk_54 + 94844530*uk_55 + 133898160*uk_56 + 265006775*uk_57 + 627647625*uk_58 + 94844530*uk_59 + 95*uk_6 + 357873264*uk_60 + 144853464*uk_61 + 204499008*uk_62 + 404737620*uk_63 + 958589100*uk_64 + 144853464*uk_65 + 58631164*uk_66 + 82773408*uk_67 + 163822370*uk_68 + 388000350*uk_69 + 225*uk_7 + 58631164*uk_70 + 116856576*uk_71 + 231278640*uk_72 + 547765200*uk_73 + 82773408*uk_74 + 457738975*uk_75 + 1084118625*uk_76 + 163822370*uk_77 + 2567649375*uk_78 + 388000350*uk_79 + 34*uk_8 + 58631164*uk_80 + 166375*uk_81 + 254100*uk_82 + 102850*uk_83 + 145200*uk_84 + 287375*uk_85 + 680625*uk_86 + 102850*uk_87 + 388080*uk_88 + 157080*uk_89 + 2572416961*uk_9 + 221760*uk_90 + 438900*uk_91 + 1039500*uk_92 + 157080*uk_93 + 63580*uk_94 + 89760*uk_95 + 177650*uk_96 + 420750*uk_97 + 63580*uk_98 + 126720*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 234740*uk_100 + 544500*uk_101 + 203280*uk_102 + 517495*uk_103 + 1200375*uk_104 + 448140*uk_105 + 2784375*uk_106 + 1039500*uk_107 + 388080*uk_108 + 614125*uk_109 + 4311115*uk_11 + 606900*uk_110 + 317900*uk_111 + 700825*uk_112 + 1625625*uk_113 + 606900*uk_114 + 599760*uk_115 + 314160*uk_116 + 692580*uk_117 + 1606500*uk_118 + 599760*uk_119 + 4260396*uk_12 + 164560*uk_120 + 362780*uk_121 + 841500*uk_122 + 314160*uk_123 + 799765*uk_124 + 1855125*uk_125 + 692580*uk_126 + 4303125*uk_127 + 1606500*uk_128 + 599760*uk_129 + 2231636*uk_13 + 592704*uk_130 + 310464*uk_131 + 684432*uk_132 + 1587600*uk_133 + 592704*uk_134 + 162624*uk_135 + 358512*uk_136 + 831600*uk_137 + 310464*uk_138 + 790356*uk_139 + 4919743*uk_14 + 1833300*uk_140 + 684432*uk_141 + 4252500*uk_142 + 1587600*uk_143 + 592704*uk_144 + 85184*uk_145 + 187792*uk_146 + 435600*uk_147 + 162624*uk_148 + 413996*uk_149 + 11411775*uk_15 + 960300*uk_150 + 358512*uk_151 + 2227500*uk_152 + 831600*uk_153 + 310464*uk_154 + 912673*uk_155 + 2117025*uk_156 + 790356*uk_157 + 4910625*uk_158 + 1833300*uk_159 + 4260396*uk_16 + 684432*uk_160 + 11390625*uk_161 + 4252500*uk_162 + 1587600*uk_163 + 592704*uk_164 + 3025*uk_17 + 4675*uk_18 + 4620*uk_19 + 55*uk_2 + 2420*uk_20 + 5335*uk_21 + 12375*uk_22 + 4620*uk_23 + 7225*uk_24 + 7140*uk_25 + 3740*uk_26 + 8245*uk_27 + 19125*uk_28 + 7140*uk_29 + 85*uk_3 + 7056*uk_30 + 3696*uk_31 + 8148*uk_32 + 18900*uk_33 + 7056*uk_34 + 1936*uk_35 + 4268*uk_36 + 9900*uk_37 + 3696*uk_38 + 9409*uk_39 + 84*uk_4 + 21825*uk_40 + 8148*uk_41 + 50625*uk_42 + 18900*uk_43 + 7056*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 218655441685*uk_47 + 216083024724*uk_48 + 113186346284*uk_49 + 44*uk_5 + 249524445217*uk_50 + 578793816225*uk_51 + 216083024724*uk_52 + 153424975*uk_53 + 237111325*uk_54 + 234321780*uk_55 + 122739980*uk_56 + 270585865*uk_57 + 627647625*uk_58 + 234321780*uk_59 + 97*uk_6 + 366444775*uk_60 + 362133660*uk_61 + 189689060*uk_62 + 418178155*uk_63 + 970000875*uk_64 + 362133660*uk_65 + 357873264*uk_66 + 187457424*uk_67 + 413258412*uk_68 + 958589100*uk_69 + 225*uk_7 + 357873264*uk_70 + 98191984*uk_71 + 216468692*uk_72 + 502118100*uk_73 + 187457424*uk_74 + 477215071*uk_75 + 1106942175*uk_76 + 413258412*uk_77 + 2567649375*uk_78 + 958589100*uk_79 + 84*uk_8 + 357873264*uk_80 + 166375*uk_81 + 257125*uk_82 + 254100*uk_83 + 133100*uk_84 + 293425*uk_85 + 680625*uk_86 + 254100*uk_87 + 397375*uk_88 + 392700*uk_89 + 2572416961*uk_9 + 205700*uk_90 + 453475*uk_91 + 1051875*uk_92 + 392700*uk_93 + 388080*uk_94 + 203280*uk_95 + 448140*uk_96 + 1039500*uk_97 + 388080*uk_98 + 106480*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 217800*uk_100 + 495000*uk_101 + 187000*uk_102 + 539055*uk_103 + 1225125*uk_104 + 462825*uk_105 + 2784375*uk_106 + 1051875*uk_107 + 397375*uk_108 + 29791*uk_109 + 1572289*uk_11 + 81685*uk_110 + 38440*uk_111 + 95139*uk_112 + 216225*uk_113 + 81685*uk_114 + 223975*uk_115 + 105400*uk_116 + 260865*uk_117 + 592875*uk_118 + 223975*uk_119 + 4311115*uk_12 + 49600*uk_120 + 122760*uk_121 + 279000*uk_122 + 105400*uk_123 + 303831*uk_124 + 690525*uk_125 + 260865*uk_126 + 1569375*uk_127 + 592875*uk_128 + 223975*uk_129 + 2028760*uk_13 + 614125*uk_130 + 289000*uk_131 + 715275*uk_132 + 1625625*uk_133 + 614125*uk_134 + 136000*uk_135 + 336600*uk_136 + 765000*uk_137 + 289000*uk_138 + 833085*uk_139 + 5021181*uk_14 + 1893375*uk_140 + 715275*uk_141 + 4303125*uk_142 + 1625625*uk_143 + 614125*uk_144 + 64000*uk_145 + 158400*uk_146 + 360000*uk_147 + 136000*uk_148 + 392040*uk_149 + 11411775*uk_15 + 891000*uk_150 + 336600*uk_151 + 2025000*uk_152 + 765000*uk_153 + 289000*uk_154 + 970299*uk_155 + 2205225*uk_156 + 833085*uk_157 + 5011875*uk_158 + 1893375*uk_159 + 4311115*uk_16 + 715275*uk_160 + 11390625*uk_161 + 4303125*uk_162 + 1625625*uk_163 + 614125*uk_164 + 3025*uk_17 + 1705*uk_18 + 4675*uk_19 + 55*uk_2 + 2200*uk_20 + 5445*uk_21 + 12375*uk_22 + 4675*uk_23 + 961*uk_24 + 2635*uk_25 + 1240*uk_26 + 3069*uk_27 + 6975*uk_28 + 2635*uk_29 + 31*uk_3 + 7225*uk_30 + 3400*uk_31 + 8415*uk_32 + 19125*uk_33 + 7225*uk_34 + 1600*uk_35 + 3960*uk_36 + 9000*uk_37 + 3400*uk_38 + 9801*uk_39 + 85*uk_4 + 22275*uk_40 + 8415*uk_41 + 50625*uk_42 + 19125*uk_43 + 7225*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 79744925791*uk_47 + 218655441685*uk_48 + 102896678440*uk_49 + 40*uk_5 + 254669279139*uk_50 + 578793816225*uk_51 + 218655441685*uk_52 + 153424975*uk_53 + 86475895*uk_54 + 237111325*uk_55 + 111581800*uk_56 + 276164955*uk_57 + 627647625*uk_58 + 237111325*uk_59 + 99*uk_6 + 48740959*uk_60 + 133644565*uk_61 + 62891560*uk_62 + 155656611*uk_63 + 353765025*uk_64 + 133644565*uk_65 + 366444775*uk_66 + 172444600*uk_67 + 426800385*uk_68 + 970000875*uk_69 + 225*uk_7 + 366444775*uk_70 + 81150400*uk_71 + 200847240*uk_72 + 456471000*uk_73 + 172444600*uk_74 + 497096919*uk_75 + 1129765725*uk_76 + 426800385*uk_77 + 2567649375*uk_78 + 970000875*uk_79 + 85*uk_8 + 366444775*uk_80 + 166375*uk_81 + 93775*uk_82 + 257125*uk_83 + 121000*uk_84 + 299475*uk_85 + 680625*uk_86 + 257125*uk_87 + 52855*uk_88 + 144925*uk_89 + 2572416961*uk_9 + 68200*uk_90 + 168795*uk_91 + 383625*uk_92 + 144925*uk_93 + 397375*uk_94 + 187000*uk_95 + 462825*uk_96 + 1051875*uk_97 + 397375*uk_98 + 88000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 222200*uk_100 + 495000*uk_101 + 68200*uk_102 + 561055*uk_103 + 1249875*uk_104 + 172205*uk_105 + 2784375*uk_106 + 383625*uk_107 + 52855*uk_108 + 4913*uk_109 + 862223*uk_11 + 8959*uk_110 + 11560*uk_111 + 29189*uk_112 + 65025*uk_113 + 8959*uk_114 + 16337*uk_115 + 21080*uk_116 + 53227*uk_117 + 118575*uk_118 + 16337*uk_119 + 1572289*uk_12 + 27200*uk_120 + 68680*uk_121 + 153000*uk_122 + 21080*uk_123 + 173417*uk_124 + 386325*uk_125 + 53227*uk_126 + 860625*uk_127 + 118575*uk_128 + 16337*uk_129 + 2028760*uk_13 + 29791*uk_130 + 38440*uk_131 + 97061*uk_132 + 216225*uk_133 + 29791*uk_134 + 49600*uk_135 + 125240*uk_136 + 279000*uk_137 + 38440*uk_138 + 316231*uk_139 + 5122619*uk_14 + 704475*uk_140 + 97061*uk_141 + 1569375*uk_142 + 216225*uk_143 + 29791*uk_144 + 64000*uk_145 + 161600*uk_146 + 360000*uk_147 + 49600*uk_148 + 408040*uk_149 + 11411775*uk_15 + 909000*uk_150 + 125240*uk_151 + 2025000*uk_152 + 279000*uk_153 + 38440*uk_154 + 1030301*uk_155 + 2295225*uk_156 + 316231*uk_157 + 5113125*uk_158 + 704475*uk_159 + 1572289*uk_16 + 97061*uk_160 + 11390625*uk_161 + 1569375*uk_162 + 216225*uk_163 + 29791*uk_164 + 3025*uk_17 + 935*uk_18 + 1705*uk_19 + 55*uk_2 + 2200*uk_20 + 5555*uk_21 + 12375*uk_22 + 1705*uk_23 + 289*uk_24 + 527*uk_25 + 680*uk_26 + 1717*uk_27 + 3825*uk_28 + 527*uk_29 + 17*uk_3 + 961*uk_30 + 1240*uk_31 + 3131*uk_32 + 6975*uk_33 + 961*uk_34 + 1600*uk_35 + 4040*uk_36 + 9000*uk_37 + 1240*uk_38 + 10201*uk_39 + 31*uk_4 + 22725*uk_40 + 3131*uk_41 + 50625*uk_42 + 6975*uk_43 + 961*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 43731088337*uk_47 + 79744925791*uk_48 + 102896678440*uk_49 + 40*uk_5 + 259814113061*uk_50 + 578793816225*uk_51 + 79744925791*uk_52 + 153424975*uk_53 + 47422265*uk_54 + 86475895*uk_55 + 111581800*uk_56 + 281744045*uk_57 + 627647625*uk_58 + 86475895*uk_59 + 101*uk_6 + 14657791*uk_60 + 26728913*uk_61 + 34488920*uk_62 + 87084523*uk_63 + 194000175*uk_64 + 26728913*uk_65 + 48740959*uk_66 + 62891560*uk_67 + 158801189*uk_68 + 353765025*uk_69 + 225*uk_7 + 48740959*uk_70 + 81150400*uk_71 + 204904760*uk_72 + 456471000*uk_73 + 62891560*uk_74 + 517384519*uk_75 + 1152589275*uk_76 + 158801189*uk_77 + 2567649375*uk_78 + 353765025*uk_79 + 31*uk_8 + 48740959*uk_80 + 166375*uk_81 + 51425*uk_82 + 93775*uk_83 + 121000*uk_84 + 305525*uk_85 + 680625*uk_86 + 93775*uk_87 + 15895*uk_88 + 28985*uk_89 + 2572416961*uk_9 + 37400*uk_90 + 94435*uk_91 + 210375*uk_92 + 28985*uk_93 + 52855*uk_94 + 68200*uk_95 + 172205*uk_96 + 383625*uk_97 + 52855*uk_98 + 88000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 226600*uk_100 + 495000*uk_101 + 37400*uk_102 + 583495*uk_103 + 1274625*uk_104 + 96305*uk_105 + 2784375*uk_106 + 210375*uk_107 + 15895*uk_108 + 79507*uk_109 + 2180917*uk_11 + 31433*uk_110 + 73960*uk_111 + 190447*uk_112 + 416025*uk_113 + 31433*uk_114 + 12427*uk_115 + 29240*uk_116 + 75293*uk_117 + 164475*uk_118 + 12427*uk_119 + 862223*uk_12 + 68800*uk_120 + 177160*uk_121 + 387000*uk_122 + 29240*uk_123 + 456187*uk_124 + 996525*uk_125 + 75293*uk_126 + 2176875*uk_127 + 164475*uk_128 + 12427*uk_129 + 2028760*uk_13 + 4913*uk_130 + 11560*uk_131 + 29767*uk_132 + 65025*uk_133 + 4913*uk_134 + 27200*uk_135 + 70040*uk_136 + 153000*uk_137 + 11560*uk_138 + 180353*uk_139 + 5224057*uk_14 + 393975*uk_140 + 29767*uk_141 + 860625*uk_142 + 65025*uk_143 + 4913*uk_144 + 64000*uk_145 + 164800*uk_146 + 360000*uk_147 + 27200*uk_148 + 424360*uk_149 + 11411775*uk_15 + 927000*uk_150 + 70040*uk_151 + 2025000*uk_152 + 153000*uk_153 + 11560*uk_154 + 1092727*uk_155 + 2387025*uk_156 + 180353*uk_157 + 5214375*uk_158 + 393975*uk_159 + 862223*uk_16 + 29767*uk_160 + 11390625*uk_161 + 860625*uk_162 + 65025*uk_163 + 4913*uk_164 + 3025*uk_17 + 2365*uk_18 + 935*uk_19 + 55*uk_2 + 2200*uk_20 + 5665*uk_21 + 12375*uk_22 + 935*uk_23 + 1849*uk_24 + 731*uk_25 + 1720*uk_26 + 4429*uk_27 + 9675*uk_28 + 731*uk_29 + 43*uk_3 + 289*uk_30 + 680*uk_31 + 1751*uk_32 + 3825*uk_33 + 289*uk_34 + 1600*uk_35 + 4120*uk_36 + 9000*uk_37 + 680*uk_38 + 10609*uk_39 + 17*uk_4 + 23175*uk_40 + 1751*uk_41 + 50625*uk_42 + 3825*uk_43 + 289*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 110613929323*uk_47 + 43731088337*uk_48 + 102896678440*uk_49 + 40*uk_5 + 264958946983*uk_50 + 578793816225*uk_51 + 43731088337*uk_52 + 153424975*uk_53 + 119950435*uk_54 + 47422265*uk_55 + 111581800*uk_56 + 287323135*uk_57 + 627647625*uk_58 + 47422265*uk_59 + 103*uk_6 + 93779431*uk_60 + 37075589*uk_61 + 87236680*uk_62 + 224634451*uk_63 + 490706325*uk_64 + 37075589*uk_65 + 14657791*uk_66 + 34488920*uk_67 + 88808969*uk_68 + 194000175*uk_69 + 225*uk_7 + 14657791*uk_70 + 81150400*uk_71 + 208962280*uk_72 + 456471000*uk_73 + 34488920*uk_74 + 538077871*uk_75 + 1175412825*uk_76 + 88808969*uk_77 + 2567649375*uk_78 + 194000175*uk_79 + 17*uk_8 + 14657791*uk_80 + 166375*uk_81 + 130075*uk_82 + 51425*uk_83 + 121000*uk_84 + 311575*uk_85 + 680625*uk_86 + 51425*uk_87 + 101695*uk_88 + 40205*uk_89 + 2572416961*uk_9 + 94600*uk_90 + 243595*uk_91 + 532125*uk_92 + 40205*uk_93 + 15895*uk_94 + 37400*uk_95 + 96305*uk_96 + 210375*uk_97 + 15895*uk_98 + 88000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 207900*uk_100 + 445500*uk_101 + 85140*uk_102 + 606375*uk_103 + 1299375*uk_104 + 248325*uk_105 + 2784375*uk_106 + 532125*uk_107 + 101695*uk_108 + 64*uk_109 + 202876*uk_11 + 688*uk_110 + 576*uk_111 + 1680*uk_112 + 3600*uk_113 + 688*uk_114 + 7396*uk_115 + 6192*uk_116 + 18060*uk_117 + 38700*uk_118 + 7396*uk_119 + 2180917*uk_12 + 5184*uk_120 + 15120*uk_121 + 32400*uk_122 + 6192*uk_123 + 44100*uk_124 + 94500*uk_125 + 18060*uk_126 + 202500*uk_127 + 38700*uk_128 + 7396*uk_129 + 1825884*uk_13 + 79507*uk_130 + 66564*uk_131 + 194145*uk_132 + 416025*uk_133 + 79507*uk_134 + 55728*uk_135 + 162540*uk_136 + 348300*uk_137 + 66564*uk_138 + 474075*uk_139 + 5325495*uk_14 + 1015875*uk_140 + 194145*uk_141 + 2176875*uk_142 + 416025*uk_143 + 79507*uk_144 + 46656*uk_145 + 136080*uk_146 + 291600*uk_147 + 55728*uk_148 + 396900*uk_149 + 11411775*uk_15 + 850500*uk_150 + 162540*uk_151 + 1822500*uk_152 + 348300*uk_153 + 66564*uk_154 + 1157625*uk_155 + 2480625*uk_156 + 474075*uk_157 + 5315625*uk_158 + 1015875*uk_159 + 2180917*uk_16 + 194145*uk_160 + 11390625*uk_161 + 2176875*uk_162 + 416025*uk_163 + 79507*uk_164 + 3025*uk_17 + 220*uk_18 + 2365*uk_19 + 55*uk_2 + 1980*uk_20 + 5775*uk_21 + 12375*uk_22 + 2365*uk_23 + 16*uk_24 + 172*uk_25 + 144*uk_26 + 420*uk_27 + 900*uk_28 + 172*uk_29 + 4*uk_3 + 1849*uk_30 + 1548*uk_31 + 4515*uk_32 + 9675*uk_33 + 1849*uk_34 + 1296*uk_35 + 3780*uk_36 + 8100*uk_37 + 1548*uk_38 + 11025*uk_39 + 43*uk_4 + 23625*uk_40 + 4515*uk_41 + 50625*uk_42 + 9675*uk_43 + 1849*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 10289667844*uk_47 + 110613929323*uk_48 + 92607010596*uk_49 + 36*uk_5 + 270103780905*uk_50 + 578793816225*uk_51 + 110613929323*uk_52 + 153424975*uk_53 + 11158180*uk_54 + 119950435*uk_55 + 100423620*uk_56 + 292902225*uk_57 + 627647625*uk_58 + 119950435*uk_59 + 105*uk_6 + 811504*uk_60 + 8723668*uk_61 + 7303536*uk_62 + 21301980*uk_63 + 45647100*uk_64 + 8723668*uk_65 + 93779431*uk_66 + 78513012*uk_67 + 228996285*uk_68 + 490706325*uk_69 + 225*uk_7 + 93779431*uk_70 + 65731824*uk_71 + 191717820*uk_72 + 410823900*uk_73 + 78513012*uk_74 + 559176975*uk_75 + 1198236375*uk_76 + 228996285*uk_77 + 2567649375*uk_78 + 490706325*uk_79 + 43*uk_8 + 93779431*uk_80 + 166375*uk_81 + 12100*uk_82 + 130075*uk_83 + 108900*uk_84 + 317625*uk_85 + 680625*uk_86 + 130075*uk_87 + 880*uk_88 + 9460*uk_89 + 2572416961*uk_9 + 7920*uk_90 + 23100*uk_91 + 49500*uk_92 + 9460*uk_93 + 101695*uk_94 + 85140*uk_95 + 248325*uk_96 + 532125*uk_97 + 101695*uk_98 + 71280*uk_99,
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|
uk_0 + 50719*uk_1 + 2789545*uk_10 + 211860*uk_100 + 445500*uk_101 + 7920*uk_102 + 629695*uk_103 + 1324125*uk_104 + 23540*uk_105 + 2784375*uk_106 + 49500*uk_107 + 880*uk_108 + uk_109 + 50719*uk_11 + 4*uk_110 + 36*uk_111 + 107*uk_112 + 225*uk_113 + 4*uk_114 + 16*uk_115 + 144*uk_116 + 428*uk_117 + 900*uk_118 + 16*uk_119 + 202876*uk_12 + 1296*uk_120 + 3852*uk_121 + 8100*uk_122 + 144*uk_123 + 11449*uk_124 + 24075*uk_125 + 428*uk_126 + 50625*uk_127 + 900*uk_128 + 16*uk_129 + 1825884*uk_13 + 64*uk_130 + 576*uk_131 + 1712*uk_132 + 3600*uk_133 + 64*uk_134 + 5184*uk_135 + 15408*uk_136 + 32400*uk_137 + 576*uk_138 + 45796*uk_139 + 5426933*uk_14 + 96300*uk_140 + 1712*uk_141 + 202500*uk_142 + 3600*uk_143 + 64*uk_144 + 46656*uk_145 + 138672*uk_146 + 291600*uk_147 + 5184*uk_148 + 412164*uk_149 + 11411775*uk_15 + 866700*uk_150 + 15408*uk_151 + 1822500*uk_152 + 32400*uk_153 + 576*uk_154 + 1225043*uk_155 + 2576025*uk_156 + 45796*uk_157 + 5416875*uk_158 + 96300*uk_159 + 202876*uk_16 + 1712*uk_160 + 11390625*uk_161 + 202500*uk_162 + 3600*uk_163 + 64*uk_164 + 3025*uk_17 + 55*uk_18 + 220*uk_19 + 55*uk_2 + 1980*uk_20 + 5885*uk_21 + 12375*uk_22 + 220*uk_23 + uk_24 + 4*uk_25 + 36*uk_26 + 107*uk_27 + 225*uk_28 + 4*uk_29 + uk_3 + 16*uk_30 + 144*uk_31 + 428*uk_32 + 900*uk_33 + 16*uk_34 + 1296*uk_35 + 3852*uk_36 + 8100*uk_37 + 144*uk_38 + 11449*uk_39 + 4*uk_4 + 24075*uk_40 + 428*uk_41 + 50625*uk_42 + 900*uk_43 + 16*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 2572416961*uk_47 + 10289667844*uk_48 + 92607010596*uk_49 + 36*uk_5 + 275248614827*uk_50 + 578793816225*uk_51 + 10289667844*uk_52 + 153424975*uk_53 + 2789545*uk_54 + 11158180*uk_55 + 100423620*uk_56 + 298481315*uk_57 + 627647625*uk_58 + 11158180*uk_59 + 107*uk_6 + 50719*uk_60 + 202876*uk_61 + 1825884*uk_62 + 5426933*uk_63 + 11411775*uk_64 + 202876*uk_65 + 811504*uk_66 + 7303536*uk_67 + 21707732*uk_68 + 45647100*uk_69 + 225*uk_7 + 811504*uk_70 + 65731824*uk_71 + 195369588*uk_72 + 410823900*uk_73 + 7303536*uk_74 + 580681831*uk_75 + 1221059925*uk_76 + 21707732*uk_77 + 2567649375*uk_78 + 45647100*uk_79 + 4*uk_8 + 811504*uk_80 + 166375*uk_81 + 3025*uk_82 + 12100*uk_83 + 108900*uk_84 + 323675*uk_85 + 680625*uk_86 + 12100*uk_87 + 55*uk_88 + 220*uk_89 + 2572416961*uk_9 + 1980*uk_90 + 5885*uk_91 + 12375*uk_92 + 220*uk_93 + 880*uk_94 + 7920*uk_95 + 23540*uk_96 + 49500*uk_97 + 880*uk_98 + 71280*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 215820*uk_100 + 445500*uk_101 + 1980*uk_102 + 653455*uk_103 + 1348875*uk_104 + 5995*uk_105 + 2784375*uk_106 + 12375*uk_107 + 55*uk_108 + 39304*uk_109 + 1724446*uk_11 + 1156*uk_110 + 41616*uk_111 + 126004*uk_112 + 260100*uk_113 + 1156*uk_114 + 34*uk_115 + 1224*uk_116 + 3706*uk_117 + 7650*uk_118 + 34*uk_119 + 50719*uk_12 + 44064*uk_120 + 133416*uk_121 + 275400*uk_122 + 1224*uk_123 + 403954*uk_124 + 833850*uk_125 + 3706*uk_126 + 1721250*uk_127 + 7650*uk_128 + 34*uk_129 + 1825884*uk_13 + uk_130 + 36*uk_131 + 109*uk_132 + 225*uk_133 + uk_134 + 1296*uk_135 + 3924*uk_136 + 8100*uk_137 + 36*uk_138 + 11881*uk_139 + 5528371*uk_14 + 24525*uk_140 + 109*uk_141 + 50625*uk_142 + 225*uk_143 + uk_144 + 46656*uk_145 + 141264*uk_146 + 291600*uk_147 + 1296*uk_148 + 427716*uk_149 + 11411775*uk_15 + 882900*uk_150 + 3924*uk_151 + 1822500*uk_152 + 8100*uk_153 + 36*uk_154 + 1295029*uk_155 + 2673225*uk_156 + 11881*uk_157 + 5518125*uk_158 + 24525*uk_159 + 50719*uk_16 + 109*uk_160 + 11390625*uk_161 + 50625*uk_162 + 225*uk_163 + uk_164 + 3025*uk_17 + 1870*uk_18 + 55*uk_19 + 55*uk_2 + 1980*uk_20 + 5995*uk_21 + 12375*uk_22 + 55*uk_23 + 1156*uk_24 + 34*uk_25 + 1224*uk_26 + 3706*uk_27 + 7650*uk_28 + 34*uk_29 + 34*uk_3 + uk_30 + 36*uk_31 + 109*uk_32 + 225*uk_33 + uk_34 + 1296*uk_35 + 3924*uk_36 + 8100*uk_37 + 36*uk_38 + 11881*uk_39 + uk_4 + 24525*uk_40 + 109*uk_41 + 50625*uk_42 + 225*uk_43 + uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 87462176674*uk_47 + 2572416961*uk_48 + 92607010596*uk_49 + 36*uk_5 + 280393448749*uk_50 + 578793816225*uk_51 + 2572416961*uk_52 + 153424975*uk_53 + 94844530*uk_54 + 2789545*uk_55 + 100423620*uk_56 + 304060405*uk_57 + 627647625*uk_58 + 2789545*uk_59 + 109*uk_6 + 58631164*uk_60 + 1724446*uk_61 + 62080056*uk_62 + 187964614*uk_63 + 388000350*uk_64 + 1724446*uk_65 + 50719*uk_66 + 1825884*uk_67 + 5528371*uk_68 + 11411775*uk_69 + 225*uk_7 + 50719*uk_70 + 65731824*uk_71 + 199021356*uk_72 + 410823900*uk_73 + 1825884*uk_74 + 602592439*uk_75 + 1243883475*uk_76 + 5528371*uk_77 + 2567649375*uk_78 + 11411775*uk_79 + uk_8 + 50719*uk_80 + 166375*uk_81 + 102850*uk_82 + 3025*uk_83 + 108900*uk_84 + 329725*uk_85 + 680625*uk_86 + 3025*uk_87 + 63580*uk_88 + 1870*uk_89 + 2572416961*uk_9 + 67320*uk_90 + 203830*uk_91 + 420750*uk_92 + 1870*uk_93 + 55*uk_94 + 1980*uk_95 + 5995*uk_96 + 12375*uk_97 + 55*uk_98 + 71280*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 219780*uk_100 + 445500*uk_101 + 67320*uk_102 + 677655*uk_103 + 1373625*uk_104 + 207570*uk_105 + 2784375*uk_106 + 420750*uk_107 + 63580*uk_108 + 1092727*uk_109 + 5224057*uk_11 + 360706*uk_110 + 381924*uk_111 + 1177599*uk_112 + 2387025*uk_113 + 360706*uk_114 + 119068*uk_115 + 126072*uk_116 + 388722*uk_117 + 787950*uk_118 + 119068*uk_119 + 1724446*uk_12 + 133488*uk_120 + 411588*uk_121 + 834300*uk_122 + 126072*uk_123 + 1269063*uk_124 + 2572425*uk_125 + 388722*uk_126 + 5214375*uk_127 + 787950*uk_128 + 119068*uk_129 + 1825884*uk_13 + 39304*uk_130 + 41616*uk_131 + 128316*uk_132 + 260100*uk_133 + 39304*uk_134 + 44064*uk_135 + 135864*uk_136 + 275400*uk_137 + 41616*uk_138 + 418914*uk_139 + 5629809*uk_14 + 849150*uk_140 + 128316*uk_141 + 1721250*uk_142 + 260100*uk_143 + 39304*uk_144 + 46656*uk_145 + 143856*uk_146 + 291600*uk_147 + 44064*uk_148 + 443556*uk_149 + 11411775*uk_15 + 899100*uk_150 + 135864*uk_151 + 1822500*uk_152 + 275400*uk_153 + 41616*uk_154 + 1367631*uk_155 + 2772225*uk_156 + 418914*uk_157 + 5619375*uk_158 + 849150*uk_159 + 1724446*uk_16 + 128316*uk_160 + 11390625*uk_161 + 1721250*uk_162 + 260100*uk_163 + 39304*uk_164 + 3025*uk_17 + 5665*uk_18 + 1870*uk_19 + 55*uk_2 + 1980*uk_20 + 6105*uk_21 + 12375*uk_22 + 1870*uk_23 + 10609*uk_24 + 3502*uk_25 + 3708*uk_26 + 11433*uk_27 + 23175*uk_28 + 3502*uk_29 + 103*uk_3 + 1156*uk_30 + 1224*uk_31 + 3774*uk_32 + 7650*uk_33 + 1156*uk_34 + 1296*uk_35 + 3996*uk_36 + 8100*uk_37 + 1224*uk_38 + 12321*uk_39 + 34*uk_4 + 24975*uk_40 + 3774*uk_41 + 50625*uk_42 + 7650*uk_43 + 1156*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 264958946983*uk_47 + 87462176674*uk_48 + 92607010596*uk_49 + 36*uk_5 + 285538282671*uk_50 + 578793816225*uk_51 + 87462176674*uk_52 + 153424975*uk_53 + 287323135*uk_54 + 94844530*uk_55 + 100423620*uk_56 + 309639495*uk_57 + 627647625*uk_58 + 94844530*uk_59 + 111*uk_6 + 538077871*uk_60 + 177617938*uk_61 + 188066052*uk_62 + 579870327*uk_63 + 1175412825*uk_64 + 177617938*uk_65 + 58631164*uk_66 + 62080056*uk_67 + 191413506*uk_68 + 388000350*uk_69 + 225*uk_7 + 58631164*uk_70 + 65731824*uk_71 + 202673124*uk_72 + 410823900*uk_73 + 62080056*uk_74 + 624908799*uk_75 + 1266707025*uk_76 + 191413506*uk_77 + 2567649375*uk_78 + 388000350*uk_79 + 34*uk_8 + 58631164*uk_80 + 166375*uk_81 + 311575*uk_82 + 102850*uk_83 + 108900*uk_84 + 335775*uk_85 + 680625*uk_86 + 102850*uk_87 + 583495*uk_88 + 192610*uk_89 + 2572416961*uk_9 + 203940*uk_90 + 628815*uk_91 + 1274625*uk_92 + 192610*uk_93 + 63580*uk_94 + 67320*uk_95 + 207570*uk_96 + 420750*uk_97 + 63580*uk_98 + 71280*uk_99,
|
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 198880*uk_100 + 396000*uk_101 + 181280*uk_102 + 702295*uk_103 + 1398375*uk_104 + 640145*uk_105 + 2784375*uk_106 + 1274625*uk_107 + 583495*uk_108 + 857375*uk_109 + 4818305*uk_11 + 929575*uk_110 + 288800*uk_111 + 1019825*uk_112 + 2030625*uk_113 + 929575*uk_114 + 1007855*uk_115 + 313120*uk_116 + 1105705*uk_117 + 2201625*uk_118 + 1007855*uk_119 + 5224057*uk_12 + 97280*uk_120 + 343520*uk_121 + 684000*uk_122 + 313120*uk_123 + 1213055*uk_124 + 2415375*uk_125 + 1105705*uk_126 + 4809375*uk_127 + 2201625*uk_128 + 1007855*uk_129 + 1623008*uk_13 + 1092727*uk_130 + 339488*uk_131 + 1198817*uk_132 + 2387025*uk_133 + 1092727*uk_134 + 105472*uk_135 + 372448*uk_136 + 741600*uk_137 + 339488*uk_138 + 1315207*uk_139 + 5731247*uk_14 + 2618775*uk_140 + 1198817*uk_141 + 5214375*uk_142 + 2387025*uk_143 + 1092727*uk_144 + 32768*uk_145 + 115712*uk_146 + 230400*uk_147 + 105472*uk_148 + 408608*uk_149 + 11411775*uk_15 + 813600*uk_150 + 372448*uk_151 + 1620000*uk_152 + 741600*uk_153 + 339488*uk_154 + 1442897*uk_155 + 2873025*uk_156 + 1315207*uk_157 + 5720625*uk_158 + 2618775*uk_159 + 5224057*uk_16 + 1198817*uk_160 + 11390625*uk_161 + 5214375*uk_162 + 2387025*uk_163 + 1092727*uk_164 + 3025*uk_17 + 5225*uk_18 + 5665*uk_19 + 55*uk_2 + 1760*uk_20 + 6215*uk_21 + 12375*uk_22 + 5665*uk_23 + 9025*uk_24 + 9785*uk_25 + 3040*uk_26 + 10735*uk_27 + 21375*uk_28 + 9785*uk_29 + 95*uk_3 + 10609*uk_30 + 3296*uk_31 + 11639*uk_32 + 23175*uk_33 + 10609*uk_34 + 1024*uk_35 + 3616*uk_36 + 7200*uk_37 + 3296*uk_38 + 12769*uk_39 + 103*uk_4 + 25425*uk_40 + 11639*uk_41 + 50625*uk_42 + 23175*uk_43 + 10609*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 244379611295*uk_47 + 264958946983*uk_48 + 82317342752*uk_49 + 32*uk_5 + 290683116593*uk_50 + 578793816225*uk_51 + 264958946983*uk_52 + 153424975*uk_53 + 265006775*uk_54 + 287323135*uk_55 + 89265440*uk_56 + 315218585*uk_57 + 627647625*uk_58 + 287323135*uk_59 + 113*uk_6 + 457738975*uk_60 + 496285415*uk_61 + 154185760*uk_62 + 544468465*uk_63 + 1084118625*uk_64 + 496285415*uk_65 + 538077871*uk_66 + 167169824*uk_67 + 590318441*uk_68 + 1175412825*uk_69 + 225*uk_7 + 538077871*uk_70 + 51936256*uk_71 + 183399904*uk_72 + 365176800*uk_73 + 167169824*uk_74 + 647630911*uk_75 + 1289530575*uk_76 + 590318441*uk_77 + 2567649375*uk_78 + 1175412825*uk_79 + 103*uk_8 + 538077871*uk_80 + 166375*uk_81 + 287375*uk_82 + 311575*uk_83 + 96800*uk_84 + 341825*uk_85 + 680625*uk_86 + 311575*uk_87 + 496375*uk_88 + 538175*uk_89 + 2572416961*uk_9 + 167200*uk_90 + 590425*uk_91 + 1175625*uk_92 + 538175*uk_93 + 583495*uk_94 + 181280*uk_95 + 640145*uk_96 + 1274625*uk_97 + 583495*uk_98 + 56320*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 177100*uk_100 + 346500*uk_101 + 146300*uk_102 + 727375*uk_103 + 1423125*uk_104 + 600875*uk_105 + 2784375*uk_106 + 1175625*uk_107 + 496375*uk_108 + 64*uk_109 + 202876*uk_11 + 1520*uk_110 + 448*uk_111 + 1840*uk_112 + 3600*uk_113 + 1520*uk_114 + 36100*uk_115 + 10640*uk_116 + 43700*uk_117 + 85500*uk_118 + 36100*uk_119 + 4818305*uk_12 + 3136*uk_120 + 12880*uk_121 + 25200*uk_122 + 10640*uk_123 + 52900*uk_124 + 103500*uk_125 + 43700*uk_126 + 202500*uk_127 + 85500*uk_128 + 36100*uk_129 + 1420132*uk_13 + 857375*uk_130 + 252700*uk_131 + 1037875*uk_132 + 2030625*uk_133 + 857375*uk_134 + 74480*uk_135 + 305900*uk_136 + 598500*uk_137 + 252700*uk_138 + 1256375*uk_139 + 5832685*uk_14 + 2458125*uk_140 + 1037875*uk_141 + 4809375*uk_142 + 2030625*uk_143 + 857375*uk_144 + 21952*uk_145 + 90160*uk_146 + 176400*uk_147 + 74480*uk_148 + 370300*uk_149 + 11411775*uk_15 + 724500*uk_150 + 305900*uk_151 + 1417500*uk_152 + 598500*uk_153 + 252700*uk_154 + 1520875*uk_155 + 2975625*uk_156 + 1256375*uk_157 + 5821875*uk_158 + 2458125*uk_159 + 4818305*uk_16 + 1037875*uk_160 + 11390625*uk_161 + 4809375*uk_162 + 2030625*uk_163 + 857375*uk_164 + 3025*uk_17 + 220*uk_18 + 5225*uk_19 + 55*uk_2 + 1540*uk_20 + 6325*uk_21 + 12375*uk_22 + 5225*uk_23 + 16*uk_24 + 380*uk_25 + 112*uk_26 + 460*uk_27 + 900*uk_28 + 380*uk_29 + 4*uk_3 + 9025*uk_30 + 2660*uk_31 + 10925*uk_32 + 21375*uk_33 + 9025*uk_34 + 784*uk_35 + 3220*uk_36 + 6300*uk_37 + 2660*uk_38 + 13225*uk_39 + 95*uk_4 + 25875*uk_40 + 10925*uk_41 + 50625*uk_42 + 21375*uk_43 + 9025*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 10289667844*uk_47 + 244379611295*uk_48 + 72027674908*uk_49 + 28*uk_5 + 295827950515*uk_50 + 578793816225*uk_51 + 244379611295*uk_52 + 153424975*uk_53 + 11158180*uk_54 + 265006775*uk_55 + 78107260*uk_56 + 320797675*uk_57 + 627647625*uk_58 + 265006775*uk_59 + 115*uk_6 + 811504*uk_60 + 19273220*uk_61 + 5680528*uk_62 + 23330740*uk_63 + 45647100*uk_64 + 19273220*uk_65 + 457738975*uk_66 + 134912540*uk_67 + 554105075*uk_68 + 1084118625*uk_69 + 225*uk_7 + 457738975*uk_70 + 39763696*uk_71 + 163315180*uk_72 + 319529700*uk_73 + 134912540*uk_74 + 670758775*uk_75 + 1312354125*uk_76 + 554105075*uk_77 + 2567649375*uk_78 + 1084118625*uk_79 + 95*uk_8 + 457738975*uk_80 + 166375*uk_81 + 12100*uk_82 + 287375*uk_83 + 84700*uk_84 + 347875*uk_85 + 680625*uk_86 + 287375*uk_87 + 880*uk_88 + 20900*uk_89 + 2572416961*uk_9 + 6160*uk_90 + 25300*uk_91 + 49500*uk_92 + 20900*uk_93 + 496375*uk_94 + 146300*uk_95 + 600875*uk_96 + 1175625*uk_97 + 496375*uk_98 + 43120*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 205920*uk_100 + 396000*uk_101 + 7040*uk_102 + 752895*uk_103 + 1447875*uk_104 + 25740*uk_105 + 2784375*uk_106 + 49500*uk_107 + 880*uk_108 + 195112*uk_109 + 2941702*uk_11 + 13456*uk_110 + 107648*uk_111 + 393588*uk_112 + 756900*uk_113 + 13456*uk_114 + 928*uk_115 + 7424*uk_116 + 27144*uk_117 + 52200*uk_118 + 928*uk_119 + 202876*uk_12 + 59392*uk_120 + 217152*uk_121 + 417600*uk_122 + 7424*uk_123 + 793962*uk_124 + 1526850*uk_125 + 27144*uk_126 + 2936250*uk_127 + 52200*uk_128 + 928*uk_129 + 1623008*uk_13 + 64*uk_130 + 512*uk_131 + 1872*uk_132 + 3600*uk_133 + 64*uk_134 + 4096*uk_135 + 14976*uk_136 + 28800*uk_137 + 512*uk_138 + 54756*uk_139 + 5934123*uk_14 + 105300*uk_140 + 1872*uk_141 + 202500*uk_142 + 3600*uk_143 + 64*uk_144 + 32768*uk_145 + 119808*uk_146 + 230400*uk_147 + 4096*uk_148 + 438048*uk_149 + 11411775*uk_15 + 842400*uk_150 + 14976*uk_151 + 1620000*uk_152 + 28800*uk_153 + 512*uk_154 + 1601613*uk_155 + 3080025*uk_156 + 54756*uk_157 + 5923125*uk_158 + 105300*uk_159 + 202876*uk_16 + 1872*uk_160 + 11390625*uk_161 + 202500*uk_162 + 3600*uk_163 + 64*uk_164 + 3025*uk_17 + 3190*uk_18 + 220*uk_19 + 55*uk_2 + 1760*uk_20 + 6435*uk_21 + 12375*uk_22 + 220*uk_23 + 3364*uk_24 + 232*uk_25 + 1856*uk_26 + 6786*uk_27 + 13050*uk_28 + 232*uk_29 + 58*uk_3 + 16*uk_30 + 128*uk_31 + 468*uk_32 + 900*uk_33 + 16*uk_34 + 1024*uk_35 + 3744*uk_36 + 7200*uk_37 + 128*uk_38 + 13689*uk_39 + 4*uk_4 + 26325*uk_40 + 468*uk_41 + 50625*uk_42 + 900*uk_43 + 16*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 149200183738*uk_47 + 10289667844*uk_48 + 82317342752*uk_49 + 32*uk_5 + 300972784437*uk_50 + 578793816225*uk_51 + 10289667844*uk_52 + 153424975*uk_53 + 161793610*uk_54 + 11158180*uk_55 + 89265440*uk_56 + 326376765*uk_57 + 627647625*uk_58 + 11158180*uk_59 + 117*uk_6 + 170618716*uk_60 + 11766808*uk_61 + 94134464*uk_62 + 344179134*uk_63 + 661882950*uk_64 + 11766808*uk_65 + 811504*uk_66 + 6492032*uk_67 + 23736492*uk_68 + 45647100*uk_69 + 225*uk_7 + 811504*uk_70 + 51936256*uk_71 + 189891936*uk_72 + 365176800*uk_73 + 6492032*uk_74 + 694292391*uk_75 + 1335177675*uk_76 + 23736492*uk_77 + 2567649375*uk_78 + 45647100*uk_79 + 4*uk_8 + 811504*uk_80 + 166375*uk_81 + 175450*uk_82 + 12100*uk_83 + 96800*uk_84 + 353925*uk_85 + 680625*uk_86 + 12100*uk_87 + 185020*uk_88 + 12760*uk_89 + 2572416961*uk_9 + 102080*uk_90 + 373230*uk_91 + 717750*uk_92 + 12760*uk_93 + 880*uk_94 + 7040*uk_95 + 25740*uk_96 + 49500*uk_97 + 880*uk_98 + 56320*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 183260*uk_100 + 346500*uk_101 + 89320*uk_102 + 778855*uk_103 + 1472625*uk_104 + 379610*uk_105 + 2784375*uk_106 + 717750*uk_107 + 185020*uk_108 + 15625*uk_109 + 1267975*uk_11 + 36250*uk_110 + 17500*uk_111 + 74375*uk_112 + 140625*uk_113 + 36250*uk_114 + 84100*uk_115 + 40600*uk_116 + 172550*uk_117 + 326250*uk_118 + 84100*uk_119 + 2941702*uk_12 + 19600*uk_120 + 83300*uk_121 + 157500*uk_122 + 40600*uk_123 + 354025*uk_124 + 669375*uk_125 + 172550*uk_126 + 1265625*uk_127 + 326250*uk_128 + 84100*uk_129 + 1420132*uk_13 + 195112*uk_130 + 94192*uk_131 + 400316*uk_132 + 756900*uk_133 + 195112*uk_134 + 45472*uk_135 + 193256*uk_136 + 365400*uk_137 + 94192*uk_138 + 821338*uk_139 + 6035561*uk_14 + 1552950*uk_140 + 400316*uk_141 + 2936250*uk_142 + 756900*uk_143 + 195112*uk_144 + 21952*uk_145 + 93296*uk_146 + 176400*uk_147 + 45472*uk_148 + 396508*uk_149 + 11411775*uk_15 + 749700*uk_150 + 193256*uk_151 + 1417500*uk_152 + 365400*uk_153 + 94192*uk_154 + 1685159*uk_155 + 3186225*uk_156 + 821338*uk_157 + 6024375*uk_158 + 1552950*uk_159 + 2941702*uk_16 + 400316*uk_160 + 11390625*uk_161 + 2936250*uk_162 + 756900*uk_163 + 195112*uk_164 + 3025*uk_17 + 1375*uk_18 + 3190*uk_19 + 55*uk_2 + 1540*uk_20 + 6545*uk_21 + 12375*uk_22 + 3190*uk_23 + 625*uk_24 + 1450*uk_25 + 700*uk_26 + 2975*uk_27 + 5625*uk_28 + 1450*uk_29 + 25*uk_3 + 3364*uk_30 + 1624*uk_31 + 6902*uk_32 + 13050*uk_33 + 3364*uk_34 + 784*uk_35 + 3332*uk_36 + 6300*uk_37 + 1624*uk_38 + 14161*uk_39 + 58*uk_4 + 26775*uk_40 + 6902*uk_41 + 50625*uk_42 + 13050*uk_43 + 3364*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 64310424025*uk_47 + 149200183738*uk_48 + 72027674908*uk_49 + 28*uk_5 + 306117618359*uk_50 + 578793816225*uk_51 + 149200183738*uk_52 + 153424975*uk_53 + 69738625*uk_54 + 161793610*uk_55 + 78107260*uk_56 + 331955855*uk_57 + 627647625*uk_58 + 161793610*uk_59 + 119*uk_6 + 31699375*uk_60 + 73542550*uk_61 + 35503300*uk_62 + 150889025*uk_63 + 285294375*uk_64 + 73542550*uk_65 + 170618716*uk_66 + 82367656*uk_67 + 350062538*uk_68 + 661882950*uk_69 + 225*uk_7 + 170618716*uk_70 + 39763696*uk_71 + 168995708*uk_72 + 319529700*uk_73 + 82367656*uk_74 + 718231759*uk_75 + 1358001225*uk_76 + 350062538*uk_77 + 2567649375*uk_78 + 661882950*uk_79 + 58*uk_8 + 170618716*uk_80 + 166375*uk_81 + 75625*uk_82 + 175450*uk_83 + 84700*uk_84 + 359975*uk_85 + 680625*uk_86 + 175450*uk_87 + 34375*uk_88 + 79750*uk_89 + 2572416961*uk_9 + 38500*uk_90 + 163625*uk_91 + 309375*uk_92 + 79750*uk_93 + 185020*uk_94 + 89320*uk_95 + 379610*uk_96 + 717750*uk_97 + 185020*uk_98 + 43120*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 186340*uk_100 + 346500*uk_101 + 38500*uk_102 + 805255*uk_103 + 1497375*uk_104 + 166375*uk_105 + 2784375*uk_106 + 309375*uk_107 + 34375*uk_108 + 8000*uk_109 + 1014380*uk_11 + 10000*uk_110 + 11200*uk_111 + 48400*uk_112 + 90000*uk_113 + 10000*uk_114 + 12500*uk_115 + 14000*uk_116 + 60500*uk_117 + 112500*uk_118 + 12500*uk_119 + 1267975*uk_12 + 15680*uk_120 + 67760*uk_121 + 126000*uk_122 + 14000*uk_123 + 292820*uk_124 + 544500*uk_125 + 60500*uk_126 + 1012500*uk_127 + 112500*uk_128 + 12500*uk_129 + 1420132*uk_13 + 15625*uk_130 + 17500*uk_131 + 75625*uk_132 + 140625*uk_133 + 15625*uk_134 + 19600*uk_135 + 84700*uk_136 + 157500*uk_137 + 17500*uk_138 + 366025*uk_139 + 6136999*uk_14 + 680625*uk_140 + 75625*uk_141 + 1265625*uk_142 + 140625*uk_143 + 15625*uk_144 + 21952*uk_145 + 94864*uk_146 + 176400*uk_147 + 19600*uk_148 + 409948*uk_149 + 11411775*uk_15 + 762300*uk_150 + 84700*uk_151 + 1417500*uk_152 + 157500*uk_153 + 17500*uk_154 + 1771561*uk_155 + 3294225*uk_156 + 366025*uk_157 + 6125625*uk_158 + 680625*uk_159 + 1267975*uk_16 + 75625*uk_160 + 11390625*uk_161 + 1265625*uk_162 + 140625*uk_163 + 15625*uk_164 + 3025*uk_17 + 1100*uk_18 + 1375*uk_19 + 55*uk_2 + 1540*uk_20 + 6655*uk_21 + 12375*uk_22 + 1375*uk_23 + 400*uk_24 + 500*uk_25 + 560*uk_26 + 2420*uk_27 + 4500*uk_28 + 500*uk_29 + 20*uk_3 + 625*uk_30 + 700*uk_31 + 3025*uk_32 + 5625*uk_33 + 625*uk_34 + 784*uk_35 + 3388*uk_36 + 6300*uk_37 + 700*uk_38 + 14641*uk_39 + 25*uk_4 + 27225*uk_40 + 3025*uk_41 + 50625*uk_42 + 5625*uk_43 + 625*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 51448339220*uk_47 + 64310424025*uk_48 + 72027674908*uk_49 + 28*uk_5 + 311262452281*uk_50 + 578793816225*uk_51 + 64310424025*uk_52 + 153424975*uk_53 + 55790900*uk_54 + 69738625*uk_55 + 78107260*uk_56 + 337534945*uk_57 + 627647625*uk_58 + 69738625*uk_59 + 121*uk_6 + 20287600*uk_60 + 25359500*uk_61 + 28402640*uk_62 + 122739980*uk_63 + 228235500*uk_64 + 25359500*uk_65 + 31699375*uk_66 + 35503300*uk_67 + 153424975*uk_68 + 285294375*uk_69 + 225*uk_7 + 31699375*uk_70 + 39763696*uk_71 + 171835972*uk_72 + 319529700*uk_73 + 35503300*uk_74 + 742576879*uk_75 + 1380824775*uk_76 + 153424975*uk_77 + 2567649375*uk_78 + 285294375*uk_79 + 25*uk_8 + 31699375*uk_80 + 166375*uk_81 + 60500*uk_82 + 75625*uk_83 + 84700*uk_84 + 366025*uk_85 + 680625*uk_86 + 75625*uk_87 + 22000*uk_88 + 27500*uk_89 + 2572416961*uk_9 + 30800*uk_90 + 133100*uk_91 + 247500*uk_92 + 27500*uk_93 + 34375*uk_94 + 38500*uk_95 + 166375*uk_96 + 309375*uk_97 + 34375*uk_98 + 43120*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 189420*uk_100 + 346500*uk_101 + 30800*uk_102 + 832095*uk_103 + 1522125*uk_104 + 135300*uk_105 + 2784375*uk_106 + 247500*uk_107 + 22000*uk_108 + 79507*uk_109 + 2180917*uk_11 + 36980*uk_110 + 51772*uk_111 + 227427*uk_112 + 416025*uk_113 + 36980*uk_114 + 17200*uk_115 + 24080*uk_116 + 105780*uk_117 + 193500*uk_118 + 17200*uk_119 + 1014380*uk_12 + 33712*uk_120 + 148092*uk_121 + 270900*uk_122 + 24080*uk_123 + 650547*uk_124 + 1190025*uk_125 + 105780*uk_126 + 2176875*uk_127 + 193500*uk_128 + 17200*uk_129 + 1420132*uk_13 + 8000*uk_130 + 11200*uk_131 + 49200*uk_132 + 90000*uk_133 + 8000*uk_134 + 15680*uk_135 + 68880*uk_136 + 126000*uk_137 + 11200*uk_138 + 302580*uk_139 + 6238437*uk_14 + 553500*uk_140 + 49200*uk_141 + 1012500*uk_142 + 90000*uk_143 + 8000*uk_144 + 21952*uk_145 + 96432*uk_146 + 176400*uk_147 + 15680*uk_148 + 423612*uk_149 + 11411775*uk_15 + 774900*uk_150 + 68880*uk_151 + 1417500*uk_152 + 126000*uk_153 + 11200*uk_154 + 1860867*uk_155 + 3404025*uk_156 + 302580*uk_157 + 6226875*uk_158 + 553500*uk_159 + 1014380*uk_16 + 49200*uk_160 + 11390625*uk_161 + 1012500*uk_162 + 90000*uk_163 + 8000*uk_164 + 3025*uk_17 + 2365*uk_18 + 1100*uk_19 + 55*uk_2 + 1540*uk_20 + 6765*uk_21 + 12375*uk_22 + 1100*uk_23 + 1849*uk_24 + 860*uk_25 + 1204*uk_26 + 5289*uk_27 + 9675*uk_28 + 860*uk_29 + 43*uk_3 + 400*uk_30 + 560*uk_31 + 2460*uk_32 + 4500*uk_33 + 400*uk_34 + 784*uk_35 + 3444*uk_36 + 6300*uk_37 + 560*uk_38 + 15129*uk_39 + 20*uk_4 + 27675*uk_40 + 2460*uk_41 + 50625*uk_42 + 4500*uk_43 + 400*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 110613929323*uk_47 + 51448339220*uk_48 + 72027674908*uk_49 + 28*uk_5 + 316407286203*uk_50 + 578793816225*uk_51 + 51448339220*uk_52 + 153424975*uk_53 + 119950435*uk_54 + 55790900*uk_55 + 78107260*uk_56 + 343114035*uk_57 + 627647625*uk_58 + 55790900*uk_59 + 123*uk_6 + 93779431*uk_60 + 43618340*uk_61 + 61065676*uk_62 + 268252791*uk_63 + 490706325*uk_64 + 43618340*uk_65 + 20287600*uk_66 + 28402640*uk_67 + 124768740*uk_68 + 228235500*uk_69 + 225*uk_7 + 20287600*uk_70 + 39763696*uk_71 + 174676236*uk_72 + 319529700*uk_73 + 28402640*uk_74 + 767327751*uk_75 + 1403648325*uk_76 + 124768740*uk_77 + 2567649375*uk_78 + 228235500*uk_79 + 20*uk_8 + 20287600*uk_80 + 166375*uk_81 + 130075*uk_82 + 60500*uk_83 + 84700*uk_84 + 372075*uk_85 + 680625*uk_86 + 60500*uk_87 + 101695*uk_88 + 47300*uk_89 + 2572416961*uk_9 + 66220*uk_90 + 290895*uk_91 + 532125*uk_92 + 47300*uk_93 + 22000*uk_94 + 30800*uk_95 + 135300*uk_96 + 247500*uk_97 + 22000*uk_98 + 43120*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 192500*uk_100 + 346500*uk_101 + 66220*uk_102 + 859375*uk_103 + 1546875*uk_104 + 295625*uk_105 + 2784375*uk_106 + 532125*uk_107 + 101695*uk_108 + 830584*uk_109 + 4767586*uk_11 + 379948*uk_110 + 247408*uk_111 + 1104500*uk_112 + 1988100*uk_113 + 379948*uk_114 + 173806*uk_115 + 113176*uk_116 + 505250*uk_117 + 909450*uk_118 + 173806*uk_119 + 2180917*uk_12 + 73696*uk_120 + 329000*uk_121 + 592200*uk_122 + 113176*uk_123 + 1468750*uk_124 + 2643750*uk_125 + 505250*uk_126 + 4758750*uk_127 + 909450*uk_128 + 173806*uk_129 + 1420132*uk_13 + 79507*uk_130 + 51772*uk_131 + 231125*uk_132 + 416025*uk_133 + 79507*uk_134 + 33712*uk_135 + 150500*uk_136 + 270900*uk_137 + 51772*uk_138 + 671875*uk_139 + 6339875*uk_14 + 1209375*uk_140 + 231125*uk_141 + 2176875*uk_142 + 416025*uk_143 + 79507*uk_144 + 21952*uk_145 + 98000*uk_146 + 176400*uk_147 + 33712*uk_148 + 437500*uk_149 + 11411775*uk_15 + 787500*uk_150 + 150500*uk_151 + 1417500*uk_152 + 270900*uk_153 + 51772*uk_154 + 1953125*uk_155 + 3515625*uk_156 + 671875*uk_157 + 6328125*uk_158 + 1209375*uk_159 + 2180917*uk_16 + 231125*uk_160 + 11390625*uk_161 + 2176875*uk_162 + 416025*uk_163 + 79507*uk_164 + 3025*uk_17 + 5170*uk_18 + 2365*uk_19 + 55*uk_2 + 1540*uk_20 + 6875*uk_21 + 12375*uk_22 + 2365*uk_23 + 8836*uk_24 + 4042*uk_25 + 2632*uk_26 + 11750*uk_27 + 21150*uk_28 + 4042*uk_29 + 94*uk_3 + 1849*uk_30 + 1204*uk_31 + 5375*uk_32 + 9675*uk_33 + 1849*uk_34 + 784*uk_35 + 3500*uk_36 + 6300*uk_37 + 1204*uk_38 + 15625*uk_39 + 43*uk_4 + 28125*uk_40 + 5375*uk_41 + 50625*uk_42 + 9675*uk_43 + 1849*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 241807194334*uk_47 + 110613929323*uk_48 + 72027674908*uk_49 + 28*uk_5 + 321552120125*uk_50 + 578793816225*uk_51 + 110613929323*uk_52 + 153424975*uk_53 + 262217230*uk_54 + 119950435*uk_55 + 78107260*uk_56 + 348693125*uk_57 + 627647625*uk_58 + 119950435*uk_59 + 125*uk_6 + 448153084*uk_60 + 205006198*uk_61 + 133492408*uk_62 + 595948250*uk_63 + 1072706850*uk_64 + 205006198*uk_65 + 93779431*uk_66 + 61065676*uk_67 + 272614625*uk_68 + 490706325*uk_69 + 225*uk_7 + 93779431*uk_70 + 39763696*uk_71 + 177516500*uk_72 + 319529700*uk_73 + 61065676*uk_74 + 792484375*uk_75 + 1426471875*uk_76 + 272614625*uk_77 + 2567649375*uk_78 + 490706325*uk_79 + 43*uk_8 + 93779431*uk_80 + 166375*uk_81 + 284350*uk_82 + 130075*uk_83 + 84700*uk_84 + 378125*uk_85 + 680625*uk_86 + 130075*uk_87 + 485980*uk_88 + 222310*uk_89 + 2572416961*uk_9 + 144760*uk_90 + 646250*uk_91 + 1163250*uk_92 + 222310*uk_93 + 101695*uk_94 + 66220*uk_95 + 295625*uk_96 + 532125*uk_97 + 101695*uk_98 + 43120*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 167640*uk_100 + 297000*uk_101 + 124080*uk_102 + 887095*uk_103 + 1571625*uk_104 + 656590*uk_105 + 2784375*uk_106 + 1163250*uk_107 + 485980*uk_108 + 97336*uk_109 + 2333074*uk_11 + 198904*uk_110 + 50784*uk_111 + 268732*uk_112 + 476100*uk_113 + 198904*uk_114 + 406456*uk_115 + 103776*uk_116 + 549148*uk_117 + 972900*uk_118 + 406456*uk_119 + 4767586*uk_12 + 26496*uk_120 + 140208*uk_121 + 248400*uk_122 + 103776*uk_123 + 741934*uk_124 + 1314450*uk_125 + 549148*uk_126 + 2328750*uk_127 + 972900*uk_128 + 406456*uk_129 + 1217256*uk_13 + 830584*uk_130 + 212064*uk_131 + 1122172*uk_132 + 1988100*uk_133 + 830584*uk_134 + 54144*uk_135 + 286512*uk_136 + 507600*uk_137 + 212064*uk_138 + 1516126*uk_139 + 6441313*uk_14 + 2686050*uk_140 + 1122172*uk_141 + 4758750*uk_142 + 1988100*uk_143 + 830584*uk_144 + 13824*uk_145 + 73152*uk_146 + 129600*uk_147 + 54144*uk_148 + 387096*uk_149 + 11411775*uk_15 + 685800*uk_150 + 286512*uk_151 + 1215000*uk_152 + 507600*uk_153 + 212064*uk_154 + 2048383*uk_155 + 3629025*uk_156 + 1516126*uk_157 + 6429375*uk_158 + 2686050*uk_159 + 4767586*uk_16 + 1122172*uk_160 + 11390625*uk_161 + 4758750*uk_162 + 1988100*uk_163 + 830584*uk_164 + 3025*uk_17 + 2530*uk_18 + 5170*uk_19 + 55*uk_2 + 1320*uk_20 + 6985*uk_21 + 12375*uk_22 + 5170*uk_23 + 2116*uk_24 + 4324*uk_25 + 1104*uk_26 + 5842*uk_27 + 10350*uk_28 + 4324*uk_29 + 46*uk_3 + 8836*uk_30 + 2256*uk_31 + 11938*uk_32 + 21150*uk_33 + 8836*uk_34 + 576*uk_35 + 3048*uk_36 + 5400*uk_37 + 2256*uk_38 + 16129*uk_39 + 94*uk_4 + 28575*uk_40 + 11938*uk_41 + 50625*uk_42 + 21150*uk_43 + 8836*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 118331180206*uk_47 + 241807194334*uk_48 + 61738007064*uk_49 + 24*uk_5 + 326696954047*uk_50 + 578793816225*uk_51 + 241807194334*uk_52 + 153424975*uk_53 + 128319070*uk_54 + 262217230*uk_55 + 66949080*uk_56 + 354272215*uk_57 + 627647625*uk_58 + 262217230*uk_59 + 127*uk_6 + 107321404*uk_60 + 219308956*uk_61 + 55993776*uk_62 + 296300398*uk_63 + 524941650*uk_64 + 219308956*uk_65 + 448153084*uk_66 + 114422064*uk_67 + 605483422*uk_68 + 1072706850*uk_69 + 225*uk_7 + 448153084*uk_70 + 29214144*uk_71 + 154591512*uk_72 + 273882600*uk_73 + 114422064*uk_74 + 818046751*uk_75 + 1449295425*uk_76 + 605483422*uk_77 + 2567649375*uk_78 + 1072706850*uk_79 + 94*uk_8 + 448153084*uk_80 + 166375*uk_81 + 139150*uk_82 + 284350*uk_83 + 72600*uk_84 + 384175*uk_85 + 680625*uk_86 + 284350*uk_87 + 116380*uk_88 + 237820*uk_89 + 2572416961*uk_9 + 60720*uk_90 + 321310*uk_91 + 569250*uk_92 + 237820*uk_93 + 485980*uk_94 + 124080*uk_95 + 656590*uk_96 + 1163250*uk_97 + 485980*uk_98 + 31680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 170280*uk_100 + 297000*uk_101 + 60720*uk_102 + 915255*uk_103 + 1596375*uk_104 + 326370*uk_105 + 2784375*uk_106 + 569250*uk_107 + 116380*uk_108 + 10648*uk_109 + 1115818*uk_11 + 22264*uk_110 + 11616*uk_111 + 62436*uk_112 + 108900*uk_113 + 22264*uk_114 + 46552*uk_115 + 24288*uk_116 + 130548*uk_117 + 227700*uk_118 + 46552*uk_119 + 2333074*uk_12 + 12672*uk_120 + 68112*uk_121 + 118800*uk_122 + 24288*uk_123 + 366102*uk_124 + 638550*uk_125 + 130548*uk_126 + 1113750*uk_127 + 227700*uk_128 + 46552*uk_129 + 1217256*uk_13 + 97336*uk_130 + 50784*uk_131 + 272964*uk_132 + 476100*uk_133 + 97336*uk_134 + 26496*uk_135 + 142416*uk_136 + 248400*uk_137 + 50784*uk_138 + 765486*uk_139 + 6542751*uk_14 + 1335150*uk_140 + 272964*uk_141 + 2328750*uk_142 + 476100*uk_143 + 97336*uk_144 + 13824*uk_145 + 74304*uk_146 + 129600*uk_147 + 26496*uk_148 + 399384*uk_149 + 11411775*uk_15 + 696600*uk_150 + 142416*uk_151 + 1215000*uk_152 + 248400*uk_153 + 50784*uk_154 + 2146689*uk_155 + 3744225*uk_156 + 765486*uk_157 + 6530625*uk_158 + 1335150*uk_159 + 2333074*uk_16 + 272964*uk_160 + 11390625*uk_161 + 2328750*uk_162 + 476100*uk_163 + 97336*uk_164 + 3025*uk_17 + 1210*uk_18 + 2530*uk_19 + 55*uk_2 + 1320*uk_20 + 7095*uk_21 + 12375*uk_22 + 2530*uk_23 + 484*uk_24 + 1012*uk_25 + 528*uk_26 + 2838*uk_27 + 4950*uk_28 + 1012*uk_29 + 22*uk_3 + 2116*uk_30 + 1104*uk_31 + 5934*uk_32 + 10350*uk_33 + 2116*uk_34 + 576*uk_35 + 3096*uk_36 + 5400*uk_37 + 1104*uk_38 + 16641*uk_39 + 46*uk_4 + 29025*uk_40 + 5934*uk_41 + 50625*uk_42 + 10350*uk_43 + 2116*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 56593173142*uk_47 + 118331180206*uk_48 + 61738007064*uk_49 + 24*uk_5 + 331841787969*uk_50 + 578793816225*uk_51 + 118331180206*uk_52 + 153424975*uk_53 + 61369990*uk_54 + 128319070*uk_55 + 66949080*uk_56 + 359851305*uk_57 + 627647625*uk_58 + 128319070*uk_59 + 129*uk_6 + 24547996*uk_60 + 51327628*uk_61 + 26779632*uk_62 + 143940522*uk_63 + 251059050*uk_64 + 51327628*uk_65 + 107321404*uk_66 + 55993776*uk_67 + 300966546*uk_68 + 524941650*uk_69 + 225*uk_7 + 107321404*uk_70 + 29214144*uk_71 + 157026024*uk_72 + 273882600*uk_73 + 55993776*uk_74 + 844014879*uk_75 + 1472118975*uk_76 + 300966546*uk_77 + 2567649375*uk_78 + 524941650*uk_79 + 46*uk_8 + 107321404*uk_80 + 166375*uk_81 + 66550*uk_82 + 139150*uk_83 + 72600*uk_84 + 390225*uk_85 + 680625*uk_86 + 139150*uk_87 + 26620*uk_88 + 55660*uk_89 + 2572416961*uk_9 + 29040*uk_90 + 156090*uk_91 + 272250*uk_92 + 55660*uk_93 + 116380*uk_94 + 60720*uk_95 + 326370*uk_96 + 569250*uk_97 + 116380*uk_98 + 31680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 172920*uk_100 + 297000*uk_101 + 29040*uk_102 + 943855*uk_103 + 1621125*uk_104 + 158510*uk_105 + 2784375*uk_106 + 272250*uk_107 + 26620*uk_108 + 10648*uk_109 + 1115818*uk_11 + 10648*uk_110 + 11616*uk_111 + 63404*uk_112 + 108900*uk_113 + 10648*uk_114 + 10648*uk_115 + 11616*uk_116 + 63404*uk_117 + 108900*uk_118 + 10648*uk_119 + 1115818*uk_12 + 12672*uk_120 + 69168*uk_121 + 118800*uk_122 + 11616*uk_123 + 377542*uk_124 + 648450*uk_125 + 63404*uk_126 + 1113750*uk_127 + 108900*uk_128 + 10648*uk_129 + 1217256*uk_13 + 10648*uk_130 + 11616*uk_131 + 63404*uk_132 + 108900*uk_133 + 10648*uk_134 + 12672*uk_135 + 69168*uk_136 + 118800*uk_137 + 11616*uk_138 + 377542*uk_139 + 6644189*uk_14 + 648450*uk_140 + 63404*uk_141 + 1113750*uk_142 + 108900*uk_143 + 10648*uk_144 + 13824*uk_145 + 75456*uk_146 + 129600*uk_147 + 12672*uk_148 + 411864*uk_149 + 11411775*uk_15 + 707400*uk_150 + 69168*uk_151 + 1215000*uk_152 + 118800*uk_153 + 11616*uk_154 + 2248091*uk_155 + 3861225*uk_156 + 377542*uk_157 + 6631875*uk_158 + 648450*uk_159 + 1115818*uk_16 + 63404*uk_160 + 11390625*uk_161 + 1113750*uk_162 + 108900*uk_163 + 10648*uk_164 + 3025*uk_17 + 1210*uk_18 + 1210*uk_19 + 55*uk_2 + 1320*uk_20 + 7205*uk_21 + 12375*uk_22 + 1210*uk_23 + 484*uk_24 + 484*uk_25 + 528*uk_26 + 2882*uk_27 + 4950*uk_28 + 484*uk_29 + 22*uk_3 + 484*uk_30 + 528*uk_31 + 2882*uk_32 + 4950*uk_33 + 484*uk_34 + 576*uk_35 + 3144*uk_36 + 5400*uk_37 + 528*uk_38 + 17161*uk_39 + 22*uk_4 + 29475*uk_40 + 2882*uk_41 + 50625*uk_42 + 4950*uk_43 + 484*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 56593173142*uk_47 + 56593173142*uk_48 + 61738007064*uk_49 + 24*uk_5 + 336986621891*uk_50 + 578793816225*uk_51 + 56593173142*uk_52 + 153424975*uk_53 + 61369990*uk_54 + 61369990*uk_55 + 66949080*uk_56 + 365430395*uk_57 + 627647625*uk_58 + 61369990*uk_59 + 131*uk_6 + 24547996*uk_60 + 24547996*uk_61 + 26779632*uk_62 + 146172158*uk_63 + 251059050*uk_64 + 24547996*uk_65 + 24547996*uk_66 + 26779632*uk_67 + 146172158*uk_68 + 251059050*uk_69 + 225*uk_7 + 24547996*uk_70 + 29214144*uk_71 + 159460536*uk_72 + 273882600*uk_73 + 26779632*uk_74 + 870388759*uk_75 + 1494942525*uk_76 + 146172158*uk_77 + 2567649375*uk_78 + 251059050*uk_79 + 22*uk_8 + 24547996*uk_80 + 166375*uk_81 + 66550*uk_82 + 66550*uk_83 + 72600*uk_84 + 396275*uk_85 + 680625*uk_86 + 66550*uk_87 + 26620*uk_88 + 26620*uk_89 + 2572416961*uk_9 + 29040*uk_90 + 158510*uk_91 + 272250*uk_92 + 26620*uk_93 + 26620*uk_94 + 29040*uk_95 + 158510*uk_96 + 272250*uk_97 + 26620*uk_98 + 31680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 175560*uk_100 + 297000*uk_101 + 29040*uk_102 + 972895*uk_103 + 1645875*uk_104 + 160930*uk_105 + 2784375*uk_106 + 272250*uk_107 + 26620*uk_108 + 97336*uk_109 + 2333074*uk_11 + 46552*uk_110 + 50784*uk_111 + 281428*uk_112 + 476100*uk_113 + 46552*uk_114 + 22264*uk_115 + 24288*uk_116 + 134596*uk_117 + 227700*uk_118 + 22264*uk_119 + 1115818*uk_12 + 26496*uk_120 + 146832*uk_121 + 248400*uk_122 + 24288*uk_123 + 813694*uk_124 + 1376550*uk_125 + 134596*uk_126 + 2328750*uk_127 + 227700*uk_128 + 22264*uk_129 + 1217256*uk_13 + 10648*uk_130 + 11616*uk_131 + 64372*uk_132 + 108900*uk_133 + 10648*uk_134 + 12672*uk_135 + 70224*uk_136 + 118800*uk_137 + 11616*uk_138 + 389158*uk_139 + 6745627*uk_14 + 658350*uk_140 + 64372*uk_141 + 1113750*uk_142 + 108900*uk_143 + 10648*uk_144 + 13824*uk_145 + 76608*uk_146 + 129600*uk_147 + 12672*uk_148 + 424536*uk_149 + 11411775*uk_15 + 718200*uk_150 + 70224*uk_151 + 1215000*uk_152 + 118800*uk_153 + 11616*uk_154 + 2352637*uk_155 + 3980025*uk_156 + 389158*uk_157 + 6733125*uk_158 + 658350*uk_159 + 1115818*uk_16 + 64372*uk_160 + 11390625*uk_161 + 1113750*uk_162 + 108900*uk_163 + 10648*uk_164 + 3025*uk_17 + 2530*uk_18 + 1210*uk_19 + 55*uk_2 + 1320*uk_20 + 7315*uk_21 + 12375*uk_22 + 1210*uk_23 + 2116*uk_24 + 1012*uk_25 + 1104*uk_26 + 6118*uk_27 + 10350*uk_28 + 1012*uk_29 + 46*uk_3 + 484*uk_30 + 528*uk_31 + 2926*uk_32 + 4950*uk_33 + 484*uk_34 + 576*uk_35 + 3192*uk_36 + 5400*uk_37 + 528*uk_38 + 17689*uk_39 + 22*uk_4 + 29925*uk_40 + 2926*uk_41 + 50625*uk_42 + 4950*uk_43 + 484*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 118331180206*uk_47 + 56593173142*uk_48 + 61738007064*uk_49 + 24*uk_5 + 342131455813*uk_50 + 578793816225*uk_51 + 56593173142*uk_52 + 153424975*uk_53 + 128319070*uk_54 + 61369990*uk_55 + 66949080*uk_56 + 371009485*uk_57 + 627647625*uk_58 + 61369990*uk_59 + 133*uk_6 + 107321404*uk_60 + 51327628*uk_61 + 55993776*uk_62 + 310298842*uk_63 + 524941650*uk_64 + 51327628*uk_65 + 24547996*uk_66 + 26779632*uk_67 + 148403794*uk_68 + 251059050*uk_69 + 225*uk_7 + 24547996*uk_70 + 29214144*uk_71 + 161895048*uk_72 + 273882600*uk_73 + 26779632*uk_74 + 897168391*uk_75 + 1517766075*uk_76 + 148403794*uk_77 + 2567649375*uk_78 + 251059050*uk_79 + 22*uk_8 + 24547996*uk_80 + 166375*uk_81 + 139150*uk_82 + 66550*uk_83 + 72600*uk_84 + 402325*uk_85 + 680625*uk_86 + 66550*uk_87 + 116380*uk_88 + 55660*uk_89 + 2572416961*uk_9 + 60720*uk_90 + 336490*uk_91 + 569250*uk_92 + 55660*uk_93 + 26620*uk_94 + 29040*uk_95 + 160930*uk_96 + 272250*uk_97 + 26620*uk_98 + 31680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 178200*uk_100 + 297000*uk_101 + 60720*uk_102 + 1002375*uk_103 + 1670625*uk_104 + 341550*uk_105 + 2784375*uk_106 + 569250*uk_107 + 116380*uk_108 + 830584*uk_109 + 4767586*uk_11 + 406456*uk_110 + 212064*uk_111 + 1192860*uk_112 + 1988100*uk_113 + 406456*uk_114 + 198904*uk_115 + 103776*uk_116 + 583740*uk_117 + 972900*uk_118 + 198904*uk_119 + 2333074*uk_12 + 54144*uk_120 + 304560*uk_121 + 507600*uk_122 + 103776*uk_123 + 1713150*uk_124 + 2855250*uk_125 + 583740*uk_126 + 4758750*uk_127 + 972900*uk_128 + 198904*uk_129 + 1217256*uk_13 + 97336*uk_130 + 50784*uk_131 + 285660*uk_132 + 476100*uk_133 + 97336*uk_134 + 26496*uk_135 + 149040*uk_136 + 248400*uk_137 + 50784*uk_138 + 838350*uk_139 + 6847065*uk_14 + 1397250*uk_140 + 285660*uk_141 + 2328750*uk_142 + 476100*uk_143 + 97336*uk_144 + 13824*uk_145 + 77760*uk_146 + 129600*uk_147 + 26496*uk_148 + 437400*uk_149 + 11411775*uk_15 + 729000*uk_150 + 149040*uk_151 + 1215000*uk_152 + 248400*uk_153 + 50784*uk_154 + 2460375*uk_155 + 4100625*uk_156 + 838350*uk_157 + 6834375*uk_158 + 1397250*uk_159 + 2333074*uk_16 + 285660*uk_160 + 11390625*uk_161 + 2328750*uk_162 + 476100*uk_163 + 97336*uk_164 + 3025*uk_17 + 5170*uk_18 + 2530*uk_19 + 55*uk_2 + 1320*uk_20 + 7425*uk_21 + 12375*uk_22 + 2530*uk_23 + 8836*uk_24 + 4324*uk_25 + 2256*uk_26 + 12690*uk_27 + 21150*uk_28 + 4324*uk_29 + 94*uk_3 + 2116*uk_30 + 1104*uk_31 + 6210*uk_32 + 10350*uk_33 + 2116*uk_34 + 576*uk_35 + 3240*uk_36 + 5400*uk_37 + 1104*uk_38 + 18225*uk_39 + 46*uk_4 + 30375*uk_40 + 6210*uk_41 + 50625*uk_42 + 10350*uk_43 + 2116*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 241807194334*uk_47 + 118331180206*uk_48 + 61738007064*uk_49 + 24*uk_5 + 347276289735*uk_50 + 578793816225*uk_51 + 118331180206*uk_52 + 153424975*uk_53 + 262217230*uk_54 + 128319070*uk_55 + 66949080*uk_56 + 376588575*uk_57 + 627647625*uk_58 + 128319070*uk_59 + 135*uk_6 + 448153084*uk_60 + 219308956*uk_61 + 114422064*uk_62 + 643624110*uk_63 + 1072706850*uk_64 + 219308956*uk_65 + 107321404*uk_66 + 55993776*uk_67 + 314964990*uk_68 + 524941650*uk_69 + 225*uk_7 + 107321404*uk_70 + 29214144*uk_71 + 164329560*uk_72 + 273882600*uk_73 + 55993776*uk_74 + 924353775*uk_75 + 1540589625*uk_76 + 314964990*uk_77 + 2567649375*uk_78 + 524941650*uk_79 + 46*uk_8 + 107321404*uk_80 + 166375*uk_81 + 284350*uk_82 + 139150*uk_83 + 72600*uk_84 + 408375*uk_85 + 680625*uk_86 + 139150*uk_87 + 485980*uk_88 + 237820*uk_89 + 2572416961*uk_9 + 124080*uk_90 + 697950*uk_91 + 1163250*uk_92 + 237820*uk_93 + 116380*uk_94 + 60720*uk_95 + 341550*uk_96 + 569250*uk_97 + 116380*uk_98 + 31680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 150700*uk_100 + 247500*uk_101 + 103400*uk_102 + 1032295*uk_103 + 1695375*uk_104 + 708290*uk_105 + 2784375*uk_106 + 1163250*uk_107 + 485980*uk_108 + 24389*uk_109 + 1470851*uk_11 + 79054*uk_110 + 16820*uk_111 + 115217*uk_112 + 189225*uk_113 + 79054*uk_114 + 256244*uk_115 + 54520*uk_116 + 373462*uk_117 + 613350*uk_118 + 256244*uk_119 + 4767586*uk_12 + 11600*uk_120 + 79460*uk_121 + 130500*uk_122 + 54520*uk_123 + 544301*uk_124 + 893925*uk_125 + 373462*uk_126 + 1468125*uk_127 + 613350*uk_128 + 256244*uk_129 + 1014380*uk_13 + 830584*uk_130 + 176720*uk_131 + 1210532*uk_132 + 1988100*uk_133 + 830584*uk_134 + 37600*uk_135 + 257560*uk_136 + 423000*uk_137 + 176720*uk_138 + 1764286*uk_139 + 6948503*uk_14 + 2897550*uk_140 + 1210532*uk_141 + 4758750*uk_142 + 1988100*uk_143 + 830584*uk_144 + 8000*uk_145 + 54800*uk_146 + 90000*uk_147 + 37600*uk_148 + 375380*uk_149 + 11411775*uk_15 + 616500*uk_150 + 257560*uk_151 + 1012500*uk_152 + 423000*uk_153 + 176720*uk_154 + 2571353*uk_155 + 4223025*uk_156 + 1764286*uk_157 + 6935625*uk_158 + 2897550*uk_159 + 4767586*uk_16 + 1210532*uk_160 + 11390625*uk_161 + 4758750*uk_162 + 1988100*uk_163 + 830584*uk_164 + 3025*uk_17 + 1595*uk_18 + 5170*uk_19 + 55*uk_2 + 1100*uk_20 + 7535*uk_21 + 12375*uk_22 + 5170*uk_23 + 841*uk_24 + 2726*uk_25 + 580*uk_26 + 3973*uk_27 + 6525*uk_28 + 2726*uk_29 + 29*uk_3 + 8836*uk_30 + 1880*uk_31 + 12878*uk_32 + 21150*uk_33 + 8836*uk_34 + 400*uk_35 + 2740*uk_36 + 4500*uk_37 + 1880*uk_38 + 18769*uk_39 + 94*uk_4 + 30825*uk_40 + 12878*uk_41 + 50625*uk_42 + 21150*uk_43 + 8836*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 74600091869*uk_47 + 241807194334*uk_48 + 51448339220*uk_49 + 20*uk_5 + 352421123657*uk_50 + 578793816225*uk_51 + 241807194334*uk_52 + 153424975*uk_53 + 80896805*uk_54 + 262217230*uk_55 + 55790900*uk_56 + 382167665*uk_57 + 627647625*uk_58 + 262217230*uk_59 + 137*uk_6 + 42654679*uk_60 + 138259994*uk_61 + 29417020*uk_62 + 201506587*uk_63 + 330941475*uk_64 + 138259994*uk_65 + 448153084*uk_66 + 95351720*uk_67 + 653159282*uk_68 + 1072706850*uk_69 + 225*uk_7 + 448153084*uk_70 + 20287600*uk_71 + 138970060*uk_72 + 228235500*uk_73 + 95351720*uk_74 + 951944911*uk_75 + 1563413175*uk_76 + 653159282*uk_77 + 2567649375*uk_78 + 1072706850*uk_79 + 94*uk_8 + 448153084*uk_80 + 166375*uk_81 + 87725*uk_82 + 284350*uk_83 + 60500*uk_84 + 414425*uk_85 + 680625*uk_86 + 284350*uk_87 + 46255*uk_88 + 149930*uk_89 + 2572416961*uk_9 + 31900*uk_90 + 218515*uk_91 + 358875*uk_92 + 149930*uk_93 + 485980*uk_94 + 103400*uk_95 + 708290*uk_96 + 1163250*uk_97 + 485980*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 183480*uk_100 + 297000*uk_101 + 38280*uk_102 + 1062655*uk_103 + 1720125*uk_104 + 221705*uk_105 + 2784375*uk_106 + 358875*uk_107 + 46255*uk_108 + 1860867*uk_109 + 6238437*uk_11 + 438741*uk_110 + 363096*uk_111 + 2102931*uk_112 + 3404025*uk_113 + 438741*uk_114 + 103443*uk_115 + 85608*uk_116 + 495813*uk_117 + 802575*uk_118 + 103443*uk_119 + 1470851*uk_12 + 70848*uk_120 + 410328*uk_121 + 664200*uk_122 + 85608*uk_123 + 2376483*uk_124 + 3846825*uk_125 + 495813*uk_126 + 6226875*uk_127 + 802575*uk_128 + 103443*uk_129 + 1217256*uk_13 + 24389*uk_130 + 20184*uk_131 + 116899*uk_132 + 189225*uk_133 + 24389*uk_134 + 16704*uk_135 + 96744*uk_136 + 156600*uk_137 + 20184*uk_138 + 560309*uk_139 + 7049941*uk_14 + 906975*uk_140 + 116899*uk_141 + 1468125*uk_142 + 189225*uk_143 + 24389*uk_144 + 13824*uk_145 + 80064*uk_146 + 129600*uk_147 + 16704*uk_148 + 463704*uk_149 + 11411775*uk_15 + 750600*uk_150 + 96744*uk_151 + 1215000*uk_152 + 156600*uk_153 + 20184*uk_154 + 2685619*uk_155 + 4347225*uk_156 + 560309*uk_157 + 7036875*uk_158 + 906975*uk_159 + 1470851*uk_16 + 116899*uk_160 + 11390625*uk_161 + 1468125*uk_162 + 189225*uk_163 + 24389*uk_164 + 3025*uk_17 + 6765*uk_18 + 1595*uk_19 + 55*uk_2 + 1320*uk_20 + 7645*uk_21 + 12375*uk_22 + 1595*uk_23 + 15129*uk_24 + 3567*uk_25 + 2952*uk_26 + 17097*uk_27 + 27675*uk_28 + 3567*uk_29 + 123*uk_3 + 841*uk_30 + 696*uk_31 + 4031*uk_32 + 6525*uk_33 + 841*uk_34 + 576*uk_35 + 3336*uk_36 + 5400*uk_37 + 696*uk_38 + 19321*uk_39 + 29*uk_4 + 31275*uk_40 + 4031*uk_41 + 50625*uk_42 + 6525*uk_43 + 841*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 316407286203*uk_47 + 74600091869*uk_48 + 61738007064*uk_49 + 24*uk_5 + 357565957579*uk_50 + 578793816225*uk_51 + 74600091869*uk_52 + 153424975*uk_53 + 343114035*uk_54 + 80896805*uk_55 + 66949080*uk_56 + 387746755*uk_57 + 627647625*uk_58 + 80896805*uk_59 + 139*uk_6 + 767327751*uk_60 + 180914673*uk_61 + 149722488*uk_62 + 867142743*uk_63 + 1403648325*uk_64 + 180914673*uk_65 + 42654679*uk_66 + 35300424*uk_67 + 204448289*uk_68 + 330941475*uk_69 + 225*uk_7 + 42654679*uk_70 + 29214144*uk_71 + 169198584*uk_72 + 273882600*uk_73 + 35300424*uk_74 + 979941799*uk_75 + 1586236725*uk_76 + 204448289*uk_77 + 2567649375*uk_78 + 330941475*uk_79 + 29*uk_8 + 42654679*uk_80 + 166375*uk_81 + 372075*uk_82 + 87725*uk_83 + 72600*uk_84 + 420475*uk_85 + 680625*uk_86 + 87725*uk_87 + 832095*uk_88 + 196185*uk_89 + 2572416961*uk_9 + 162360*uk_90 + 940335*uk_91 + 1522125*uk_92 + 196185*uk_93 + 46255*uk_94 + 38280*uk_95 + 221705*uk_96 + 358875*uk_97 + 46255*uk_98 + 31680*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 155100*uk_100 + 247500*uk_101 + 135300*uk_102 + 1093455*uk_103 + 1744875*uk_104 + 953865*uk_105 + 2784375*uk_106 + 1522125*uk_107 + 832095*uk_108 + 1000000*uk_109 + 5071900*uk_11 + 1230000*uk_110 + 200000*uk_111 + 1410000*uk_112 + 2250000*uk_113 + 1230000*uk_114 + 1512900*uk_115 + 246000*uk_116 + 1734300*uk_117 + 2767500*uk_118 + 1512900*uk_119 + 6238437*uk_12 + 40000*uk_120 + 282000*uk_121 + 450000*uk_122 + 246000*uk_123 + 1988100*uk_124 + 3172500*uk_125 + 1734300*uk_126 + 5062500*uk_127 + 2767500*uk_128 + 1512900*uk_129 + 1014380*uk_13 + 1860867*uk_130 + 302580*uk_131 + 2133189*uk_132 + 3404025*uk_133 + 1860867*uk_134 + 49200*uk_135 + 346860*uk_136 + 553500*uk_137 + 302580*uk_138 + 2445363*uk_139 + 7151379*uk_14 + 3902175*uk_140 + 2133189*uk_141 + 6226875*uk_142 + 3404025*uk_143 + 1860867*uk_144 + 8000*uk_145 + 56400*uk_146 + 90000*uk_147 + 49200*uk_148 + 397620*uk_149 + 11411775*uk_15 + 634500*uk_150 + 346860*uk_151 + 1012500*uk_152 + 553500*uk_153 + 302580*uk_154 + 2803221*uk_155 + 4473225*uk_156 + 2445363*uk_157 + 7138125*uk_158 + 3902175*uk_159 + 6238437*uk_16 + 2133189*uk_160 + 11390625*uk_161 + 6226875*uk_162 + 3404025*uk_163 + 1860867*uk_164 + 3025*uk_17 + 5500*uk_18 + 6765*uk_19 + 55*uk_2 + 1100*uk_20 + 7755*uk_21 + 12375*uk_22 + 6765*uk_23 + 10000*uk_24 + 12300*uk_25 + 2000*uk_26 + 14100*uk_27 + 22500*uk_28 + 12300*uk_29 + 100*uk_3 + 15129*uk_30 + 2460*uk_31 + 17343*uk_32 + 27675*uk_33 + 15129*uk_34 + 400*uk_35 + 2820*uk_36 + 4500*uk_37 + 2460*uk_38 + 19881*uk_39 + 123*uk_4 + 31725*uk_40 + 17343*uk_41 + 50625*uk_42 + 27675*uk_43 + 15129*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 257241696100*uk_47 + 316407286203*uk_48 + 51448339220*uk_49 + 20*uk_5 + 362710791501*uk_50 + 578793816225*uk_51 + 316407286203*uk_52 + 153424975*uk_53 + 278954500*uk_54 + 343114035*uk_55 + 55790900*uk_56 + 393325845*uk_57 + 627647625*uk_58 + 343114035*uk_59 + 141*uk_6 + 507190000*uk_60 + 623843700*uk_61 + 101438000*uk_62 + 715137900*uk_63 + 1141177500*uk_64 + 623843700*uk_65 + 767327751*uk_66 + 124768740*uk_67 + 879619617*uk_68 + 1403648325*uk_69 + 225*uk_7 + 767327751*uk_70 + 20287600*uk_71 + 143027580*uk_72 + 228235500*uk_73 + 124768740*uk_74 + 1008344439*uk_75 + 1609060275*uk_76 + 879619617*uk_77 + 2567649375*uk_78 + 1403648325*uk_79 + 123*uk_8 + 767327751*uk_80 + 166375*uk_81 + 302500*uk_82 + 372075*uk_83 + 60500*uk_84 + 426525*uk_85 + 680625*uk_86 + 372075*uk_87 + 550000*uk_88 + 676500*uk_89 + 2572416961*uk_9 + 110000*uk_90 + 775500*uk_91 + 1237500*uk_92 + 676500*uk_93 + 832095*uk_94 + 135300*uk_95 + 953865*uk_96 + 1522125*uk_97 + 832095*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 157300*uk_100 + 247500*uk_101 + 110000*uk_102 + 1124695*uk_103 + 1769625*uk_104 + 786500*uk_105 + 2784375*uk_106 + 1237500*uk_107 + 550000*uk_108 + 912673*uk_109 + 4919743*uk_11 + 940900*uk_110 + 188180*uk_111 + 1345487*uk_112 + 2117025*uk_113 + 940900*uk_114 + 970000*uk_115 + 194000*uk_116 + 1387100*uk_117 + 2182500*uk_118 + 970000*uk_119 + 5071900*uk_12 + 38800*uk_120 + 277420*uk_121 + 436500*uk_122 + 194000*uk_123 + 1983553*uk_124 + 3120975*uk_125 + 1387100*uk_126 + 4910625*uk_127 + 2182500*uk_128 + 970000*uk_129 + 1014380*uk_13 + 1000000*uk_130 + 200000*uk_131 + 1430000*uk_132 + 2250000*uk_133 + 1000000*uk_134 + 40000*uk_135 + 286000*uk_136 + 450000*uk_137 + 200000*uk_138 + 2044900*uk_139 + 7252817*uk_14 + 3217500*uk_140 + 1430000*uk_141 + 5062500*uk_142 + 2250000*uk_143 + 1000000*uk_144 + 8000*uk_145 + 57200*uk_146 + 90000*uk_147 + 40000*uk_148 + 408980*uk_149 + 11411775*uk_15 + 643500*uk_150 + 286000*uk_151 + 1012500*uk_152 + 450000*uk_153 + 200000*uk_154 + 2924207*uk_155 + 4601025*uk_156 + 2044900*uk_157 + 7239375*uk_158 + 3217500*uk_159 + 5071900*uk_16 + 1430000*uk_160 + 11390625*uk_161 + 5062500*uk_162 + 2250000*uk_163 + 1000000*uk_164 + 3025*uk_17 + 5335*uk_18 + 5500*uk_19 + 55*uk_2 + 1100*uk_20 + 7865*uk_21 + 12375*uk_22 + 5500*uk_23 + 9409*uk_24 + 9700*uk_25 + 1940*uk_26 + 13871*uk_27 + 21825*uk_28 + 9700*uk_29 + 97*uk_3 + 10000*uk_30 + 2000*uk_31 + 14300*uk_32 + 22500*uk_33 + 10000*uk_34 + 400*uk_35 + 2860*uk_36 + 4500*uk_37 + 2000*uk_38 + 20449*uk_39 + 100*uk_4 + 32175*uk_40 + 14300*uk_41 + 50625*uk_42 + 22500*uk_43 + 10000*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 249524445217*uk_47 + 257241696100*uk_48 + 51448339220*uk_49 + 20*uk_5 + 367855625423*uk_50 + 578793816225*uk_51 + 257241696100*uk_52 + 153424975*uk_53 + 270585865*uk_54 + 278954500*uk_55 + 55790900*uk_56 + 398904935*uk_57 + 627647625*uk_58 + 278954500*uk_59 + 143*uk_6 + 477215071*uk_60 + 491974300*uk_61 + 98394860*uk_62 + 703523249*uk_63 + 1106942175*uk_64 + 491974300*uk_65 + 507190000*uk_66 + 101438000*uk_67 + 725281700*uk_68 + 1141177500*uk_69 + 225*uk_7 + 507190000*uk_70 + 20287600*uk_71 + 145056340*uk_72 + 228235500*uk_73 + 101438000*uk_74 + 1037152831*uk_75 + 1631883825*uk_76 + 725281700*uk_77 + 2567649375*uk_78 + 1141177500*uk_79 + 100*uk_8 + 507190000*uk_80 + 166375*uk_81 + 293425*uk_82 + 302500*uk_83 + 60500*uk_84 + 432575*uk_85 + 680625*uk_86 + 302500*uk_87 + 517495*uk_88 + 533500*uk_89 + 2572416961*uk_9 + 106700*uk_90 + 762905*uk_91 + 1200375*uk_92 + 533500*uk_93 + 550000*uk_94 + 110000*uk_95 + 786500*uk_96 + 1237500*uk_97 + 550000*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 159500*uk_100 + 247500*uk_101 + 106700*uk_102 + 1156375*uk_103 + 1794375*uk_104 + 773575*uk_105 + 2784375*uk_106 + 1200375*uk_107 + 517495*uk_108 + 1481544*uk_109 + 5781966*uk_11 + 1260612*uk_110 + 259920*uk_111 + 1884420*uk_112 + 2924100*uk_113 + 1260612*uk_114 + 1072626*uk_115 + 221160*uk_116 + 1603410*uk_117 + 2488050*uk_118 + 1072626*uk_119 + 4919743*uk_12 + 45600*uk_120 + 330600*uk_121 + 513000*uk_122 + 221160*uk_123 + 2396850*uk_124 + 3719250*uk_125 + 1603410*uk_126 + 5771250*uk_127 + 2488050*uk_128 + 1072626*uk_129 + 1014380*uk_13 + 912673*uk_130 + 188180*uk_131 + 1364305*uk_132 + 2117025*uk_133 + 912673*uk_134 + 38800*uk_135 + 281300*uk_136 + 436500*uk_137 + 188180*uk_138 + 2039425*uk_139 + 7354255*uk_14 + 3164625*uk_140 + 1364305*uk_141 + 4910625*uk_142 + 2117025*uk_143 + 912673*uk_144 + 8000*uk_145 + 58000*uk_146 + 90000*uk_147 + 38800*uk_148 + 420500*uk_149 + 11411775*uk_15 + 652500*uk_150 + 281300*uk_151 + 1012500*uk_152 + 436500*uk_153 + 188180*uk_154 + 3048625*uk_155 + 4730625*uk_156 + 2039425*uk_157 + 7340625*uk_158 + 3164625*uk_159 + 4919743*uk_16 + 1364305*uk_160 + 11390625*uk_161 + 4910625*uk_162 + 2117025*uk_163 + 912673*uk_164 + 3025*uk_17 + 6270*uk_18 + 5335*uk_19 + 55*uk_2 + 1100*uk_20 + 7975*uk_21 + 12375*uk_22 + 5335*uk_23 + 12996*uk_24 + 11058*uk_25 + 2280*uk_26 + 16530*uk_27 + 25650*uk_28 + 11058*uk_29 + 114*uk_3 + 9409*uk_30 + 1940*uk_31 + 14065*uk_32 + 21825*uk_33 + 9409*uk_34 + 400*uk_35 + 2900*uk_36 + 4500*uk_37 + 1940*uk_38 + 21025*uk_39 + 97*uk_4 + 32625*uk_40 + 14065*uk_41 + 50625*uk_42 + 21825*uk_43 + 9409*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 293255533554*uk_47 + 249524445217*uk_48 + 51448339220*uk_49 + 20*uk_5 + 373000459345*uk_50 + 578793816225*uk_51 + 249524445217*uk_52 + 153424975*uk_53 + 318008130*uk_54 + 270585865*uk_55 + 55790900*uk_56 + 404484025*uk_57 + 627647625*uk_58 + 270585865*uk_59 + 145*uk_6 + 659144124*uk_60 + 560850702*uk_61 + 115639320*uk_62 + 838385070*uk_63 + 1300942350*uk_64 + 560850702*uk_65 + 477215071*uk_66 + 98394860*uk_67 + 713362735*uk_68 + 1106942175*uk_69 + 225*uk_7 + 477215071*uk_70 + 20287600*uk_71 + 147085100*uk_72 + 228235500*uk_73 + 98394860*uk_74 + 1066366975*uk_75 + 1654707375*uk_76 + 713362735*uk_77 + 2567649375*uk_78 + 1106942175*uk_79 + 97*uk_8 + 477215071*uk_80 + 166375*uk_81 + 344850*uk_82 + 293425*uk_83 + 60500*uk_84 + 438625*uk_85 + 680625*uk_86 + 293425*uk_87 + 714780*uk_88 + 608190*uk_89 + 2572416961*uk_9 + 125400*uk_90 + 909150*uk_91 + 1410750*uk_92 + 608190*uk_93 + 517495*uk_94 + 106700*uk_95 + 773575*uk_96 + 1200375*uk_97 + 517495*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 129360*uk_100 + 198000*uk_101 + 100320*uk_102 + 1188495*uk_103 + 1819125*uk_104 + 921690*uk_105 + 2784375*uk_106 + 1410750*uk_107 + 714780*uk_108 + 64*uk_109 + 202876*uk_11 + 1824*uk_110 + 256*uk_111 + 2352*uk_112 + 3600*uk_113 + 1824*uk_114 + 51984*uk_115 + 7296*uk_116 + 67032*uk_117 + 102600*uk_118 + 51984*uk_119 + 5781966*uk_12 + 1024*uk_120 + 9408*uk_121 + 14400*uk_122 + 7296*uk_123 + 86436*uk_124 + 132300*uk_125 + 67032*uk_126 + 202500*uk_127 + 102600*uk_128 + 51984*uk_129 + 811504*uk_13 + 1481544*uk_130 + 207936*uk_131 + 1910412*uk_132 + 2924100*uk_133 + 1481544*uk_134 + 29184*uk_135 + 268128*uk_136 + 410400*uk_137 + 207936*uk_138 + 2463426*uk_139 + 7455693*uk_14 + 3770550*uk_140 + 1910412*uk_141 + 5771250*uk_142 + 2924100*uk_143 + 1481544*uk_144 + 4096*uk_145 + 37632*uk_146 + 57600*uk_147 + 29184*uk_148 + 345744*uk_149 + 11411775*uk_15 + 529200*uk_150 + 268128*uk_151 + 810000*uk_152 + 410400*uk_153 + 207936*uk_154 + 3176523*uk_155 + 4862025*uk_156 + 2463426*uk_157 + 7441875*uk_158 + 3770550*uk_159 + 5781966*uk_16 + 1910412*uk_160 + 11390625*uk_161 + 5771250*uk_162 + 2924100*uk_163 + 1481544*uk_164 + 3025*uk_17 + 220*uk_18 + 6270*uk_19 + 55*uk_2 + 880*uk_20 + 8085*uk_21 + 12375*uk_22 + 6270*uk_23 + 16*uk_24 + 456*uk_25 + 64*uk_26 + 588*uk_27 + 900*uk_28 + 456*uk_29 + 4*uk_3 + 12996*uk_30 + 1824*uk_31 + 16758*uk_32 + 25650*uk_33 + 12996*uk_34 + 256*uk_35 + 2352*uk_36 + 3600*uk_37 + 1824*uk_38 + 21609*uk_39 + 114*uk_4 + 33075*uk_40 + 16758*uk_41 + 50625*uk_42 + 25650*uk_43 + 12996*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 10289667844*uk_47 + 293255533554*uk_48 + 41158671376*uk_49 + 16*uk_5 + 378145293267*uk_50 + 578793816225*uk_51 + 293255533554*uk_52 + 153424975*uk_53 + 11158180*uk_54 + 318008130*uk_55 + 44632720*uk_56 + 410063115*uk_57 + 627647625*uk_58 + 318008130*uk_59 + 147*uk_6 + 811504*uk_60 + 23127864*uk_61 + 3246016*uk_62 + 29822772*uk_63 + 45647100*uk_64 + 23127864*uk_65 + 659144124*uk_66 + 92511456*uk_67 + 849949002*uk_68 + 1300942350*uk_69 + 225*uk_7 + 659144124*uk_70 + 12984064*uk_71 + 119291088*uk_72 + 182588400*uk_73 + 92511456*uk_74 + 1095986871*uk_75 + 1677530925*uk_76 + 849949002*uk_77 + 2567649375*uk_78 + 1300942350*uk_79 + 114*uk_8 + 659144124*uk_80 + 166375*uk_81 + 12100*uk_82 + 344850*uk_83 + 48400*uk_84 + 444675*uk_85 + 680625*uk_86 + 344850*uk_87 + 880*uk_88 + 25080*uk_89 + 2572416961*uk_9 + 3520*uk_90 + 32340*uk_91 + 49500*uk_92 + 25080*uk_93 + 714780*uk_94 + 100320*uk_95 + 921690*uk_96 + 1410750*uk_97 + 714780*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 163900*uk_100 + 247500*uk_101 + 4400*uk_102 + 1221055*uk_103 + 1843875*uk_104 + 32780*uk_105 + 2784375*uk_106 + 49500*uk_107 + 880*uk_108 + 205379*uk_109 + 2992421*uk_11 + 13924*uk_110 + 69620*uk_111 + 518669*uk_112 + 783225*uk_113 + 13924*uk_114 + 944*uk_115 + 4720*uk_116 + 35164*uk_117 + 53100*uk_118 + 944*uk_119 + 202876*uk_12 + 23600*uk_120 + 175820*uk_121 + 265500*uk_122 + 4720*uk_123 + 1309859*uk_124 + 1977975*uk_125 + 35164*uk_126 + 2986875*uk_127 + 53100*uk_128 + 944*uk_129 + 1014380*uk_13 + 64*uk_130 + 320*uk_131 + 2384*uk_132 + 3600*uk_133 + 64*uk_134 + 1600*uk_135 + 11920*uk_136 + 18000*uk_137 + 320*uk_138 + 88804*uk_139 + 7557131*uk_14 + 134100*uk_140 + 2384*uk_141 + 202500*uk_142 + 3600*uk_143 + 64*uk_144 + 8000*uk_145 + 59600*uk_146 + 90000*uk_147 + 1600*uk_148 + 444020*uk_149 + 11411775*uk_15 + 670500*uk_150 + 11920*uk_151 + 1012500*uk_152 + 18000*uk_153 + 320*uk_154 + 3307949*uk_155 + 4995225*uk_156 + 88804*uk_157 + 7543125*uk_158 + 134100*uk_159 + 202876*uk_16 + 2384*uk_160 + 11390625*uk_161 + 202500*uk_162 + 3600*uk_163 + 64*uk_164 + 3025*uk_17 + 3245*uk_18 + 220*uk_19 + 55*uk_2 + 1100*uk_20 + 8195*uk_21 + 12375*uk_22 + 220*uk_23 + 3481*uk_24 + 236*uk_25 + 1180*uk_26 + 8791*uk_27 + 13275*uk_28 + 236*uk_29 + 59*uk_3 + 16*uk_30 + 80*uk_31 + 596*uk_32 + 900*uk_33 + 16*uk_34 + 400*uk_35 + 2980*uk_36 + 4500*uk_37 + 80*uk_38 + 22201*uk_39 + 4*uk_4 + 33525*uk_40 + 596*uk_41 + 50625*uk_42 + 900*uk_43 + 16*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 151772600699*uk_47 + 10289667844*uk_48 + 51448339220*uk_49 + 20*uk_5 + 383290127189*uk_50 + 578793816225*uk_51 + 10289667844*uk_52 + 153424975*uk_53 + 164583155*uk_54 + 11158180*uk_55 + 55790900*uk_56 + 415642205*uk_57 + 627647625*uk_58 + 11158180*uk_59 + 149*uk_6 + 176552839*uk_60 + 11969684*uk_61 + 59848420*uk_62 + 445870729*uk_63 + 673294725*uk_64 + 11969684*uk_65 + 811504*uk_66 + 4057520*uk_67 + 30228524*uk_68 + 45647100*uk_69 + 225*uk_7 + 811504*uk_70 + 20287600*uk_71 + 151142620*uk_72 + 228235500*uk_73 + 4057520*uk_74 + 1126012519*uk_75 + 1700354475*uk_76 + 30228524*uk_77 + 2567649375*uk_78 + 45647100*uk_79 + 4*uk_8 + 811504*uk_80 + 166375*uk_81 + 178475*uk_82 + 12100*uk_83 + 60500*uk_84 + 450725*uk_85 + 680625*uk_86 + 12100*uk_87 + 191455*uk_88 + 12980*uk_89 + 2572416961*uk_9 + 64900*uk_90 + 483505*uk_91 + 730125*uk_92 + 12980*uk_93 + 880*uk_94 + 4400*uk_95 + 32780*uk_96 + 49500*uk_97 + 880*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 166100*uk_100 + 247500*uk_101 + 64900*uk_102 + 1254055*uk_103 + 1868625*uk_104 + 489995*uk_105 + 2784375*uk_106 + 730125*uk_107 + 191455*uk_108 + 2406104*uk_109 + 6796346*uk_11 + 1059404*uk_110 + 359120*uk_111 + 2711356*uk_112 + 4040100*uk_113 + 1059404*uk_114 + 466454*uk_115 + 158120*uk_116 + 1193806*uk_117 + 1778850*uk_118 + 466454*uk_119 + 2992421*uk_12 + 53600*uk_120 + 404680*uk_121 + 603000*uk_122 + 158120*uk_123 + 3055334*uk_124 + 4552650*uk_125 + 1193806*uk_126 + 6783750*uk_127 + 1778850*uk_128 + 466454*uk_129 + 1014380*uk_13 + 205379*uk_130 + 69620*uk_131 + 525631*uk_132 + 783225*uk_133 + 205379*uk_134 + 23600*uk_135 + 178180*uk_136 + 265500*uk_137 + 69620*uk_138 + 1345259*uk_139 + 7658569*uk_14 + 2004525*uk_140 + 525631*uk_141 + 2986875*uk_142 + 783225*uk_143 + 205379*uk_144 + 8000*uk_145 + 60400*uk_146 + 90000*uk_147 + 23600*uk_148 + 456020*uk_149 + 11411775*uk_15 + 679500*uk_150 + 178180*uk_151 + 1012500*uk_152 + 265500*uk_153 + 69620*uk_154 + 3442951*uk_155 + 5130225*uk_156 + 1345259*uk_157 + 7644375*uk_158 + 2004525*uk_159 + 2992421*uk_16 + 525631*uk_160 + 11390625*uk_161 + 2986875*uk_162 + 783225*uk_163 + 205379*uk_164 + 3025*uk_17 + 7370*uk_18 + 3245*uk_19 + 55*uk_2 + 1100*uk_20 + 8305*uk_21 + 12375*uk_22 + 3245*uk_23 + 17956*uk_24 + 7906*uk_25 + 2680*uk_26 + 20234*uk_27 + 30150*uk_28 + 7906*uk_29 + 134*uk_3 + 3481*uk_30 + 1180*uk_31 + 8909*uk_32 + 13275*uk_33 + 3481*uk_34 + 400*uk_35 + 3020*uk_36 + 4500*uk_37 + 1180*uk_38 + 22801*uk_39 + 59*uk_4 + 33975*uk_40 + 8909*uk_41 + 50625*uk_42 + 13275*uk_43 + 3481*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 344703872774*uk_47 + 151772600699*uk_48 + 51448339220*uk_49 + 20*uk_5 + 388434961111*uk_50 + 578793816225*uk_51 + 151772600699*uk_52 + 153424975*uk_53 + 373799030*uk_54 + 164583155*uk_55 + 55790900*uk_56 + 421221295*uk_57 + 627647625*uk_58 + 164583155*uk_59 + 151*uk_6 + 910710364*uk_60 + 400984414*uk_61 + 135926920*uk_62 + 1026248246*uk_63 + 1529177850*uk_64 + 400984414*uk_65 + 176552839*uk_66 + 59848420*uk_67 + 451855571*uk_68 + 673294725*uk_69 + 225*uk_7 + 176552839*uk_70 + 20287600*uk_71 + 153171380*uk_72 + 228235500*uk_73 + 59848420*uk_74 + 1156443919*uk_75 + 1723178025*uk_76 + 451855571*uk_77 + 2567649375*uk_78 + 673294725*uk_79 + 59*uk_8 + 176552839*uk_80 + 166375*uk_81 + 405350*uk_82 + 178475*uk_83 + 60500*uk_84 + 456775*uk_85 + 680625*uk_86 + 178475*uk_87 + 987580*uk_88 + 434830*uk_89 + 2572416961*uk_9 + 147400*uk_90 + 1112870*uk_91 + 1658250*uk_92 + 434830*uk_93 + 191455*uk_94 + 64900*uk_95 + 489995*uk_96 + 730125*uk_97 + 191455*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 134640*uk_100 + 198000*uk_101 + 117920*uk_102 + 1287495*uk_103 + 1893375*uk_104 + 1127610*uk_105 + 2784375*uk_106 + 1658250*uk_107 + 987580*uk_108 + 438976*uk_109 + 3854644*uk_11 + 773984*uk_110 + 92416*uk_111 + 883728*uk_112 + 1299600*uk_113 + 773984*uk_114 + 1364656*uk_115 + 162944*uk_116 + 1558152*uk_117 + 2291400*uk_118 + 1364656*uk_119 + 6796346*uk_12 + 19456*uk_120 + 186048*uk_121 + 273600*uk_122 + 162944*uk_123 + 1779084*uk_124 + 2616300*uk_125 + 1558152*uk_126 + 3847500*uk_127 + 2291400*uk_128 + 1364656*uk_129 + 811504*uk_13 + 2406104*uk_130 + 287296*uk_131 + 2747268*uk_132 + 4040100*uk_133 + 2406104*uk_134 + 34304*uk_135 + 328032*uk_136 + 482400*uk_137 + 287296*uk_138 + 3136806*uk_139 + 7760007*uk_14 + 4612950*uk_140 + 2747268*uk_141 + 6783750*uk_142 + 4040100*uk_143 + 2406104*uk_144 + 4096*uk_145 + 39168*uk_146 + 57600*uk_147 + 34304*uk_148 + 374544*uk_149 + 11411775*uk_15 + 550800*uk_150 + 328032*uk_151 + 810000*uk_152 + 482400*uk_153 + 287296*uk_154 + 3581577*uk_155 + 5267025*uk_156 + 3136806*uk_157 + 7745625*uk_158 + 4612950*uk_159 + 6796346*uk_16 + 2747268*uk_160 + 11390625*uk_161 + 6783750*uk_162 + 4040100*uk_163 + 2406104*uk_164 + 3025*uk_17 + 4180*uk_18 + 7370*uk_19 + 55*uk_2 + 880*uk_20 + 8415*uk_21 + 12375*uk_22 + 7370*uk_23 + 5776*uk_24 + 10184*uk_25 + 1216*uk_26 + 11628*uk_27 + 17100*uk_28 + 10184*uk_29 + 76*uk_3 + 17956*uk_30 + 2144*uk_31 + 20502*uk_32 + 30150*uk_33 + 17956*uk_34 + 256*uk_35 + 2448*uk_36 + 3600*uk_37 + 2144*uk_38 + 23409*uk_39 + 134*uk_4 + 34425*uk_40 + 20502*uk_41 + 50625*uk_42 + 30150*uk_43 + 17956*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 195503689036*uk_47 + 344703872774*uk_48 + 41158671376*uk_49 + 16*uk_5 + 393579795033*uk_50 + 578793816225*uk_51 + 344703872774*uk_52 + 153424975*uk_53 + 212005420*uk_54 + 373799030*uk_55 + 44632720*uk_56 + 426800385*uk_57 + 627647625*uk_58 + 373799030*uk_59 + 153*uk_6 + 292952944*uk_60 + 516522296*uk_61 + 61674304*uk_62 + 589760532*uk_63 + 867294900*uk_64 + 516522296*uk_65 + 910710364*uk_66 + 108741536*uk_67 + 1039840938*uk_68 + 1529177850*uk_69 + 225*uk_7 + 910710364*uk_70 + 12984064*uk_71 + 124160112*uk_72 + 182588400*uk_73 + 108741536*uk_74 + 1187281071*uk_75 + 1746001575*uk_76 + 1039840938*uk_77 + 2567649375*uk_78 + 1529177850*uk_79 + 134*uk_8 + 910710364*uk_80 + 166375*uk_81 + 229900*uk_82 + 405350*uk_83 + 48400*uk_84 + 462825*uk_85 + 680625*uk_86 + 405350*uk_87 + 317680*uk_88 + 560120*uk_89 + 2572416961*uk_9 + 66880*uk_90 + 639540*uk_91 + 940500*uk_92 + 560120*uk_93 + 987580*uk_94 + 117920*uk_95 + 1127610*uk_96 + 1658250*uk_97 + 987580*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 136400*uk_100 + 198000*uk_101 + 66880*uk_102 + 1321375*uk_103 + 1918125*uk_104 + 647900*uk_105 + 2784375*uk_106 + 940500*uk_107 + 317680*uk_108 + 39304*uk_109 + 1724446*uk_11 + 87856*uk_110 + 18496*uk_111 + 179180*uk_112 + 260100*uk_113 + 87856*uk_114 + 196384*uk_115 + 41344*uk_116 + 400520*uk_117 + 581400*uk_118 + 196384*uk_119 + 3854644*uk_12 + 8704*uk_120 + 84320*uk_121 + 122400*uk_122 + 41344*uk_123 + 816850*uk_124 + 1185750*uk_125 + 400520*uk_126 + 1721250*uk_127 + 581400*uk_128 + 196384*uk_129 + 811504*uk_13 + 438976*uk_130 + 92416*uk_131 + 895280*uk_132 + 1299600*uk_133 + 438976*uk_134 + 19456*uk_135 + 188480*uk_136 + 273600*uk_137 + 92416*uk_138 + 1825900*uk_139 + 7861445*uk_14 + 2650500*uk_140 + 895280*uk_141 + 3847500*uk_142 + 1299600*uk_143 + 438976*uk_144 + 4096*uk_145 + 39680*uk_146 + 57600*uk_147 + 19456*uk_148 + 384400*uk_149 + 11411775*uk_15 + 558000*uk_150 + 188480*uk_151 + 810000*uk_152 + 273600*uk_153 + 92416*uk_154 + 3723875*uk_155 + 5405625*uk_156 + 1825900*uk_157 + 7846875*uk_158 + 2650500*uk_159 + 3854644*uk_16 + 895280*uk_160 + 11390625*uk_161 + 3847500*uk_162 + 1299600*uk_163 + 438976*uk_164 + 3025*uk_17 + 1870*uk_18 + 4180*uk_19 + 55*uk_2 + 880*uk_20 + 8525*uk_21 + 12375*uk_22 + 4180*uk_23 + 1156*uk_24 + 2584*uk_25 + 544*uk_26 + 5270*uk_27 + 7650*uk_28 + 2584*uk_29 + 34*uk_3 + 5776*uk_30 + 1216*uk_31 + 11780*uk_32 + 17100*uk_33 + 5776*uk_34 + 256*uk_35 + 2480*uk_36 + 3600*uk_37 + 1216*uk_38 + 24025*uk_39 + 76*uk_4 + 34875*uk_40 + 11780*uk_41 + 50625*uk_42 + 17100*uk_43 + 5776*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 87462176674*uk_47 + 195503689036*uk_48 + 41158671376*uk_49 + 16*uk_5 + 398724628955*uk_50 + 578793816225*uk_51 + 195503689036*uk_52 + 153424975*uk_53 + 94844530*uk_54 + 212005420*uk_55 + 44632720*uk_56 + 432379475*uk_57 + 627647625*uk_58 + 212005420*uk_59 + 155*uk_6 + 58631164*uk_60 + 131057896*uk_61 + 27591136*uk_62 + 267289130*uk_63 + 388000350*uk_64 + 131057896*uk_65 + 292952944*uk_66 + 61674304*uk_67 + 597469820*uk_68 + 867294900*uk_69 + 225*uk_7 + 292952944*uk_70 + 12984064*uk_71 + 125783120*uk_72 + 182588400*uk_73 + 61674304*uk_74 + 1218523975*uk_75 + 1768825125*uk_76 + 597469820*uk_77 + 2567649375*uk_78 + 867294900*uk_79 + 76*uk_8 + 292952944*uk_80 + 166375*uk_81 + 102850*uk_82 + 229900*uk_83 + 48400*uk_84 + 468875*uk_85 + 680625*uk_86 + 229900*uk_87 + 63580*uk_88 + 142120*uk_89 + 2572416961*uk_9 + 29920*uk_90 + 289850*uk_91 + 420750*uk_92 + 142120*uk_93 + 317680*uk_94 + 66880*uk_95 + 647900*uk_96 + 940500*uk_97 + 317680*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 138160*uk_100 + 198000*uk_101 + 29920*uk_102 + 1355695*uk_103 + 1942875*uk_104 + 293590*uk_105 + 2784375*uk_106 + 420750*uk_107 + 63580*uk_108 + 512*uk_109 + 405752*uk_11 + 2176*uk_110 + 1024*uk_111 + 10048*uk_112 + 14400*uk_113 + 2176*uk_114 + 9248*uk_115 + 4352*uk_116 + 42704*uk_117 + 61200*uk_118 + 9248*uk_119 + 1724446*uk_12 + 2048*uk_120 + 20096*uk_121 + 28800*uk_122 + 4352*uk_123 + 197192*uk_124 + 282600*uk_125 + 42704*uk_126 + 405000*uk_127 + 61200*uk_128 + 9248*uk_129 + 811504*uk_13 + 39304*uk_130 + 18496*uk_131 + 181492*uk_132 + 260100*uk_133 + 39304*uk_134 + 8704*uk_135 + 85408*uk_136 + 122400*uk_137 + 18496*uk_138 + 838066*uk_139 + 7962883*uk_14 + 1201050*uk_140 + 181492*uk_141 + 1721250*uk_142 + 260100*uk_143 + 39304*uk_144 + 4096*uk_145 + 40192*uk_146 + 57600*uk_147 + 8704*uk_148 + 394384*uk_149 + 11411775*uk_15 + 565200*uk_150 + 85408*uk_151 + 810000*uk_152 + 122400*uk_153 + 18496*uk_154 + 3869893*uk_155 + 5546025*uk_156 + 838066*uk_157 + 7948125*uk_158 + 1201050*uk_159 + 1724446*uk_16 + 181492*uk_160 + 11390625*uk_161 + 1721250*uk_162 + 260100*uk_163 + 39304*uk_164 + 3025*uk_17 + 440*uk_18 + 1870*uk_19 + 55*uk_2 + 880*uk_20 + 8635*uk_21 + 12375*uk_22 + 1870*uk_23 + 64*uk_24 + 272*uk_25 + 128*uk_26 + 1256*uk_27 + 1800*uk_28 + 272*uk_29 + 8*uk_3 + 1156*uk_30 + 544*uk_31 + 5338*uk_32 + 7650*uk_33 + 1156*uk_34 + 256*uk_35 + 2512*uk_36 + 3600*uk_37 + 544*uk_38 + 24649*uk_39 + 34*uk_4 + 35325*uk_40 + 5338*uk_41 + 50625*uk_42 + 7650*uk_43 + 1156*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 20579335688*uk_47 + 87462176674*uk_48 + 41158671376*uk_49 + 16*uk_5 + 403869462877*uk_50 + 578793816225*uk_51 + 87462176674*uk_52 + 153424975*uk_53 + 22316360*uk_54 + 94844530*uk_55 + 44632720*uk_56 + 437958565*uk_57 + 627647625*uk_58 + 94844530*uk_59 + 157*uk_6 + 3246016*uk_60 + 13795568*uk_61 + 6492032*uk_62 + 63703064*uk_63 + 91294200*uk_64 + 13795568*uk_65 + 58631164*uk_66 + 27591136*uk_67 + 270738022*uk_68 + 388000350*uk_69 + 225*uk_7 + 58631164*uk_70 + 12984064*uk_71 + 127406128*uk_72 + 182588400*uk_73 + 27591136*uk_74 + 1250172631*uk_75 + 1791648675*uk_76 + 270738022*uk_77 + 2567649375*uk_78 + 388000350*uk_79 + 34*uk_8 + 58631164*uk_80 + 166375*uk_81 + 24200*uk_82 + 102850*uk_83 + 48400*uk_84 + 474925*uk_85 + 680625*uk_86 + 102850*uk_87 + 3520*uk_88 + 14960*uk_89 + 2572416961*uk_9 + 7040*uk_90 + 69080*uk_91 + 99000*uk_92 + 14960*uk_93 + 63580*uk_94 + 29920*uk_95 + 293590*uk_96 + 420750*uk_97 + 63580*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 174900*uk_100 + 247500*uk_101 + 8800*uk_102 + 1390455*uk_103 + 1967625*uk_104 + 69960*uk_105 + 2784375*uk_106 + 99000*uk_107 + 3520*uk_108 + 3869893*uk_109 + 7962883*uk_11 + 197192*uk_110 + 492980*uk_111 + 3919191*uk_112 + 5546025*uk_113 + 197192*uk_114 + 10048*uk_115 + 25120*uk_116 + 199704*uk_117 + 282600*uk_118 + 10048*uk_119 + 405752*uk_12 + 62800*uk_120 + 499260*uk_121 + 706500*uk_122 + 25120*uk_123 + 3969117*uk_124 + 5616675*uk_125 + 199704*uk_126 + 7948125*uk_127 + 282600*uk_128 + 10048*uk_129 + 1014380*uk_13 + 512*uk_130 + 1280*uk_131 + 10176*uk_132 + 14400*uk_133 + 512*uk_134 + 3200*uk_135 + 25440*uk_136 + 36000*uk_137 + 1280*uk_138 + 202248*uk_139 + 8064321*uk_14 + 286200*uk_140 + 10176*uk_141 + 405000*uk_142 + 14400*uk_143 + 512*uk_144 + 8000*uk_145 + 63600*uk_146 + 90000*uk_147 + 3200*uk_148 + 505620*uk_149 + 11411775*uk_15 + 715500*uk_150 + 25440*uk_151 + 1012500*uk_152 + 36000*uk_153 + 1280*uk_154 + 4019679*uk_155 + 5688225*uk_156 + 202248*uk_157 + 8049375*uk_158 + 286200*uk_159 + 405752*uk_16 + 10176*uk_160 + 11390625*uk_161 + 405000*uk_162 + 14400*uk_163 + 512*uk_164 + 3025*uk_17 + 8635*uk_18 + 440*uk_19 + 55*uk_2 + 1100*uk_20 + 8745*uk_21 + 12375*uk_22 + 440*uk_23 + 24649*uk_24 + 1256*uk_25 + 3140*uk_26 + 24963*uk_27 + 35325*uk_28 + 1256*uk_29 + 157*uk_3 + 64*uk_30 + 160*uk_31 + 1272*uk_32 + 1800*uk_33 + 64*uk_34 + 400*uk_35 + 3180*uk_36 + 4500*uk_37 + 160*uk_38 + 25281*uk_39 + 8*uk_4 + 35775*uk_40 + 1272*uk_41 + 50625*uk_42 + 1800*uk_43 + 64*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 403869462877*uk_47 + 20579335688*uk_48 + 51448339220*uk_49 + 20*uk_5 + 409014296799*uk_50 + 578793816225*uk_51 + 20579335688*uk_52 + 153424975*uk_53 + 437958565*uk_54 + 22316360*uk_55 + 55790900*uk_56 + 443537655*uk_57 + 627647625*uk_58 + 22316360*uk_59 + 159*uk_6 + 1250172631*uk_60 + 63703064*uk_61 + 159257660*uk_62 + 1266098397*uk_63 + 1791648675*uk_64 + 63703064*uk_65 + 3246016*uk_66 + 8115040*uk_67 + 64514568*uk_68 + 91294200*uk_69 + 225*uk_7 + 3246016*uk_70 + 20287600*uk_71 + 161286420*uk_72 + 228235500*uk_73 + 8115040*uk_74 + 1282227039*uk_75 + 1814472225*uk_76 + 64514568*uk_77 + 2567649375*uk_78 + 91294200*uk_79 + 8*uk_8 + 3246016*uk_80 + 166375*uk_81 + 474925*uk_82 + 24200*uk_83 + 60500*uk_84 + 480975*uk_85 + 680625*uk_86 + 24200*uk_87 + 1355695*uk_88 + 69080*uk_89 + 2572416961*uk_9 + 172700*uk_90 + 1372965*uk_91 + 1942875*uk_92 + 69080*uk_93 + 3520*uk_94 + 8800*uk_95 + 69960*uk_96 + 99000*uk_97 + 3520*uk_98 + 22000*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 106260*uk_100 + 148500*uk_101 + 103620*uk_102 + 1425655*uk_103 + 1992375*uk_104 + 1390235*uk_105 + 2784375*uk_106 + 1942875*uk_107 + 1355695*uk_108 + 64*uk_109 + 202876*uk_11 + 2512*uk_110 + 192*uk_111 + 2576*uk_112 + 3600*uk_113 + 2512*uk_114 + 98596*uk_115 + 7536*uk_116 + 101108*uk_117 + 141300*uk_118 + 98596*uk_119 + 7962883*uk_12 + 576*uk_120 + 7728*uk_121 + 10800*uk_122 + 7536*uk_123 + 103684*uk_124 + 144900*uk_125 + 101108*uk_126 + 202500*uk_127 + 141300*uk_128 + 98596*uk_129 + 608628*uk_13 + 3869893*uk_130 + 295788*uk_131 + 3968489*uk_132 + 5546025*uk_133 + 3869893*uk_134 + 22608*uk_135 + 303324*uk_136 + 423900*uk_137 + 295788*uk_138 + 4069597*uk_139 + 8165759*uk_14 + 5687325*uk_140 + 3968489*uk_141 + 7948125*uk_142 + 5546025*uk_143 + 3869893*uk_144 + 1728*uk_145 + 23184*uk_146 + 32400*uk_147 + 22608*uk_148 + 311052*uk_149 + 11411775*uk_15 + 434700*uk_150 + 303324*uk_151 + 607500*uk_152 + 423900*uk_153 + 295788*uk_154 + 4173281*uk_155 + 5832225*uk_156 + 4069597*uk_157 + 8150625*uk_158 + 5687325*uk_159 + 7962883*uk_16 + 3968489*uk_160 + 11390625*uk_161 + 7948125*uk_162 + 5546025*uk_163 + 3869893*uk_164 + 3025*uk_17 + 220*uk_18 + 8635*uk_19 + 55*uk_2 + 660*uk_20 + 8855*uk_21 + 12375*uk_22 + 8635*uk_23 + 16*uk_24 + 628*uk_25 + 48*uk_26 + 644*uk_27 + 900*uk_28 + 628*uk_29 + 4*uk_3 + 24649*uk_30 + 1884*uk_31 + 25277*uk_32 + 35325*uk_33 + 24649*uk_34 + 144*uk_35 + 1932*uk_36 + 2700*uk_37 + 1884*uk_38 + 25921*uk_39 + 157*uk_4 + 36225*uk_40 + 25277*uk_41 + 50625*uk_42 + 35325*uk_43 + 24649*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 10289667844*uk_47 + 403869462877*uk_48 + 30869003532*uk_49 + 12*uk_5 + 414159130721*uk_50 + 578793816225*uk_51 + 403869462877*uk_52 + 153424975*uk_53 + 11158180*uk_54 + 437958565*uk_55 + 33474540*uk_56 + 449116745*uk_57 + 627647625*uk_58 + 437958565*uk_59 + 161*uk_6 + 811504*uk_60 + 31851532*uk_61 + 2434512*uk_62 + 32663036*uk_63 + 45647100*uk_64 + 31851532*uk_65 + 1250172631*uk_66 + 95554596*uk_67 + 1282024163*uk_68 + 1791648675*uk_69 + 225*uk_7 + 1250172631*uk_70 + 7303536*uk_71 + 97989108*uk_72 + 136941300*uk_73 + 95554596*uk_74 + 1314687199*uk_75 + 1837295775*uk_76 + 1282024163*uk_77 + 2567649375*uk_78 + 1791648675*uk_79 + 157*uk_8 + 1250172631*uk_80 + 166375*uk_81 + 12100*uk_82 + 474925*uk_83 + 36300*uk_84 + 487025*uk_85 + 680625*uk_86 + 474925*uk_87 + 880*uk_88 + 34540*uk_89 + 2572416961*uk_9 + 2640*uk_90 + 35420*uk_91 + 49500*uk_92 + 34540*uk_93 + 1355695*uk_94 + 103620*uk_95 + 1390235*uk_96 + 1942875*uk_97 + 1355695*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 143440*uk_100 + 198000*uk_101 + 3520*uk_102 + 1461295*uk_103 + 2017125*uk_104 + 35860*uk_105 + 2784375*uk_106 + 49500*uk_107 + 880*uk_108 + 17576*uk_109 + 1318694*uk_11 + 2704*uk_110 + 10816*uk_111 + 110188*uk_112 + 152100*uk_113 + 2704*uk_114 + 416*uk_115 + 1664*uk_116 + 16952*uk_117 + 23400*uk_118 + 416*uk_119 + 202876*uk_12 + 6656*uk_120 + 67808*uk_121 + 93600*uk_122 + 1664*uk_123 + 690794*uk_124 + 953550*uk_125 + 16952*uk_126 + 1316250*uk_127 + 23400*uk_128 + 416*uk_129 + 811504*uk_13 + 64*uk_130 + 256*uk_131 + 2608*uk_132 + 3600*uk_133 + 64*uk_134 + 1024*uk_135 + 10432*uk_136 + 14400*uk_137 + 256*uk_138 + 106276*uk_139 + 8267197*uk_14 + 146700*uk_140 + 2608*uk_141 + 202500*uk_142 + 3600*uk_143 + 64*uk_144 + 4096*uk_145 + 41728*uk_146 + 57600*uk_147 + 1024*uk_148 + 425104*uk_149 + 11411775*uk_15 + 586800*uk_150 + 10432*uk_151 + 810000*uk_152 + 14400*uk_153 + 256*uk_154 + 4330747*uk_155 + 5978025*uk_156 + 106276*uk_157 + 8251875*uk_158 + 146700*uk_159 + 202876*uk_16 + 2608*uk_160 + 11390625*uk_161 + 202500*uk_162 + 3600*uk_163 + 64*uk_164 + 3025*uk_17 + 1430*uk_18 + 220*uk_19 + 55*uk_2 + 880*uk_20 + 8965*uk_21 + 12375*uk_22 + 220*uk_23 + 676*uk_24 + 104*uk_25 + 416*uk_26 + 4238*uk_27 + 5850*uk_28 + 104*uk_29 + 26*uk_3 + 16*uk_30 + 64*uk_31 + 652*uk_32 + 900*uk_33 + 16*uk_34 + 256*uk_35 + 2608*uk_36 + 3600*uk_37 + 64*uk_38 + 26569*uk_39 + 4*uk_4 + 36675*uk_40 + 652*uk_41 + 50625*uk_42 + 900*uk_43 + 16*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 66882840986*uk_47 + 10289667844*uk_48 + 41158671376*uk_49 + 16*uk_5 + 419303964643*uk_50 + 578793816225*uk_51 + 10289667844*uk_52 + 153424975*uk_53 + 72528170*uk_54 + 11158180*uk_55 + 44632720*uk_56 + 454695835*uk_57 + 627647625*uk_58 + 11158180*uk_59 + 163*uk_6 + 34286044*uk_60 + 5274776*uk_61 + 21099104*uk_62 + 214947122*uk_63 + 296706150*uk_64 + 5274776*uk_65 + 811504*uk_66 + 3246016*uk_67 + 33068788*uk_68 + 45647100*uk_69 + 225*uk_7 + 811504*uk_70 + 12984064*uk_71 + 132275152*uk_72 + 182588400*uk_73 + 3246016*uk_74 + 1347553111*uk_75 + 1860119325*uk_76 + 33068788*uk_77 + 2567649375*uk_78 + 45647100*uk_79 + 4*uk_8 + 811504*uk_80 + 166375*uk_81 + 78650*uk_82 + 12100*uk_83 + 48400*uk_84 + 493075*uk_85 + 680625*uk_86 + 12100*uk_87 + 37180*uk_88 + 5720*uk_89 + 2572416961*uk_9 + 22880*uk_90 + 233090*uk_91 + 321750*uk_92 + 5720*uk_93 + 880*uk_94 + 3520*uk_95 + 35860*uk_96 + 49500*uk_97 + 880*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 145200*uk_100 + 198000*uk_101 + 22880*uk_102 + 1497375*uk_103 + 2041875*uk_104 + 235950*uk_105 + 2784375*uk_106 + 321750*uk_107 + 37180*uk_108 + 262144*uk_109 + 3246016*uk_11 + 106496*uk_110 + 65536*uk_111 + 675840*uk_112 + 921600*uk_113 + 106496*uk_114 + 43264*uk_115 + 26624*uk_116 + 274560*uk_117 + 374400*uk_118 + 43264*uk_119 + 1318694*uk_12 + 16384*uk_120 + 168960*uk_121 + 230400*uk_122 + 26624*uk_123 + 1742400*uk_124 + 2376000*uk_125 + 274560*uk_126 + 3240000*uk_127 + 374400*uk_128 + 43264*uk_129 + 811504*uk_13 + 17576*uk_130 + 10816*uk_131 + 111540*uk_132 + 152100*uk_133 + 17576*uk_134 + 6656*uk_135 + 68640*uk_136 + 93600*uk_137 + 10816*uk_138 + 707850*uk_139 + 8368635*uk_14 + 965250*uk_140 + 111540*uk_141 + 1316250*uk_142 + 152100*uk_143 + 17576*uk_144 + 4096*uk_145 + 42240*uk_146 + 57600*uk_147 + 6656*uk_148 + 435600*uk_149 + 11411775*uk_15 + 594000*uk_150 + 68640*uk_151 + 810000*uk_152 + 93600*uk_153 + 10816*uk_154 + 4492125*uk_155 + 6125625*uk_156 + 707850*uk_157 + 8353125*uk_158 + 965250*uk_159 + 1318694*uk_16 + 111540*uk_160 + 11390625*uk_161 + 1316250*uk_162 + 152100*uk_163 + 17576*uk_164 + 3025*uk_17 + 3520*uk_18 + 1430*uk_19 + 55*uk_2 + 880*uk_20 + 9075*uk_21 + 12375*uk_22 + 1430*uk_23 + 4096*uk_24 + 1664*uk_25 + 1024*uk_26 + 10560*uk_27 + 14400*uk_28 + 1664*uk_29 + 64*uk_3 + 676*uk_30 + 416*uk_31 + 4290*uk_32 + 5850*uk_33 + 676*uk_34 + 256*uk_35 + 2640*uk_36 + 3600*uk_37 + 416*uk_38 + 27225*uk_39 + 26*uk_4 + 37125*uk_40 + 4290*uk_41 + 50625*uk_42 + 5850*uk_43 + 676*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 164634685504*uk_47 + 66882840986*uk_48 + 41158671376*uk_49 + 16*uk_5 + 424448798565*uk_50 + 578793816225*uk_51 + 66882840986*uk_52 + 153424975*uk_53 + 178530880*uk_54 + 72528170*uk_55 + 44632720*uk_56 + 460274925*uk_57 + 627647625*uk_58 + 72528170*uk_59 + 165*uk_6 + 207745024*uk_60 + 84396416*uk_61 + 51936256*uk_62 + 535592640*uk_63 + 730353600*uk_64 + 84396416*uk_65 + 34286044*uk_66 + 21099104*uk_67 + 217584510*uk_68 + 296706150*uk_69 + 225*uk_7 + 34286044*uk_70 + 12984064*uk_71 + 133898160*uk_72 + 182588400*uk_73 + 21099104*uk_74 + 1380824775*uk_75 + 1882942875*uk_76 + 217584510*uk_77 + 2567649375*uk_78 + 296706150*uk_79 + 26*uk_8 + 34286044*uk_80 + 166375*uk_81 + 193600*uk_82 + 78650*uk_83 + 48400*uk_84 + 499125*uk_85 + 680625*uk_86 + 78650*uk_87 + 225280*uk_88 + 91520*uk_89 + 2572416961*uk_9 + 56320*uk_90 + 580800*uk_91 + 792000*uk_92 + 91520*uk_93 + 37180*uk_94 + 22880*uk_95 + 235950*uk_96 + 321750*uk_97 + 37180*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 146960*uk_100 + 198000*uk_101 + 56320*uk_102 + 1533895*uk_103 + 2066625*uk_104 + 587840*uk_105 + 2784375*uk_106 + 792000*uk_107 + 225280*uk_108 + 1643032*uk_109 + 5984842*uk_11 + 891136*uk_110 + 222784*uk_111 + 2325308*uk_112 + 3132900*uk_113 + 891136*uk_114 + 483328*uk_115 + 120832*uk_116 + 1261184*uk_117 + 1699200*uk_118 + 483328*uk_119 + 3246016*uk_12 + 30208*uk_120 + 315296*uk_121 + 424800*uk_122 + 120832*uk_123 + 3290902*uk_124 + 4433850*uk_125 + 1261184*uk_126 + 5973750*uk_127 + 1699200*uk_128 + 483328*uk_129 + 811504*uk_13 + 262144*uk_130 + 65536*uk_131 + 684032*uk_132 + 921600*uk_133 + 262144*uk_134 + 16384*uk_135 + 171008*uk_136 + 230400*uk_137 + 65536*uk_138 + 1784896*uk_139 + 8470073*uk_14 + 2404800*uk_140 + 684032*uk_141 + 3240000*uk_142 + 921600*uk_143 + 262144*uk_144 + 4096*uk_145 + 42752*uk_146 + 57600*uk_147 + 16384*uk_148 + 446224*uk_149 + 11411775*uk_15 + 601200*uk_150 + 171008*uk_151 + 810000*uk_152 + 230400*uk_153 + 65536*uk_154 + 4657463*uk_155 + 6275025*uk_156 + 1784896*uk_157 + 8454375*uk_158 + 2404800*uk_159 + 3246016*uk_16 + 684032*uk_160 + 11390625*uk_161 + 3240000*uk_162 + 921600*uk_163 + 262144*uk_164 + 3025*uk_17 + 6490*uk_18 + 3520*uk_19 + 55*uk_2 + 880*uk_20 + 9185*uk_21 + 12375*uk_22 + 3520*uk_23 + 13924*uk_24 + 7552*uk_25 + 1888*uk_26 + 19706*uk_27 + 26550*uk_28 + 7552*uk_29 + 118*uk_3 + 4096*uk_30 + 1024*uk_31 + 10688*uk_32 + 14400*uk_33 + 4096*uk_34 + 256*uk_35 + 2672*uk_36 + 3600*uk_37 + 1024*uk_38 + 27889*uk_39 + 64*uk_4 + 37575*uk_40 + 10688*uk_41 + 50625*uk_42 + 14400*uk_43 + 4096*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 303545201398*uk_47 + 164634685504*uk_48 + 41158671376*uk_49 + 16*uk_5 + 429593632487*uk_50 + 578793816225*uk_51 + 164634685504*uk_52 + 153424975*uk_53 + 329166310*uk_54 + 178530880*uk_55 + 44632720*uk_56 + 465854015*uk_57 + 627647625*uk_58 + 178530880*uk_59 + 167*uk_6 + 706211356*uk_60 + 383029888*uk_61 + 95757472*uk_62 + 999468614*uk_63 + 1346589450*uk_64 + 383029888*uk_65 + 207745024*uk_66 + 51936256*uk_67 + 542084672*uk_68 + 730353600*uk_69 + 225*uk_7 + 207745024*uk_70 + 12984064*uk_71 + 135521168*uk_72 + 182588400*uk_73 + 51936256*uk_74 + 1414502191*uk_75 + 1905766425*uk_76 + 542084672*uk_77 + 2567649375*uk_78 + 730353600*uk_79 + 64*uk_8 + 207745024*uk_80 + 166375*uk_81 + 356950*uk_82 + 193600*uk_83 + 48400*uk_84 + 505175*uk_85 + 680625*uk_86 + 193600*uk_87 + 765820*uk_88 + 415360*uk_89 + 2572416961*uk_9 + 103840*uk_90 + 1083830*uk_91 + 1460250*uk_92 + 415360*uk_93 + 225280*uk_94 + 56320*uk_95 + 587840*uk_96 + 792000*uk_97 + 225280*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 111540*uk_100 + 148500*uk_101 + 77880*uk_102 + 1570855*uk_103 + 2091375*uk_104 + 1096810*uk_105 + 2784375*uk_106 + 1460250*uk_107 + 765820*uk_108 + 6859*uk_109 + 963661*uk_11 + 42598*uk_110 + 4332*uk_111 + 61009*uk_112 + 81225*uk_113 + 42598*uk_114 + 264556*uk_115 + 26904*uk_116 + 378898*uk_117 + 504450*uk_118 + 264556*uk_119 + 5984842*uk_12 + 2736*uk_120 + 38532*uk_121 + 51300*uk_122 + 26904*uk_123 + 542659*uk_124 + 722475*uk_125 + 378898*uk_126 + 961875*uk_127 + 504450*uk_128 + 264556*uk_129 + 608628*uk_13 + 1643032*uk_130 + 167088*uk_131 + 2353156*uk_132 + 3132900*uk_133 + 1643032*uk_134 + 16992*uk_135 + 239304*uk_136 + 318600*uk_137 + 167088*uk_138 + 3370198*uk_139 + 8571511*uk_14 + 4486950*uk_140 + 2353156*uk_141 + 5973750*uk_142 + 3132900*uk_143 + 1643032*uk_144 + 1728*uk_145 + 24336*uk_146 + 32400*uk_147 + 16992*uk_148 + 342732*uk_149 + 11411775*uk_15 + 456300*uk_150 + 239304*uk_151 + 607500*uk_152 + 318600*uk_153 + 167088*uk_154 + 4826809*uk_155 + 6426225*uk_156 + 3370198*uk_157 + 8555625*uk_158 + 4486950*uk_159 + 5984842*uk_16 + 2353156*uk_160 + 11390625*uk_161 + 5973750*uk_162 + 3132900*uk_163 + 1643032*uk_164 + 3025*uk_17 + 1045*uk_18 + 6490*uk_19 + 55*uk_2 + 660*uk_20 + 9295*uk_21 + 12375*uk_22 + 6490*uk_23 + 361*uk_24 + 2242*uk_25 + 228*uk_26 + 3211*uk_27 + 4275*uk_28 + 2242*uk_29 + 19*uk_3 + 13924*uk_30 + 1416*uk_31 + 19942*uk_32 + 26550*uk_33 + 13924*uk_34 + 144*uk_35 + 2028*uk_36 + 2700*uk_37 + 1416*uk_38 + 28561*uk_39 + 118*uk_4 + 38025*uk_40 + 19942*uk_41 + 50625*uk_42 + 26550*uk_43 + 13924*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 48875922259*uk_47 + 303545201398*uk_48 + 30869003532*uk_49 + 12*uk_5 + 434738466409*uk_50 + 578793816225*uk_51 + 303545201398*uk_52 + 153424975*uk_53 + 53001355*uk_54 + 329166310*uk_55 + 33474540*uk_56 + 471433105*uk_57 + 627647625*uk_58 + 329166310*uk_59 + 169*uk_6 + 18309559*uk_60 + 113711998*uk_61 + 11563932*uk_62 + 162858709*uk_63 + 216823725*uk_64 + 113711998*uk_65 + 706211356*uk_66 + 71818104*uk_67 + 1011438298*uk_68 + 1346589450*uk_69 + 225*uk_7 + 706211356*uk_70 + 7303536*uk_71 + 102858132*uk_72 + 136941300*uk_73 + 71818104*uk_74 + 1448585359*uk_75 + 1928589975*uk_76 + 1011438298*uk_77 + 2567649375*uk_78 + 1346589450*uk_79 + 118*uk_8 + 706211356*uk_80 + 166375*uk_81 + 57475*uk_82 + 356950*uk_83 + 36300*uk_84 + 511225*uk_85 + 680625*uk_86 + 356950*uk_87 + 19855*uk_88 + 123310*uk_89 + 2572416961*uk_9 + 12540*uk_90 + 176605*uk_91 + 235125*uk_92 + 123310*uk_93 + 765820*uk_94 + 77880*uk_95 + 1096810*uk_96 + 1460250*uk_97 + 765820*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 150480*uk_100 + 198000*uk_101 + 16720*uk_102 + 1608255*uk_103 + 2116125*uk_104 + 178695*uk_105 + 2784375*uk_106 + 235125*uk_107 + 19855*uk_108 + 1092727*uk_109 + 5224057*uk_11 + 201571*uk_110 + 169744*uk_111 + 1814139*uk_112 + 2387025*uk_113 + 201571*uk_114 + 37183*uk_115 + 31312*uk_116 + 334647*uk_117 + 440325*uk_118 + 37183*uk_119 + 963661*uk_12 + 26368*uk_120 + 281808*uk_121 + 370800*uk_122 + 31312*uk_123 + 3011823*uk_124 + 3962925*uk_125 + 334647*uk_126 + 5214375*uk_127 + 440325*uk_128 + 37183*uk_129 + 811504*uk_13 + 6859*uk_130 + 5776*uk_131 + 61731*uk_132 + 81225*uk_133 + 6859*uk_134 + 4864*uk_135 + 51984*uk_136 + 68400*uk_137 + 5776*uk_138 + 555579*uk_139 + 8672949*uk_14 + 731025*uk_140 + 61731*uk_141 + 961875*uk_142 + 81225*uk_143 + 6859*uk_144 + 4096*uk_145 + 43776*uk_146 + 57600*uk_147 + 4864*uk_148 + 467856*uk_149 + 11411775*uk_15 + 615600*uk_150 + 51984*uk_151 + 810000*uk_152 + 68400*uk_153 + 5776*uk_154 + 5000211*uk_155 + 6579225*uk_156 + 555579*uk_157 + 8656875*uk_158 + 731025*uk_159 + 963661*uk_16 + 61731*uk_160 + 11390625*uk_161 + 961875*uk_162 + 81225*uk_163 + 6859*uk_164 + 3025*uk_17 + 5665*uk_18 + 1045*uk_19 + 55*uk_2 + 880*uk_20 + 9405*uk_21 + 12375*uk_22 + 1045*uk_23 + 10609*uk_24 + 1957*uk_25 + 1648*uk_26 + 17613*uk_27 + 23175*uk_28 + 1957*uk_29 + 103*uk_3 + 361*uk_30 + 304*uk_31 + 3249*uk_32 + 4275*uk_33 + 361*uk_34 + 256*uk_35 + 2736*uk_36 + 3600*uk_37 + 304*uk_38 + 29241*uk_39 + 19*uk_4 + 38475*uk_40 + 3249*uk_41 + 50625*uk_42 + 4275*uk_43 + 361*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 264958946983*uk_47 + 48875922259*uk_48 + 41158671376*uk_49 + 16*uk_5 + 439883300331*uk_50 + 578793816225*uk_51 + 48875922259*uk_52 + 153424975*uk_53 + 287323135*uk_54 + 53001355*uk_55 + 44632720*uk_56 + 477012195*uk_57 + 627647625*uk_58 + 53001355*uk_59 + 171*uk_6 + 538077871*uk_60 + 99257083*uk_61 + 83584912*uk_62 + 893313747*uk_63 + 1175412825*uk_64 + 99257083*uk_65 + 18309559*uk_66 + 15418576*uk_67 + 164786031*uk_68 + 216823725*uk_69 + 225*uk_7 + 18309559*uk_70 + 12984064*uk_71 + 138767184*uk_72 + 182588400*uk_73 + 15418576*uk_74 + 1483074279*uk_75 + 1951413525*uk_76 + 164786031*uk_77 + 2567649375*uk_78 + 216823725*uk_79 + 19*uk_8 + 18309559*uk_80 + 166375*uk_81 + 311575*uk_82 + 57475*uk_83 + 48400*uk_84 + 517275*uk_85 + 680625*uk_86 + 57475*uk_87 + 583495*uk_88 + 107635*uk_89 + 2572416961*uk_9 + 90640*uk_90 + 968715*uk_91 + 1274625*uk_92 + 107635*uk_93 + 19855*uk_94 + 16720*uk_95 + 178695*uk_96 + 235125*uk_97 + 19855*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 114180*uk_100 + 148500*uk_101 + 67980*uk_102 + 1646095*uk_103 + 2140875*uk_104 + 980045*uk_105 + 2784375*uk_106 + 1274625*uk_107 + 583495*uk_108 + 27000*uk_109 + 1521570*uk_11 + 92700*uk_110 + 10800*uk_111 + 155700*uk_112 + 202500*uk_113 + 92700*uk_114 + 318270*uk_115 + 37080*uk_116 + 534570*uk_117 + 695250*uk_118 + 318270*uk_119 + 5224057*uk_12 + 4320*uk_120 + 62280*uk_121 + 81000*uk_122 + 37080*uk_123 + 897870*uk_124 + 1167750*uk_125 + 534570*uk_126 + 1518750*uk_127 + 695250*uk_128 + 318270*uk_129 + 608628*uk_13 + 1092727*uk_130 + 127308*uk_131 + 1835357*uk_132 + 2387025*uk_133 + 1092727*uk_134 + 14832*uk_135 + 213828*uk_136 + 278100*uk_137 + 127308*uk_138 + 3082687*uk_139 + 8774387*uk_14 + 4009275*uk_140 + 1835357*uk_141 + 5214375*uk_142 + 2387025*uk_143 + 1092727*uk_144 + 1728*uk_145 + 24912*uk_146 + 32400*uk_147 + 14832*uk_148 + 359148*uk_149 + 11411775*uk_15 + 467100*uk_150 + 213828*uk_151 + 607500*uk_152 + 278100*uk_153 + 127308*uk_154 + 5177717*uk_155 + 6734025*uk_156 + 3082687*uk_157 + 8758125*uk_158 + 4009275*uk_159 + 5224057*uk_16 + 1835357*uk_160 + 11390625*uk_161 + 5214375*uk_162 + 2387025*uk_163 + 1092727*uk_164 + 3025*uk_17 + 1650*uk_18 + 5665*uk_19 + 55*uk_2 + 660*uk_20 + 9515*uk_21 + 12375*uk_22 + 5665*uk_23 + 900*uk_24 + 3090*uk_25 + 360*uk_26 + 5190*uk_27 + 6750*uk_28 + 3090*uk_29 + 30*uk_3 + 10609*uk_30 + 1236*uk_31 + 17819*uk_32 + 23175*uk_33 + 10609*uk_34 + 144*uk_35 + 2076*uk_36 + 2700*uk_37 + 1236*uk_38 + 29929*uk_39 + 103*uk_4 + 38925*uk_40 + 17819*uk_41 + 50625*uk_42 + 23175*uk_43 + 10609*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 77172508830*uk_47 + 264958946983*uk_48 + 30869003532*uk_49 + 12*uk_5 + 445028134253*uk_50 + 578793816225*uk_51 + 264958946983*uk_52 + 153424975*uk_53 + 83686350*uk_54 + 287323135*uk_55 + 33474540*uk_56 + 482591285*uk_57 + 627647625*uk_58 + 287323135*uk_59 + 173*uk_6 + 45647100*uk_60 + 156721710*uk_61 + 18258840*uk_62 + 263231610*uk_63 + 342353250*uk_64 + 156721710*uk_65 + 538077871*uk_66 + 62688684*uk_67 + 903761861*uk_68 + 1175412825*uk_69 + 225*uk_7 + 538077871*uk_70 + 7303536*uk_71 + 105292644*uk_72 + 136941300*uk_73 + 62688684*uk_74 + 1517968951*uk_75 + 1974237075*uk_76 + 903761861*uk_77 + 2567649375*uk_78 + 1175412825*uk_79 + 103*uk_8 + 538077871*uk_80 + 166375*uk_81 + 90750*uk_82 + 311575*uk_83 + 36300*uk_84 + 523325*uk_85 + 680625*uk_86 + 311575*uk_87 + 49500*uk_88 + 169950*uk_89 + 2572416961*uk_9 + 19800*uk_90 + 285450*uk_91 + 371250*uk_92 + 169950*uk_93 + 583495*uk_94 + 67980*uk_95 + 980045*uk_96 + 1274625*uk_97 + 583495*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 154000*uk_100 + 198000*uk_101 + 26400*uk_102 + 1684375*uk_103 + 2165625*uk_104 + 288750*uk_105 + 2784375*uk_106 + 371250*uk_107 + 49500*uk_108 + 2985984*uk_109 + 7303536*uk_11 + 622080*uk_110 + 331776*uk_111 + 3628800*uk_112 + 4665600*uk_113 + 622080*uk_114 + 129600*uk_115 + 69120*uk_116 + 756000*uk_117 + 972000*uk_118 + 129600*uk_119 + 1521570*uk_12 + 36864*uk_120 + 403200*uk_121 + 518400*uk_122 + 69120*uk_123 + 4410000*uk_124 + 5670000*uk_125 + 756000*uk_126 + 7290000*uk_127 + 972000*uk_128 + 129600*uk_129 + 811504*uk_13 + 27000*uk_130 + 14400*uk_131 + 157500*uk_132 + 202500*uk_133 + 27000*uk_134 + 7680*uk_135 + 84000*uk_136 + 108000*uk_137 + 14400*uk_138 + 918750*uk_139 + 8875825*uk_14 + 1181250*uk_140 + 157500*uk_141 + 1518750*uk_142 + 202500*uk_143 + 27000*uk_144 + 4096*uk_145 + 44800*uk_146 + 57600*uk_147 + 7680*uk_148 + 490000*uk_149 + 11411775*uk_15 + 630000*uk_150 + 84000*uk_151 + 810000*uk_152 + 108000*uk_153 + 14400*uk_154 + 5359375*uk_155 + 6890625*uk_156 + 918750*uk_157 + 8859375*uk_158 + 1181250*uk_159 + 1521570*uk_16 + 157500*uk_160 + 11390625*uk_161 + 1518750*uk_162 + 202500*uk_163 + 27000*uk_164 + 3025*uk_17 + 7920*uk_18 + 1650*uk_19 + 55*uk_2 + 880*uk_20 + 9625*uk_21 + 12375*uk_22 + 1650*uk_23 + 20736*uk_24 + 4320*uk_25 + 2304*uk_26 + 25200*uk_27 + 32400*uk_28 + 4320*uk_29 + 144*uk_3 + 900*uk_30 + 480*uk_31 + 5250*uk_32 + 6750*uk_33 + 900*uk_34 + 256*uk_35 + 2800*uk_36 + 3600*uk_37 + 480*uk_38 + 30625*uk_39 + 30*uk_4 + 39375*uk_40 + 5250*uk_41 + 50625*uk_42 + 6750*uk_43 + 900*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 370428042384*uk_47 + 77172508830*uk_48 + 41158671376*uk_49 + 16*uk_5 + 450172968175*uk_50 + 578793816225*uk_51 + 77172508830*uk_52 + 153424975*uk_53 + 401694480*uk_54 + 83686350*uk_55 + 44632720*uk_56 + 488170375*uk_57 + 627647625*uk_58 + 83686350*uk_59 + 175*uk_6 + 1051709184*uk_60 + 219106080*uk_61 + 116856576*uk_62 + 1278118800*uk_63 + 1643295600*uk_64 + 219106080*uk_65 + 45647100*uk_66 + 24345120*uk_67 + 266274750*uk_68 + 342353250*uk_69 + 225*uk_7 + 45647100*uk_70 + 12984064*uk_71 + 142013200*uk_72 + 182588400*uk_73 + 24345120*uk_74 + 1553269375*uk_75 + 1997060625*uk_76 + 266274750*uk_77 + 2567649375*uk_78 + 342353250*uk_79 + 30*uk_8 + 45647100*uk_80 + 166375*uk_81 + 435600*uk_82 + 90750*uk_83 + 48400*uk_84 + 529375*uk_85 + 680625*uk_86 + 90750*uk_87 + 1140480*uk_88 + 237600*uk_89 + 2572416961*uk_9 + 126720*uk_90 + 1386000*uk_91 + 1782000*uk_92 + 237600*uk_93 + 49500*uk_94 + 26400*uk_95 + 288750*uk_96 + 371250*uk_97 + 49500*uk_98 + 14080*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 116820*uk_100 + 148500*uk_101 + 95040*uk_102 + 1723095*uk_103 + 2190375*uk_104 + 1401840*uk_105 + 2784375*uk_106 + 1782000*uk_107 + 1140480*uk_108 + 912673*uk_109 + 4919743*uk_11 + 1354896*uk_110 + 112908*uk_111 + 1665393*uk_112 + 2117025*uk_113 + 1354896*uk_114 + 2011392*uk_115 + 167616*uk_116 + 2472336*uk_117 + 3142800*uk_118 + 2011392*uk_119 + 7303536*uk_12 + 13968*uk_120 + 206028*uk_121 + 261900*uk_122 + 167616*uk_123 + 3038913*uk_124 + 3863025*uk_125 + 2472336*uk_126 + 4910625*uk_127 + 3142800*uk_128 + 2011392*uk_129 + 608628*uk_13 + 2985984*uk_130 + 248832*uk_131 + 3670272*uk_132 + 4665600*uk_133 + 2985984*uk_134 + 20736*uk_135 + 305856*uk_136 + 388800*uk_137 + 248832*uk_138 + 4511376*uk_139 + 8977263*uk_14 + 5734800*uk_140 + 3670272*uk_141 + 7290000*uk_142 + 4665600*uk_143 + 2985984*uk_144 + 1728*uk_145 + 25488*uk_146 + 32400*uk_147 + 20736*uk_148 + 375948*uk_149 + 11411775*uk_15 + 477900*uk_150 + 305856*uk_151 + 607500*uk_152 + 388800*uk_153 + 248832*uk_154 + 5545233*uk_155 + 7049025*uk_156 + 4511376*uk_157 + 8960625*uk_158 + 5734800*uk_159 + 7303536*uk_16 + 3670272*uk_160 + 11390625*uk_161 + 7290000*uk_162 + 4665600*uk_163 + 2985984*uk_164 + 3025*uk_17 + 5335*uk_18 + 7920*uk_19 + 55*uk_2 + 660*uk_20 + 9735*uk_21 + 12375*uk_22 + 7920*uk_23 + 9409*uk_24 + 13968*uk_25 + 1164*uk_26 + 17169*uk_27 + 21825*uk_28 + 13968*uk_29 + 97*uk_3 + 20736*uk_30 + 1728*uk_31 + 25488*uk_32 + 32400*uk_33 + 20736*uk_34 + 144*uk_35 + 2124*uk_36 + 2700*uk_37 + 1728*uk_38 + 31329*uk_39 + 144*uk_4 + 39825*uk_40 + 25488*uk_41 + 50625*uk_42 + 32400*uk_43 + 20736*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 249524445217*uk_47 + 370428042384*uk_48 + 30869003532*uk_49 + 12*uk_5 + 455317802097*uk_50 + 578793816225*uk_51 + 370428042384*uk_52 + 153424975*uk_53 + 270585865*uk_54 + 401694480*uk_55 + 33474540*uk_56 + 493749465*uk_57 + 627647625*uk_58 + 401694480*uk_59 + 177*uk_6 + 477215071*uk_60 + 708442992*uk_61 + 59036916*uk_62 + 870794511*uk_63 + 1106942175*uk_64 + 708442992*uk_65 + 1051709184*uk_66 + 87642432*uk_67 + 1292725872*uk_68 + 1643295600*uk_69 + 225*uk_7 + 1051709184*uk_70 + 7303536*uk_71 + 107727156*uk_72 + 136941300*uk_73 + 87642432*uk_74 + 1588975551*uk_75 + 2019884175*uk_76 + 1292725872*uk_77 + 2567649375*uk_78 + 1643295600*uk_79 + 144*uk_8 + 1051709184*uk_80 + 166375*uk_81 + 293425*uk_82 + 435600*uk_83 + 36300*uk_84 + 535425*uk_85 + 680625*uk_86 + 435600*uk_87 + 517495*uk_88 + 768240*uk_89 + 2572416961*uk_9 + 64020*uk_90 + 944295*uk_91 + 1200375*uk_92 + 768240*uk_93 + 1140480*uk_94 + 95040*uk_95 + 1401840*uk_96 + 1782000*uk_97 + 1140480*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 118140*uk_100 + 148500*uk_101 + 64020*uk_102 + 1762255*uk_103 + 2215125*uk_104 + 954965*uk_105 + 2784375*uk_106 + 1200375*uk_107 + 517495*uk_108 + 238328*uk_109 + 3144578*uk_11 + 372868*uk_110 + 46128*uk_111 + 688076*uk_112 + 864900*uk_113 + 372868*uk_114 + 583358*uk_115 + 72168*uk_116 + 1076506*uk_117 + 1353150*uk_118 + 583358*uk_119 + 4919743*uk_12 + 8928*uk_120 + 133176*uk_121 + 167400*uk_122 + 72168*uk_123 + 1986542*uk_124 + 2497050*uk_125 + 1076506*uk_126 + 3138750*uk_127 + 1353150*uk_128 + 583358*uk_129 + 608628*uk_13 + 912673*uk_130 + 112908*uk_131 + 1684211*uk_132 + 2117025*uk_133 + 912673*uk_134 + 13968*uk_135 + 208356*uk_136 + 261900*uk_137 + 112908*uk_138 + 3107977*uk_139 + 9078701*uk_14 + 3906675*uk_140 + 1684211*uk_141 + 4910625*uk_142 + 2117025*uk_143 + 912673*uk_144 + 1728*uk_145 + 25776*uk_146 + 32400*uk_147 + 13968*uk_148 + 384492*uk_149 + 11411775*uk_15 + 483300*uk_150 + 208356*uk_151 + 607500*uk_152 + 261900*uk_153 + 112908*uk_154 + 5735339*uk_155 + 7209225*uk_156 + 3107977*uk_157 + 9061875*uk_158 + 3906675*uk_159 + 4919743*uk_16 + 1684211*uk_160 + 11390625*uk_161 + 4910625*uk_162 + 2117025*uk_163 + 912673*uk_164 + 3025*uk_17 + 3410*uk_18 + 5335*uk_19 + 55*uk_2 + 660*uk_20 + 9845*uk_21 + 12375*uk_22 + 5335*uk_23 + 3844*uk_24 + 6014*uk_25 + 744*uk_26 + 11098*uk_27 + 13950*uk_28 + 6014*uk_29 + 62*uk_3 + 9409*uk_30 + 1164*uk_31 + 17363*uk_32 + 21825*uk_33 + 9409*uk_34 + 144*uk_35 + 2148*uk_36 + 2700*uk_37 + 1164*uk_38 + 32041*uk_39 + 97*uk_4 + 40275*uk_40 + 17363*uk_41 + 50625*uk_42 + 21825*uk_43 + 9409*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 159489851582*uk_47 + 249524445217*uk_48 + 30869003532*uk_49 + 12*uk_5 + 460462636019*uk_50 + 578793816225*uk_51 + 249524445217*uk_52 + 153424975*uk_53 + 172951790*uk_54 + 270585865*uk_55 + 33474540*uk_56 + 499328555*uk_57 + 627647625*uk_58 + 270585865*uk_59 + 179*uk_6 + 194963836*uk_60 + 305024066*uk_61 + 37734936*uk_62 + 562879462*uk_63 + 707530050*uk_64 + 305024066*uk_65 + 477215071*uk_66 + 59036916*uk_67 + 880633997*uk_68 + 1106942175*uk_69 + 225*uk_7 + 477215071*uk_70 + 7303536*uk_71 + 108944412*uk_72 + 136941300*uk_73 + 59036916*uk_74 + 1625087479*uk_75 + 2042707725*uk_76 + 880633997*uk_77 + 2567649375*uk_78 + 1106942175*uk_79 + 97*uk_8 + 477215071*uk_80 + 166375*uk_81 + 187550*uk_82 + 293425*uk_83 + 36300*uk_84 + 541475*uk_85 + 680625*uk_86 + 293425*uk_87 + 211420*uk_88 + 330770*uk_89 + 2572416961*uk_9 + 40920*uk_90 + 610390*uk_91 + 767250*uk_92 + 330770*uk_93 + 517495*uk_94 + 64020*uk_95 + 954965*uk_96 + 1200375*uk_97 + 517495*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 119460*uk_100 + 148500*uk_101 + 40920*uk_102 + 1801855*uk_103 + 2239875*uk_104 + 617210*uk_105 + 2784375*uk_106 + 767250*uk_107 + 211420*uk_108 + 59319*uk_109 + 1978041*uk_11 + 94302*uk_110 + 18252*uk_111 + 275301*uk_112 + 342225*uk_113 + 94302*uk_114 + 149916*uk_115 + 29016*uk_116 + 437658*uk_117 + 544050*uk_118 + 149916*uk_119 + 3144578*uk_12 + 5616*uk_120 + 84708*uk_121 + 105300*uk_122 + 29016*uk_123 + 1277679*uk_124 + 1588275*uk_125 + 437658*uk_126 + 1974375*uk_127 + 544050*uk_128 + 149916*uk_129 + 608628*uk_13 + 238328*uk_130 + 46128*uk_131 + 695764*uk_132 + 864900*uk_133 + 238328*uk_134 + 8928*uk_135 + 134664*uk_136 + 167400*uk_137 + 46128*uk_138 + 2031182*uk_139 + 9180139*uk_14 + 2524950*uk_140 + 695764*uk_141 + 3138750*uk_142 + 864900*uk_143 + 238328*uk_144 + 1728*uk_145 + 26064*uk_146 + 32400*uk_147 + 8928*uk_148 + 393132*uk_149 + 11411775*uk_15 + 488700*uk_150 + 134664*uk_151 + 607500*uk_152 + 167400*uk_153 + 46128*uk_154 + 5929741*uk_155 + 7371225*uk_156 + 2031182*uk_157 + 9163125*uk_158 + 2524950*uk_159 + 3144578*uk_16 + 695764*uk_160 + 11390625*uk_161 + 3138750*uk_162 + 864900*uk_163 + 238328*uk_164 + 3025*uk_17 + 2145*uk_18 + 3410*uk_19 + 55*uk_2 + 660*uk_20 + 9955*uk_21 + 12375*uk_22 + 3410*uk_23 + 1521*uk_24 + 2418*uk_25 + 468*uk_26 + 7059*uk_27 + 8775*uk_28 + 2418*uk_29 + 39*uk_3 + 3844*uk_30 + 744*uk_31 + 11222*uk_32 + 13950*uk_33 + 3844*uk_34 + 144*uk_35 + 2172*uk_36 + 2700*uk_37 + 744*uk_38 + 32761*uk_39 + 62*uk_4 + 40725*uk_40 + 11222*uk_41 + 50625*uk_42 + 13950*uk_43 + 3844*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 100324261479*uk_47 + 159489851582*uk_48 + 30869003532*uk_49 + 12*uk_5 + 465607469941*uk_50 + 578793816225*uk_51 + 159489851582*uk_52 + 153424975*uk_53 + 108792255*uk_54 + 172951790*uk_55 + 33474540*uk_56 + 504907645*uk_57 + 627647625*uk_58 + 172951790*uk_59 + 181*uk_6 + 77143599*uk_60 + 122638542*uk_61 + 23736492*uk_62 + 358025421*uk_63 + 445059225*uk_64 + 122638542*uk_65 + 194963836*uk_66 + 37734936*uk_67 + 569168618*uk_68 + 707530050*uk_69 + 225*uk_7 + 194963836*uk_70 + 7303536*uk_71 + 110161668*uk_72 + 136941300*uk_73 + 37734936*uk_74 + 1661605159*uk_75 + 2065531275*uk_76 + 569168618*uk_77 + 2567649375*uk_78 + 707530050*uk_79 + 62*uk_8 + 194963836*uk_80 + 166375*uk_81 + 117975*uk_82 + 187550*uk_83 + 36300*uk_84 + 547525*uk_85 + 680625*uk_86 + 187550*uk_87 + 83655*uk_88 + 132990*uk_89 + 2572416961*uk_9 + 25740*uk_90 + 388245*uk_91 + 482625*uk_92 + 132990*uk_93 + 211420*uk_94 + 40920*uk_95 + 617210*uk_96 + 767250*uk_97 + 211420*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 120780*uk_100 + 148500*uk_101 + 25740*uk_102 + 1841895*uk_103 + 2264625*uk_104 + 392535*uk_105 + 2784375*uk_106 + 482625*uk_107 + 83655*uk_108 + 21952*uk_109 + 1420132*uk_11 + 30576*uk_110 + 9408*uk_111 + 143472*uk_112 + 176400*uk_113 + 30576*uk_114 + 42588*uk_115 + 13104*uk_116 + 199836*uk_117 + 245700*uk_118 + 42588*uk_119 + 1978041*uk_12 + 4032*uk_120 + 61488*uk_121 + 75600*uk_122 + 13104*uk_123 + 937692*uk_124 + 1152900*uk_125 + 199836*uk_126 + 1417500*uk_127 + 245700*uk_128 + 42588*uk_129 + 608628*uk_13 + 59319*uk_130 + 18252*uk_131 + 278343*uk_132 + 342225*uk_133 + 59319*uk_134 + 5616*uk_135 + 85644*uk_136 + 105300*uk_137 + 18252*uk_138 + 1306071*uk_139 + 9281577*uk_14 + 1605825*uk_140 + 278343*uk_141 + 1974375*uk_142 + 342225*uk_143 + 59319*uk_144 + 1728*uk_145 + 26352*uk_146 + 32400*uk_147 + 5616*uk_148 + 401868*uk_149 + 11411775*uk_15 + 494100*uk_150 + 85644*uk_151 + 607500*uk_152 + 105300*uk_153 + 18252*uk_154 + 6128487*uk_155 + 7535025*uk_156 + 1306071*uk_157 + 9264375*uk_158 + 1605825*uk_159 + 1978041*uk_16 + 278343*uk_160 + 11390625*uk_161 + 1974375*uk_162 + 342225*uk_163 + 59319*uk_164 + 3025*uk_17 + 1540*uk_18 + 2145*uk_19 + 55*uk_2 + 660*uk_20 + 10065*uk_21 + 12375*uk_22 + 2145*uk_23 + 784*uk_24 + 1092*uk_25 + 336*uk_26 + 5124*uk_27 + 6300*uk_28 + 1092*uk_29 + 28*uk_3 + 1521*uk_30 + 468*uk_31 + 7137*uk_32 + 8775*uk_33 + 1521*uk_34 + 144*uk_35 + 2196*uk_36 + 2700*uk_37 + 468*uk_38 + 33489*uk_39 + 39*uk_4 + 41175*uk_40 + 7137*uk_41 + 50625*uk_42 + 8775*uk_43 + 1521*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 72027674908*uk_47 + 100324261479*uk_48 + 30869003532*uk_49 + 12*uk_5 + 470752303863*uk_50 + 578793816225*uk_51 + 100324261479*uk_52 + 153424975*uk_53 + 78107260*uk_54 + 108792255*uk_55 + 33474540*uk_56 + 510486735*uk_57 + 627647625*uk_58 + 108792255*uk_59 + 183*uk_6 + 39763696*uk_60 + 55385148*uk_61 + 17041584*uk_62 + 259884156*uk_63 + 319529700*uk_64 + 55385148*uk_65 + 77143599*uk_66 + 23736492*uk_67 + 361981503*uk_68 + 445059225*uk_69 + 225*uk_7 + 77143599*uk_70 + 7303536*uk_71 + 111378924*uk_72 + 136941300*uk_73 + 23736492*uk_74 + 1698528591*uk_75 + 2088354825*uk_76 + 361981503*uk_77 + 2567649375*uk_78 + 445059225*uk_79 + 39*uk_8 + 77143599*uk_80 + 166375*uk_81 + 84700*uk_82 + 117975*uk_83 + 36300*uk_84 + 553575*uk_85 + 680625*uk_86 + 117975*uk_87 + 43120*uk_88 + 60060*uk_89 + 2572416961*uk_9 + 18480*uk_90 + 281820*uk_91 + 346500*uk_92 + 60060*uk_93 + 83655*uk_94 + 25740*uk_95 + 392535*uk_96 + 482625*uk_97 + 83655*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 123420*uk_100 + 148500*uk_101 + 19140*uk_102 + 1923295*uk_103 + 2314125*uk_104 + 298265*uk_105 + 2784375*uk_106 + 358875*uk_107 + 46255*uk_108 + 74088*uk_109 + 2130198*uk_11 + 51156*uk_110 + 21168*uk_111 + 329868*uk_112 + 396900*uk_113 + 51156*uk_114 + 35322*uk_115 + 14616*uk_116 + 227766*uk_117 + 274050*uk_118 + 35322*uk_119 + 1470851*uk_12 + 6048*uk_120 + 94248*uk_121 + 113400*uk_122 + 14616*uk_123 + 1468698*uk_124 + 1767150*uk_125 + 227766*uk_126 + 2126250*uk_127 + 274050*uk_128 + 35322*uk_129 + 608628*uk_13 + 24389*uk_130 + 10092*uk_131 + 157267*uk_132 + 189225*uk_133 + 24389*uk_134 + 4176*uk_135 + 65076*uk_136 + 78300*uk_137 + 10092*uk_138 + 1014101*uk_139 + 9484453*uk_14 + 1220175*uk_140 + 157267*uk_141 + 1468125*uk_142 + 189225*uk_143 + 24389*uk_144 + 1728*uk_145 + 26928*uk_146 + 32400*uk_147 + 4176*uk_148 + 419628*uk_149 + 11411775*uk_15 + 504900*uk_150 + 65076*uk_151 + 607500*uk_152 + 78300*uk_153 + 10092*uk_154 + 6539203*uk_155 + 7868025*uk_156 + 1014101*uk_157 + 9466875*uk_158 + 1220175*uk_159 + 1470851*uk_16 + 157267*uk_160 + 11390625*uk_161 + 1468125*uk_162 + 189225*uk_163 + 24389*uk_164 + 3025*uk_17 + 2310*uk_18 + 1595*uk_19 + 55*uk_2 + 660*uk_20 + 10285*uk_21 + 12375*uk_22 + 1595*uk_23 + 1764*uk_24 + 1218*uk_25 + 504*uk_26 + 7854*uk_27 + 9450*uk_28 + 1218*uk_29 + 42*uk_3 + 841*uk_30 + 348*uk_31 + 5423*uk_32 + 6525*uk_33 + 841*uk_34 + 144*uk_35 + 2244*uk_36 + 2700*uk_37 + 348*uk_38 + 34969*uk_39 + 29*uk_4 + 42075*uk_40 + 5423*uk_41 + 50625*uk_42 + 6525*uk_43 + 841*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 108041512362*uk_47 + 74600091869*uk_48 + 30869003532*uk_49 + 12*uk_5 + 481041971707*uk_50 + 578793816225*uk_51 + 74600091869*uk_52 + 153424975*uk_53 + 117160890*uk_54 + 80896805*uk_55 + 33474540*uk_56 + 521644915*uk_57 + 627647625*uk_58 + 80896805*uk_59 + 187*uk_6 + 89468316*uk_60 + 61775742*uk_61 + 25562376*uk_62 + 398347026*uk_63 + 479294550*uk_64 + 61775742*uk_65 + 42654679*uk_66 + 17650212*uk_67 + 275049137*uk_68 + 330941475*uk_69 + 225*uk_7 + 42654679*uk_70 + 7303536*uk_71 + 113813436*uk_72 + 136941300*uk_73 + 17650212*uk_74 + 1773592711*uk_75 + 2134001925*uk_76 + 275049137*uk_77 + 2567649375*uk_78 + 330941475*uk_79 + 29*uk_8 + 42654679*uk_80 + 166375*uk_81 + 127050*uk_82 + 87725*uk_83 + 36300*uk_84 + 565675*uk_85 + 680625*uk_86 + 87725*uk_87 + 97020*uk_88 + 66990*uk_89 + 2572416961*uk_9 + 27720*uk_90 + 431970*uk_91 + 519750*uk_92 + 66990*uk_93 + 46255*uk_94 + 19140*uk_95 + 298265*uk_96 + 358875*uk_97 + 46255*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 124740*uk_100 + 148500*uk_101 + 27720*uk_102 + 1964655*uk_103 + 2338875*uk_104 + 436590*uk_105 + 2784375*uk_106 + 519750*uk_107 + 97020*uk_108 + 300763*uk_109 + 3398173*uk_11 + 188538*uk_110 + 53868*uk_111 + 848421*uk_112 + 1010025*uk_113 + 188538*uk_114 + 118188*uk_115 + 33768*uk_116 + 531846*uk_117 + 633150*uk_118 + 118188*uk_119 + 2130198*uk_12 + 9648*uk_120 + 151956*uk_121 + 180900*uk_122 + 33768*uk_123 + 2393307*uk_124 + 2849175*uk_125 + 531846*uk_126 + 3391875*uk_127 + 633150*uk_128 + 118188*uk_129 + 608628*uk_13 + 74088*uk_130 + 21168*uk_131 + 333396*uk_132 + 396900*uk_133 + 74088*uk_134 + 6048*uk_135 + 95256*uk_136 + 113400*uk_137 + 21168*uk_138 + 1500282*uk_139 + 9585891*uk_14 + 1786050*uk_140 + 333396*uk_141 + 2126250*uk_142 + 396900*uk_143 + 74088*uk_144 + 1728*uk_145 + 27216*uk_146 + 32400*uk_147 + 6048*uk_148 + 428652*uk_149 + 11411775*uk_15 + 510300*uk_150 + 95256*uk_151 + 607500*uk_152 + 113400*uk_153 + 21168*uk_154 + 6751269*uk_155 + 8037225*uk_156 + 1500282*uk_157 + 9568125*uk_158 + 1786050*uk_159 + 2130198*uk_16 + 333396*uk_160 + 11390625*uk_161 + 2126250*uk_162 + 396900*uk_163 + 74088*uk_164 + 3025*uk_17 + 3685*uk_18 + 2310*uk_19 + 55*uk_2 + 660*uk_20 + 10395*uk_21 + 12375*uk_22 + 2310*uk_23 + 4489*uk_24 + 2814*uk_25 + 804*uk_26 + 12663*uk_27 + 15075*uk_28 + 2814*uk_29 + 67*uk_3 + 1764*uk_30 + 504*uk_31 + 7938*uk_32 + 9450*uk_33 + 1764*uk_34 + 144*uk_35 + 2268*uk_36 + 2700*uk_37 + 504*uk_38 + 35721*uk_39 + 42*uk_4 + 42525*uk_40 + 7938*uk_41 + 50625*uk_42 + 9450*uk_43 + 1764*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 172351936387*uk_47 + 108041512362*uk_48 + 30869003532*uk_49 + 12*uk_5 + 486186805629*uk_50 + 578793816225*uk_51 + 108041512362*uk_52 + 153424975*uk_53 + 186899515*uk_54 + 117160890*uk_55 + 33474540*uk_56 + 527224005*uk_57 + 627647625*uk_58 + 117160890*uk_59 + 189*uk_6 + 227677591*uk_60 + 142723266*uk_61 + 40778076*uk_62 + 642254697*uk_63 + 764588925*uk_64 + 142723266*uk_65 + 89468316*uk_66 + 25562376*uk_67 + 402607422*uk_68 + 479294550*uk_69 + 225*uk_7 + 89468316*uk_70 + 7303536*uk_71 + 115030692*uk_72 + 136941300*uk_73 + 25562376*uk_74 + 1811733399*uk_75 + 2156825475*uk_76 + 402607422*uk_77 + 2567649375*uk_78 + 479294550*uk_79 + 42*uk_8 + 89468316*uk_80 + 166375*uk_81 + 202675*uk_82 + 127050*uk_83 + 36300*uk_84 + 571725*uk_85 + 680625*uk_86 + 127050*uk_87 + 246895*uk_88 + 154770*uk_89 + 2572416961*uk_9 + 44220*uk_90 + 696465*uk_91 + 829125*uk_92 + 154770*uk_93 + 97020*uk_94 + 27720*uk_95 + 436590*uk_96 + 519750*uk_97 + 97020*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 126060*uk_100 + 148500*uk_101 + 44220*uk_102 + 2006455*uk_103 + 2363625*uk_104 + 703835*uk_105 + 2784375*uk_106 + 829125*uk_107 + 246895*uk_108 + 1124864*uk_109 + 5274776*uk_11 + 724672*uk_110 + 129792*uk_111 + 2065856*uk_112 + 2433600*uk_113 + 724672*uk_114 + 466856*uk_115 + 83616*uk_116 + 1330888*uk_117 + 1567800*uk_118 + 466856*uk_119 + 3398173*uk_12 + 14976*uk_120 + 238368*uk_121 + 280800*uk_122 + 83616*uk_123 + 3794024*uk_124 + 4469400*uk_125 + 1330888*uk_126 + 5265000*uk_127 + 1567800*uk_128 + 466856*uk_129 + 608628*uk_13 + 300763*uk_130 + 53868*uk_131 + 857399*uk_132 + 1010025*uk_133 + 300763*uk_134 + 9648*uk_135 + 153564*uk_136 + 180900*uk_137 + 53868*uk_138 + 2444227*uk_139 + 9687329*uk_14 + 2879325*uk_140 + 857399*uk_141 + 3391875*uk_142 + 1010025*uk_143 + 300763*uk_144 + 1728*uk_145 + 27504*uk_146 + 32400*uk_147 + 9648*uk_148 + 437772*uk_149 + 11411775*uk_15 + 515700*uk_150 + 153564*uk_151 + 607500*uk_152 + 180900*uk_153 + 53868*uk_154 + 6967871*uk_155 + 8208225*uk_156 + 2444227*uk_157 + 9669375*uk_158 + 2879325*uk_159 + 3398173*uk_16 + 857399*uk_160 + 11390625*uk_161 + 3391875*uk_162 + 1010025*uk_163 + 300763*uk_164 + 3025*uk_17 + 5720*uk_18 + 3685*uk_19 + 55*uk_2 + 660*uk_20 + 10505*uk_21 + 12375*uk_22 + 3685*uk_23 + 10816*uk_24 + 6968*uk_25 + 1248*uk_26 + 19864*uk_27 + 23400*uk_28 + 6968*uk_29 + 104*uk_3 + 4489*uk_30 + 804*uk_31 + 12797*uk_32 + 15075*uk_33 + 4489*uk_34 + 144*uk_35 + 2292*uk_36 + 2700*uk_37 + 804*uk_38 + 36481*uk_39 + 67*uk_4 + 42975*uk_40 + 12797*uk_41 + 50625*uk_42 + 15075*uk_43 + 4489*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 267531363944*uk_47 + 172351936387*uk_48 + 30869003532*uk_49 + 12*uk_5 + 491331639551*uk_50 + 578793816225*uk_51 + 172351936387*uk_52 + 153424975*uk_53 + 290112680*uk_54 + 186899515*uk_55 + 33474540*uk_56 + 532803095*uk_57 + 627647625*uk_58 + 186899515*uk_59 + 191*uk_6 + 548576704*uk_60 + 353409992*uk_61 + 63297312*uk_62 + 1007482216*uk_63 + 1186824600*uk_64 + 353409992*uk_65 + 227677591*uk_66 + 40778076*uk_67 + 649051043*uk_68 + 764588925*uk_69 + 225*uk_7 + 227677591*uk_70 + 7303536*uk_71 + 116247948*uk_72 + 136941300*uk_73 + 40778076*uk_74 + 1850279839*uk_75 + 2179649025*uk_76 + 649051043*uk_77 + 2567649375*uk_78 + 764588925*uk_79 + 67*uk_8 + 227677591*uk_80 + 166375*uk_81 + 314600*uk_82 + 202675*uk_83 + 36300*uk_84 + 577775*uk_85 + 680625*uk_86 + 202675*uk_87 + 594880*uk_88 + 383240*uk_89 + 2572416961*uk_9 + 68640*uk_90 + 1092520*uk_91 + 1287000*uk_92 + 383240*uk_93 + 246895*uk_94 + 44220*uk_95 + 703835*uk_96 + 829125*uk_97 + 246895*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 131340*uk_100 + 148500*uk_101 + 59400*uk_102 + 2178055*uk_103 + 2462625*uk_104 + 985050*uk_105 + 2784375*uk_106 + 1113750*uk_107 + 445500*uk_108 + 5177717*uk_109 + 8774387*uk_11 + 2693610*uk_110 + 359148*uk_111 + 5955871*uk_112 + 6734025*uk_113 + 2693610*uk_114 + 1401300*uk_115 + 186840*uk_116 + 3098430*uk_117 + 3503250*uk_118 + 1401300*uk_119 + 4564710*uk_12 + 24912*uk_120 + 413124*uk_121 + 467100*uk_122 + 186840*uk_123 + 6850973*uk_124 + 7746075*uk_125 + 3098430*uk_126 + 8758125*uk_127 + 3503250*uk_128 + 1401300*uk_129 + 608628*uk_13 + 729000*uk_130 + 97200*uk_131 + 1611900*uk_132 + 1822500*uk_133 + 729000*uk_134 + 12960*uk_135 + 214920*uk_136 + 243000*uk_137 + 97200*uk_138 + 3564090*uk_139 + 10093081*uk_14 + 4029750*uk_140 + 1611900*uk_141 + 4556250*uk_142 + 1822500*uk_143 + 729000*uk_144 + 1728*uk_145 + 28656*uk_146 + 32400*uk_147 + 12960*uk_148 + 475212*uk_149 + 11411775*uk_15 + 537300*uk_150 + 214920*uk_151 + 607500*uk_152 + 243000*uk_153 + 97200*uk_154 + 7880599*uk_155 + 8910225*uk_156 + 3564090*uk_157 + 10074375*uk_158 + 4029750*uk_159 + 4564710*uk_16 + 1611900*uk_160 + 11390625*uk_161 + 4556250*uk_162 + 1822500*uk_163 + 729000*uk_164 + 3025*uk_17 + 9515*uk_18 + 4950*uk_19 + 55*uk_2 + 660*uk_20 + 10945*uk_21 + 12375*uk_22 + 4950*uk_23 + 29929*uk_24 + 15570*uk_25 + 2076*uk_26 + 34427*uk_27 + 38925*uk_28 + 15570*uk_29 + 173*uk_3 + 8100*uk_30 + 1080*uk_31 + 17910*uk_32 + 20250*uk_33 + 8100*uk_34 + 144*uk_35 + 2388*uk_36 + 2700*uk_37 + 1080*uk_38 + 39601*uk_39 + 90*uk_4 + 44775*uk_40 + 17910*uk_41 + 50625*uk_42 + 20250*uk_43 + 8100*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 445028134253*uk_47 + 231517526490*uk_48 + 30869003532*uk_49 + 12*uk_5 + 511910975239*uk_50 + 578793816225*uk_51 + 231517526490*uk_52 + 153424975*uk_53 + 482591285*uk_54 + 251059050*uk_55 + 33474540*uk_56 + 555119455*uk_57 + 627647625*uk_58 + 251059050*uk_59 + 199*uk_6 + 1517968951*uk_60 + 789694830*uk_61 + 105292644*uk_62 + 1746103013*uk_63 + 1974237075*uk_64 + 789694830*uk_65 + 410823900*uk_66 + 54776520*uk_67 + 908377290*uk_68 + 1027059750*uk_69 + 225*uk_7 + 410823900*uk_70 + 7303536*uk_71 + 121116972*uk_72 + 136941300*uk_73 + 54776520*uk_74 + 2008523119*uk_75 + 2270943225*uk_76 + 908377290*uk_77 + 2567649375*uk_78 + 1027059750*uk_79 + 90*uk_8 + 410823900*uk_80 + 166375*uk_81 + 523325*uk_82 + 272250*uk_83 + 36300*uk_84 + 601975*uk_85 + 680625*uk_86 + 272250*uk_87 + 1646095*uk_88 + 856350*uk_89 + 2572416961*uk_9 + 114180*uk_90 + 1893485*uk_91 + 2140875*uk_92 + 856350*uk_93 + 445500*uk_94 + 59400*uk_95 + 985050*uk_96 + 1113750*uk_97 + 445500*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 88440*uk_100 + 99000*uk_101 + 76120*uk_102 + 2222055*uk_103 + 2487375*uk_104 + 1912515*uk_105 + 2784375*uk_106 + 2140875*uk_107 + 1646095*uk_108 + 300763*uk_109 + 3398173*uk_11 + 776597*uk_110 + 35912*uk_111 + 902289*uk_112 + 1010025*uk_113 + 776597*uk_114 + 2005243*uk_115 + 92728*uk_116 + 2329791*uk_117 + 2607975*uk_118 + 2005243*uk_119 + 8774387*uk_12 + 4288*uk_120 + 107736*uk_121 + 120600*uk_122 + 92728*uk_123 + 2706867*uk_124 + 3030075*uk_125 + 2329791*uk_126 + 3391875*uk_127 + 2607975*uk_128 + 2005243*uk_129 + 405752*uk_13 + 5177717*uk_130 + 239432*uk_131 + 6015729*uk_132 + 6734025*uk_133 + 5177717*uk_134 + 11072*uk_135 + 278184*uk_136 + 311400*uk_137 + 239432*uk_138 + 6989373*uk_139 + 10194519*uk_14 + 7823925*uk_140 + 6015729*uk_141 + 8758125*uk_142 + 6734025*uk_143 + 5177717*uk_144 + 512*uk_145 + 12864*uk_146 + 14400*uk_147 + 11072*uk_148 + 323208*uk_149 + 11411775*uk_15 + 361800*uk_150 + 278184*uk_151 + 405000*uk_152 + 311400*uk_153 + 239432*uk_154 + 8120601*uk_155 + 9090225*uk_156 + 6989373*uk_157 + 10175625*uk_158 + 7823925*uk_159 + 8774387*uk_16 + 6015729*uk_160 + 11390625*uk_161 + 8758125*uk_162 + 6734025*uk_163 + 5177717*uk_164 + 3025*uk_17 + 3685*uk_18 + 9515*uk_19 + 55*uk_2 + 440*uk_20 + 11055*uk_21 + 12375*uk_22 + 9515*uk_23 + 4489*uk_24 + 11591*uk_25 + 536*uk_26 + 13467*uk_27 + 15075*uk_28 + 11591*uk_29 + 67*uk_3 + 29929*uk_30 + 1384*uk_31 + 34773*uk_32 + 38925*uk_33 + 29929*uk_34 + 64*uk_35 + 1608*uk_36 + 1800*uk_37 + 1384*uk_38 + 40401*uk_39 + 173*uk_4 + 45225*uk_40 + 34773*uk_41 + 50625*uk_42 + 38925*uk_43 + 29929*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 172351936387*uk_47 + 445028134253*uk_48 + 20579335688*uk_49 + 8*uk_5 + 517055809161*uk_50 + 578793816225*uk_51 + 445028134253*uk_52 + 153424975*uk_53 + 186899515*uk_54 + 482591285*uk_55 + 22316360*uk_56 + 560698545*uk_57 + 627647625*uk_58 + 482591285*uk_59 + 201*uk_6 + 227677591*uk_60 + 587883929*uk_61 + 27185384*uk_62 + 683032773*uk_63 + 764588925*uk_64 + 587883929*uk_65 + 1517968951*uk_66 + 70195096*uk_67 + 1763651787*uk_68 + 1974237075*uk_69 + 225*uk_7 + 1517968951*uk_70 + 3246016*uk_71 + 81556152*uk_72 + 91294200*uk_73 + 70195096*uk_74 + 2049098319*uk_75 + 2293766775*uk_76 + 1763651787*uk_77 + 2567649375*uk_78 + 1974237075*uk_79 + 173*uk_8 + 1517968951*uk_80 + 166375*uk_81 + 202675*uk_82 + 523325*uk_83 + 24200*uk_84 + 608025*uk_85 + 680625*uk_86 + 523325*uk_87 + 246895*uk_88 + 637505*uk_89 + 2572416961*uk_9 + 29480*uk_90 + 740685*uk_91 + 829125*uk_92 + 637505*uk_93 + 1646095*uk_94 + 76120*uk_95 + 1912515*uk_96 + 2140875*uk_97 + 1646095*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 133980*uk_100 + 148500*uk_101 + 44220*uk_102 + 2266495*uk_103 + 2512125*uk_104 + 748055*uk_105 + 2784375*uk_106 + 829125*uk_107 + 246895*uk_108 + 5088448*uk_109 + 8723668*uk_11 + 1982128*uk_110 + 355008*uk_111 + 6005552*uk_112 + 6656400*uk_113 + 1982128*uk_114 + 772108*uk_115 + 138288*uk_116 + 2339372*uk_117 + 2592900*uk_118 + 772108*uk_119 + 3398173*uk_12 + 24768*uk_120 + 418992*uk_121 + 464400*uk_122 + 138288*uk_123 + 7087948*uk_124 + 7856100*uk_125 + 2339372*uk_126 + 8707500*uk_127 + 2592900*uk_128 + 772108*uk_129 + 608628*uk_13 + 300763*uk_130 + 53868*uk_131 + 911267*uk_132 + 1010025*uk_133 + 300763*uk_134 + 9648*uk_135 + 163212*uk_136 + 180900*uk_137 + 53868*uk_138 + 2761003*uk_139 + 10295957*uk_14 + 3060225*uk_140 + 911267*uk_141 + 3391875*uk_142 + 1010025*uk_143 + 300763*uk_144 + 1728*uk_145 + 29232*uk_146 + 32400*uk_147 + 9648*uk_148 + 494508*uk_149 + 11411775*uk_15 + 548100*uk_150 + 163212*uk_151 + 607500*uk_152 + 180900*uk_153 + 53868*uk_154 + 8365427*uk_155 + 9272025*uk_156 + 2761003*uk_157 + 10276875*uk_158 + 3060225*uk_159 + 3398173*uk_16 + 911267*uk_160 + 11390625*uk_161 + 3391875*uk_162 + 1010025*uk_163 + 300763*uk_164 + 3025*uk_17 + 9460*uk_18 + 3685*uk_19 + 55*uk_2 + 660*uk_20 + 11165*uk_21 + 12375*uk_22 + 3685*uk_23 + 29584*uk_24 + 11524*uk_25 + 2064*uk_26 + 34916*uk_27 + 38700*uk_28 + 11524*uk_29 + 172*uk_3 + 4489*uk_30 + 804*uk_31 + 13601*uk_32 + 15075*uk_33 + 4489*uk_34 + 144*uk_35 + 2436*uk_36 + 2700*uk_37 + 804*uk_38 + 41209*uk_39 + 67*uk_4 + 45675*uk_40 + 13601*uk_41 + 50625*uk_42 + 15075*uk_43 + 4489*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 442455717292*uk_47 + 172351936387*uk_48 + 30869003532*uk_49 + 12*uk_5 + 522200643083*uk_50 + 578793816225*uk_51 + 172351936387*uk_52 + 153424975*uk_53 + 479801740*uk_54 + 186899515*uk_55 + 33474540*uk_56 + 566277635*uk_57 + 627647625*uk_58 + 186899515*uk_59 + 203*uk_6 + 1500470896*uk_60 + 584485756*uk_61 + 104684016*uk_62 + 1770904604*uk_63 + 1962825300*uk_64 + 584485756*uk_65 + 227677591*uk_66 + 40778076*uk_67 + 689829119*uk_68 + 764588925*uk_69 + 225*uk_7 + 227677591*uk_70 + 7303536*uk_71 + 123551484*uk_72 + 136941300*uk_73 + 40778076*uk_74 + 2090079271*uk_75 + 2316590325*uk_76 + 689829119*uk_77 + 2567649375*uk_78 + 764588925*uk_79 + 67*uk_8 + 227677591*uk_80 + 166375*uk_81 + 520300*uk_82 + 202675*uk_83 + 36300*uk_84 + 614075*uk_85 + 680625*uk_86 + 202675*uk_87 + 1627120*uk_88 + 633820*uk_89 + 2572416961*uk_9 + 113520*uk_90 + 1920380*uk_91 + 2128500*uk_92 + 633820*uk_93 + 246895*uk_94 + 44220*uk_95 + 748055*uk_96 + 829125*uk_97 + 246895*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 90200*uk_100 + 99000*uk_101 + 75680*uk_102 + 2311375*uk_103 + 2536875*uk_104 + 1939300*uk_105 + 2784375*uk_106 + 2128500*uk_107 + 1627120*uk_108 + 592704*uk_109 + 4260396*uk_11 + 1213632*uk_110 + 56448*uk_111 + 1446480*uk_112 + 1587600*uk_113 + 1213632*uk_114 + 2485056*uk_115 + 115584*uk_116 + 2961840*uk_117 + 3250800*uk_118 + 2485056*uk_119 + 8723668*uk_12 + 5376*uk_120 + 137760*uk_121 + 151200*uk_122 + 115584*uk_123 + 3530100*uk_124 + 3874500*uk_125 + 2961840*uk_126 + 4252500*uk_127 + 3250800*uk_128 + 2485056*uk_129 + 405752*uk_13 + 5088448*uk_130 + 236672*uk_131 + 6064720*uk_132 + 6656400*uk_133 + 5088448*uk_134 + 11008*uk_135 + 282080*uk_136 + 309600*uk_137 + 236672*uk_138 + 7228300*uk_139 + 10397395*uk_14 + 7933500*uk_140 + 6064720*uk_141 + 8707500*uk_142 + 6656400*uk_143 + 5088448*uk_144 + 512*uk_145 + 13120*uk_146 + 14400*uk_147 + 11008*uk_148 + 336200*uk_149 + 11411775*uk_15 + 369000*uk_150 + 282080*uk_151 + 405000*uk_152 + 309600*uk_153 + 236672*uk_154 + 8615125*uk_155 + 9455625*uk_156 + 7228300*uk_157 + 10378125*uk_158 + 7933500*uk_159 + 8723668*uk_16 + 6064720*uk_160 + 11390625*uk_161 + 8707500*uk_162 + 6656400*uk_163 + 5088448*uk_164 + 3025*uk_17 + 4620*uk_18 + 9460*uk_19 + 55*uk_2 + 440*uk_20 + 11275*uk_21 + 12375*uk_22 + 9460*uk_23 + 7056*uk_24 + 14448*uk_25 + 672*uk_26 + 17220*uk_27 + 18900*uk_28 + 14448*uk_29 + 84*uk_3 + 29584*uk_30 + 1376*uk_31 + 35260*uk_32 + 38700*uk_33 + 29584*uk_34 + 64*uk_35 + 1640*uk_36 + 1800*uk_37 + 1376*uk_38 + 42025*uk_39 + 172*uk_4 + 46125*uk_40 + 35260*uk_41 + 50625*uk_42 + 38700*uk_43 + 29584*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 216083024724*uk_47 + 442455717292*uk_48 + 20579335688*uk_49 + 8*uk_5 + 527345477005*uk_50 + 578793816225*uk_51 + 442455717292*uk_52 + 153424975*uk_53 + 234321780*uk_54 + 479801740*uk_55 + 22316360*uk_56 + 571856725*uk_57 + 627647625*uk_58 + 479801740*uk_59 + 205*uk_6 + 357873264*uk_60 + 732788112*uk_61 + 34083168*uk_62 + 873381180*uk_63 + 958589100*uk_64 + 732788112*uk_65 + 1500470896*uk_66 + 69789344*uk_67 + 1788351940*uk_68 + 1962825300*uk_69 + 225*uk_7 + 1500470896*uk_70 + 3246016*uk_71 + 83179160*uk_72 + 91294200*uk_73 + 69789344*uk_74 + 2131465975*uk_75 + 2339413875*uk_76 + 1788351940*uk_77 + 2567649375*uk_78 + 1962825300*uk_79 + 172*uk_8 + 1500470896*uk_80 + 166375*uk_81 + 254100*uk_82 + 520300*uk_83 + 24200*uk_84 + 620125*uk_85 + 680625*uk_86 + 520300*uk_87 + 388080*uk_88 + 794640*uk_89 + 2572416961*uk_9 + 36960*uk_90 + 947100*uk_91 + 1039500*uk_92 + 794640*uk_93 + 1627120*uk_94 + 75680*uk_95 + 1939300*uk_96 + 2128500*uk_97 + 1627120*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 91080*uk_100 + 99000*uk_101 + 36960*uk_102 + 2356695*uk_103 + 2561625*uk_104 + 956340*uk_105 + 2784375*uk_106 + 1039500*uk_107 + 388080*uk_108 + 64*uk_109 + 202876*uk_11 + 1344*uk_110 + 128*uk_111 + 3312*uk_112 + 3600*uk_113 + 1344*uk_114 + 28224*uk_115 + 2688*uk_116 + 69552*uk_117 + 75600*uk_118 + 28224*uk_119 + 4260396*uk_12 + 256*uk_120 + 6624*uk_121 + 7200*uk_122 + 2688*uk_123 + 171396*uk_124 + 186300*uk_125 + 69552*uk_126 + 202500*uk_127 + 75600*uk_128 + 28224*uk_129 + 405752*uk_13 + 592704*uk_130 + 56448*uk_131 + 1460592*uk_132 + 1587600*uk_133 + 592704*uk_134 + 5376*uk_135 + 139104*uk_136 + 151200*uk_137 + 56448*uk_138 + 3599316*uk_139 + 10498833*uk_14 + 3912300*uk_140 + 1460592*uk_141 + 4252500*uk_142 + 1587600*uk_143 + 592704*uk_144 + 512*uk_145 + 13248*uk_146 + 14400*uk_147 + 5376*uk_148 + 342792*uk_149 + 11411775*uk_15 + 372600*uk_150 + 139104*uk_151 + 405000*uk_152 + 151200*uk_153 + 56448*uk_154 + 8869743*uk_155 + 9641025*uk_156 + 3599316*uk_157 + 10479375*uk_158 + 3912300*uk_159 + 4260396*uk_16 + 1460592*uk_160 + 11390625*uk_161 + 4252500*uk_162 + 1587600*uk_163 + 592704*uk_164 + 3025*uk_17 + 220*uk_18 + 4620*uk_19 + 55*uk_2 + 440*uk_20 + 11385*uk_21 + 12375*uk_22 + 4620*uk_23 + 16*uk_24 + 336*uk_25 + 32*uk_26 + 828*uk_27 + 900*uk_28 + 336*uk_29 + 4*uk_3 + 7056*uk_30 + 672*uk_31 + 17388*uk_32 + 18900*uk_33 + 7056*uk_34 + 64*uk_35 + 1656*uk_36 + 1800*uk_37 + 672*uk_38 + 42849*uk_39 + 84*uk_4 + 46575*uk_40 + 17388*uk_41 + 50625*uk_42 + 18900*uk_43 + 7056*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 10289667844*uk_47 + 216083024724*uk_48 + 20579335688*uk_49 + 8*uk_5 + 532490310927*uk_50 + 578793816225*uk_51 + 216083024724*uk_52 + 153424975*uk_53 + 11158180*uk_54 + 234321780*uk_55 + 22316360*uk_56 + 577435815*uk_57 + 627647625*uk_58 + 234321780*uk_59 + 207*uk_6 + 811504*uk_60 + 17041584*uk_61 + 1623008*uk_62 + 41995332*uk_63 + 45647100*uk_64 + 17041584*uk_65 + 357873264*uk_66 + 34083168*uk_67 + 881901972*uk_68 + 958589100*uk_69 + 225*uk_7 + 357873264*uk_70 + 3246016*uk_71 + 83990664*uk_72 + 91294200*uk_73 + 34083168*uk_74 + 2173258431*uk_75 + 2362237425*uk_76 + 881901972*uk_77 + 2567649375*uk_78 + 958589100*uk_79 + 84*uk_8 + 357873264*uk_80 + 166375*uk_81 + 12100*uk_82 + 254100*uk_83 + 24200*uk_84 + 626175*uk_85 + 680625*uk_86 + 254100*uk_87 + 880*uk_88 + 18480*uk_89 + 2572416961*uk_9 + 1760*uk_90 + 45540*uk_91 + 49500*uk_92 + 18480*uk_93 + 388080*uk_94 + 36960*uk_95 + 956340*uk_96 + 1039500*uk_97 + 388080*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 92840*uk_100 + 99000*uk_101 + 62040*uk_102 + 2448655*uk_103 + 2611125*uk_104 + 1636305*uk_105 + 2784375*uk_106 + 1744875*uk_107 + 1093455*uk_108 + 493039*uk_109 + 4006801*uk_11 + 879981*uk_110 + 49928*uk_111 + 1316851*uk_112 + 1404225*uk_113 + 879981*uk_114 + 1570599*uk_115 + 89112*uk_116 + 2350329*uk_117 + 2506275*uk_118 + 1570599*uk_119 + 7151379*uk_12 + 5056*uk_120 + 133352*uk_121 + 142200*uk_122 + 89112*uk_123 + 3517159*uk_124 + 3750525*uk_125 + 2350329*uk_126 + 3999375*uk_127 + 2506275*uk_128 + 1570599*uk_129 + 405752*uk_13 + 2803221*uk_130 + 159048*uk_131 + 4194891*uk_132 + 4473225*uk_133 + 2803221*uk_134 + 9024*uk_135 + 238008*uk_136 + 253800*uk_137 + 159048*uk_138 + 6277461*uk_139 + 10701709*uk_14 + 6693975*uk_140 + 4194891*uk_141 + 7138125*uk_142 + 4473225*uk_143 + 2803221*uk_144 + 512*uk_145 + 13504*uk_146 + 14400*uk_147 + 9024*uk_148 + 356168*uk_149 + 11411775*uk_15 + 379800*uk_150 + 238008*uk_151 + 405000*uk_152 + 253800*uk_153 + 159048*uk_154 + 9393931*uk_155 + 10017225*uk_156 + 6277461*uk_157 + 10681875*uk_158 + 6693975*uk_159 + 7151379*uk_16 + 4194891*uk_160 + 11390625*uk_161 + 7138125*uk_162 + 4473225*uk_163 + 2803221*uk_164 + 3025*uk_17 + 4345*uk_18 + 7755*uk_19 + 55*uk_2 + 440*uk_20 + 11605*uk_21 + 12375*uk_22 + 7755*uk_23 + 6241*uk_24 + 11139*uk_25 + 632*uk_26 + 16669*uk_27 + 17775*uk_28 + 11139*uk_29 + 79*uk_3 + 19881*uk_30 + 1128*uk_31 + 29751*uk_32 + 31725*uk_33 + 19881*uk_34 + 64*uk_35 + 1688*uk_36 + 1800*uk_37 + 1128*uk_38 + 44521*uk_39 + 141*uk_4 + 47475*uk_40 + 29751*uk_41 + 50625*uk_42 + 31725*uk_43 + 19881*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 203220939919*uk_47 + 362710791501*uk_48 + 20579335688*uk_49 + 8*uk_5 + 542779978771*uk_50 + 578793816225*uk_51 + 362710791501*uk_52 + 153424975*uk_53 + 220374055*uk_54 + 393325845*uk_55 + 22316360*uk_56 + 588593995*uk_57 + 627647625*uk_58 + 393325845*uk_59 + 211*uk_6 + 316537279*uk_60 + 564958941*uk_61 + 32054408*uk_62 + 845435011*uk_63 + 901530225*uk_64 + 564958941*uk_65 + 1008344439*uk_66 + 57211032*uk_67 + 1508940969*uk_68 + 1609060275*uk_69 + 225*uk_7 + 1008344439*uk_70 + 3246016*uk_71 + 85613672*uk_72 + 91294200*uk_73 + 57211032*uk_74 + 2258060599*uk_75 + 2407884525*uk_76 + 1508940969*uk_77 + 2567649375*uk_78 + 1609060275*uk_79 + 141*uk_8 + 1008344439*uk_80 + 166375*uk_81 + 238975*uk_82 + 426525*uk_83 + 24200*uk_84 + 638275*uk_85 + 680625*uk_86 + 426525*uk_87 + 343255*uk_88 + 612645*uk_89 + 2572416961*uk_9 + 34760*uk_90 + 916795*uk_91 + 977625*uk_92 + 612645*uk_93 + 1093455*uk_94 + 62040*uk_95 + 1636305*uk_96 + 1744875*uk_97 + 1093455*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 93720*uk_100 + 99000*uk_101 + 34760*uk_102 + 2495295*uk_103 + 2635875*uk_104 + 925485*uk_105 + 2784375*uk_106 + 977625*uk_107 + 343255*uk_108 + 15625*uk_109 + 1267975*uk_11 + 49375*uk_110 + 5000*uk_111 + 133125*uk_112 + 140625*uk_113 + 49375*uk_114 + 156025*uk_115 + 15800*uk_116 + 420675*uk_117 + 444375*uk_118 + 156025*uk_119 + 4006801*uk_12 + 1600*uk_120 + 42600*uk_121 + 45000*uk_122 + 15800*uk_123 + 1134225*uk_124 + 1198125*uk_125 + 420675*uk_126 + 1265625*uk_127 + 444375*uk_128 + 156025*uk_129 + 405752*uk_13 + 493039*uk_130 + 49928*uk_131 + 1329333*uk_132 + 1404225*uk_133 + 493039*uk_134 + 5056*uk_135 + 134616*uk_136 + 142200*uk_137 + 49928*uk_138 + 3584151*uk_139 + 10803147*uk_14 + 3786075*uk_140 + 1329333*uk_141 + 3999375*uk_142 + 1404225*uk_143 + 493039*uk_144 + 512*uk_145 + 13632*uk_146 + 14400*uk_147 + 5056*uk_148 + 362952*uk_149 + 11411775*uk_15 + 383400*uk_150 + 134616*uk_151 + 405000*uk_152 + 142200*uk_153 + 49928*uk_154 + 9663597*uk_155 + 10208025*uk_156 + 3584151*uk_157 + 10783125*uk_158 + 3786075*uk_159 + 4006801*uk_16 + 1329333*uk_160 + 11390625*uk_161 + 3999375*uk_162 + 1404225*uk_163 + 493039*uk_164 + 3025*uk_17 + 1375*uk_18 + 4345*uk_19 + 55*uk_2 + 440*uk_20 + 11715*uk_21 + 12375*uk_22 + 4345*uk_23 + 625*uk_24 + 1975*uk_25 + 200*uk_26 + 5325*uk_27 + 5625*uk_28 + 1975*uk_29 + 25*uk_3 + 6241*uk_30 + 632*uk_31 + 16827*uk_32 + 17775*uk_33 + 6241*uk_34 + 64*uk_35 + 1704*uk_36 + 1800*uk_37 + 632*uk_38 + 45369*uk_39 + 79*uk_4 + 47925*uk_40 + 16827*uk_41 + 50625*uk_42 + 17775*uk_43 + 6241*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 64310424025*uk_47 + 203220939919*uk_48 + 20579335688*uk_49 + 8*uk_5 + 547924812693*uk_50 + 578793816225*uk_51 + 203220939919*uk_52 + 153424975*uk_53 + 69738625*uk_54 + 220374055*uk_55 + 22316360*uk_56 + 594173085*uk_57 + 627647625*uk_58 + 220374055*uk_59 + 213*uk_6 + 31699375*uk_60 + 100170025*uk_61 + 10143800*uk_62 + 270078675*uk_63 + 285294375*uk_64 + 100170025*uk_65 + 316537279*uk_66 + 32054408*uk_67 + 853448613*uk_68 + 901530225*uk_69 + 225*uk_7 + 316537279*uk_70 + 3246016*uk_71 + 86425176*uk_72 + 91294200*uk_73 + 32054408*uk_74 + 2301070311*uk_75 + 2430708075*uk_76 + 853448613*uk_77 + 2567649375*uk_78 + 901530225*uk_79 + 79*uk_8 + 316537279*uk_80 + 166375*uk_81 + 75625*uk_82 + 238975*uk_83 + 24200*uk_84 + 644325*uk_85 + 680625*uk_86 + 238975*uk_87 + 34375*uk_88 + 108625*uk_89 + 2572416961*uk_9 + 11000*uk_90 + 292875*uk_91 + 309375*uk_92 + 108625*uk_93 + 343255*uk_94 + 34760*uk_95 + 925485*uk_96 + 977625*uk_97 + 343255*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 141900*uk_100 + 148500*uk_101 + 16500*uk_102 + 2542375*uk_103 + 2660625*uk_104 + 295625*uk_105 + 2784375*uk_106 + 309375*uk_107 + 34375*uk_108 + 7301384*uk_109 + 9839486*uk_11 + 940900*uk_110 + 451632*uk_111 + 8091740*uk_112 + 8468100*uk_113 + 940900*uk_114 + 121250*uk_115 + 58200*uk_116 + 1042750*uk_117 + 1091250*uk_118 + 121250*uk_119 + 1267975*uk_12 + 27936*uk_120 + 500520*uk_121 + 523800*uk_122 + 58200*uk_123 + 8967650*uk_124 + 9384750*uk_125 + 1042750*uk_126 + 9821250*uk_127 + 1091250*uk_128 + 121250*uk_129 + 608628*uk_13 + 15625*uk_130 + 7500*uk_131 + 134375*uk_132 + 140625*uk_133 + 15625*uk_134 + 3600*uk_135 + 64500*uk_136 + 67500*uk_137 + 7500*uk_138 + 1155625*uk_139 + 10904585*uk_14 + 1209375*uk_140 + 134375*uk_141 + 1265625*uk_142 + 140625*uk_143 + 15625*uk_144 + 1728*uk_145 + 30960*uk_146 + 32400*uk_147 + 3600*uk_148 + 554700*uk_149 + 11411775*uk_15 + 580500*uk_150 + 64500*uk_151 + 607500*uk_152 + 67500*uk_153 + 7500*uk_154 + 9938375*uk_155 + 10400625*uk_156 + 1155625*uk_157 + 10884375*uk_158 + 1209375*uk_159 + 1267975*uk_16 + 134375*uk_160 + 11390625*uk_161 + 1265625*uk_162 + 140625*uk_163 + 15625*uk_164 + 3025*uk_17 + 10670*uk_18 + 1375*uk_19 + 55*uk_2 + 660*uk_20 + 11825*uk_21 + 12375*uk_22 + 1375*uk_23 + 37636*uk_24 + 4850*uk_25 + 2328*uk_26 + 41710*uk_27 + 43650*uk_28 + 4850*uk_29 + 194*uk_3 + 625*uk_30 + 300*uk_31 + 5375*uk_32 + 5625*uk_33 + 625*uk_34 + 144*uk_35 + 2580*uk_36 + 2700*uk_37 + 300*uk_38 + 46225*uk_39 + 25*uk_4 + 48375*uk_40 + 5375*uk_41 + 50625*uk_42 + 5625*uk_43 + 625*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 499048890434*uk_47 + 64310424025*uk_48 + 30869003532*uk_49 + 12*uk_5 + 553069646615*uk_50 + 578793816225*uk_51 + 64310424025*uk_52 + 153424975*uk_53 + 541171730*uk_54 + 69738625*uk_55 + 33474540*uk_56 + 599752175*uk_57 + 627647625*uk_58 + 69738625*uk_59 + 215*uk_6 + 1908860284*uk_60 + 245987150*uk_61 + 118073832*uk_62 + 2115489490*uk_63 + 2213884350*uk_64 + 245987150*uk_65 + 31699375*uk_66 + 15215700*uk_67 + 272614625*uk_68 + 285294375*uk_69 + 225*uk_7 + 31699375*uk_70 + 7303536*uk_71 + 130855020*uk_72 + 136941300*uk_73 + 15215700*uk_74 + 2344485775*uk_75 + 2453531625*uk_76 + 272614625*uk_77 + 2567649375*uk_78 + 285294375*uk_79 + 25*uk_8 + 31699375*uk_80 + 166375*uk_81 + 586850*uk_82 + 75625*uk_83 + 36300*uk_84 + 650375*uk_85 + 680625*uk_86 + 75625*uk_87 + 2069980*uk_88 + 266750*uk_89 + 2572416961*uk_9 + 128040*uk_90 + 2294050*uk_91 + 2400750*uk_92 + 266750*uk_93 + 34375*uk_94 + 16500*uk_95 + 295625*uk_96 + 309375*uk_97 + 34375*uk_98 + 7920*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 95480*uk_100 + 99000*uk_101 + 85360*uk_102 + 2589895*uk_103 + 2685375*uk_104 + 2315390*uk_105 + 2784375*uk_106 + 2400750*uk_107 + 2069980*uk_108 + 3944312*uk_109 + 8013602*uk_11 + 4843016*uk_110 + 199712*uk_111 + 5417188*uk_112 + 5616900*uk_113 + 4843016*uk_114 + 5946488*uk_115 + 245216*uk_116 + 6651484*uk_117 + 6896700*uk_118 + 5946488*uk_119 + 9839486*uk_12 + 10112*uk_120 + 274288*uk_121 + 284400*uk_122 + 245216*uk_123 + 7440062*uk_124 + 7714350*uk_125 + 6651484*uk_126 + 7998750*uk_127 + 6896700*uk_128 + 5946488*uk_129 + 405752*uk_13 + 7301384*uk_130 + 301088*uk_131 + 8167012*uk_132 + 8468100*uk_133 + 7301384*uk_134 + 12416*uk_135 + 336784*uk_136 + 349200*uk_137 + 301088*uk_138 + 9135266*uk_139 + 11006023*uk_14 + 9472050*uk_140 + 8167012*uk_141 + 9821250*uk_142 + 8468100*uk_143 + 7301384*uk_144 + 512*uk_145 + 13888*uk_146 + 14400*uk_147 + 12416*uk_148 + 376712*uk_149 + 11411775*uk_15 + 390600*uk_150 + 336784*uk_151 + 405000*uk_152 + 349200*uk_153 + 301088*uk_154 + 10218313*uk_155 + 10595025*uk_156 + 9135266*uk_157 + 10985625*uk_158 + 9472050*uk_159 + 9839486*uk_16 + 8167012*uk_160 + 11390625*uk_161 + 9821250*uk_162 + 8468100*uk_163 + 7301384*uk_164 + 3025*uk_17 + 8690*uk_18 + 10670*uk_19 + 55*uk_2 + 440*uk_20 + 11935*uk_21 + 12375*uk_22 + 10670*uk_23 + 24964*uk_24 + 30652*uk_25 + 1264*uk_26 + 34286*uk_27 + 35550*uk_28 + 30652*uk_29 + 158*uk_3 + 37636*uk_30 + 1552*uk_31 + 42098*uk_32 + 43650*uk_33 + 37636*uk_34 + 64*uk_35 + 1736*uk_36 + 1800*uk_37 + 1552*uk_38 + 47089*uk_39 + 194*uk_4 + 48825*uk_40 + 42098*uk_41 + 50625*uk_42 + 43650*uk_43 + 37636*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 406441879838*uk_47 + 499048890434*uk_48 + 20579335688*uk_49 + 8*uk_5 + 558214480537*uk_50 + 578793816225*uk_51 + 499048890434*uk_52 + 153424975*uk_53 + 440748110*uk_54 + 541171730*uk_55 + 22316360*uk_56 + 605331265*uk_57 + 627647625*uk_58 + 541171730*uk_59 + 217*uk_6 + 1266149116*uk_60 + 1554638788*uk_61 + 64108816*uk_62 + 1738951634*uk_63 + 1803060450*uk_64 + 1554638788*uk_65 + 1908860284*uk_66 + 78715888*uk_67 + 2135168462*uk_68 + 2213884350*uk_69 + 225*uk_7 + 1908860284*uk_70 + 3246016*uk_71 + 88048184*uk_72 + 91294200*uk_73 + 78715888*uk_74 + 2388306991*uk_75 + 2476355175*uk_76 + 2135168462*uk_77 + 2567649375*uk_78 + 2213884350*uk_79 + 194*uk_8 + 1908860284*uk_80 + 166375*uk_81 + 477950*uk_82 + 586850*uk_83 + 24200*uk_84 + 656425*uk_85 + 680625*uk_86 + 586850*uk_87 + 1373020*uk_88 + 1685860*uk_89 + 2572416961*uk_9 + 69520*uk_90 + 1885730*uk_91 + 1955250*uk_92 + 1685860*uk_93 + 2069980*uk_94 + 85360*uk_95 + 2315390*uk_96 + 2400750*uk_97 + 2069980*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 98120*uk_100 + 99000*uk_101 + 48400*uk_102 + 2735095*uk_103 + 2759625*uk_104 + 1349150*uk_105 + 2784375*uk_106 + 1361250*uk_107 + 665500*uk_108 + 941192*uk_109 + 4970462*uk_11 + 1056440*uk_110 + 76832*uk_111 + 2141692*uk_112 + 2160900*uk_113 + 1056440*uk_114 + 1185800*uk_115 + 86240*uk_116 + 2403940*uk_117 + 2425500*uk_118 + 1185800*uk_119 + 5579090*uk_12 + 6272*uk_120 + 174832*uk_121 + 176400*uk_122 + 86240*uk_123 + 4873442*uk_124 + 4917150*uk_125 + 2403940*uk_126 + 4961250*uk_127 + 2425500*uk_128 + 1185800*uk_129 + 405752*uk_13 + 1331000*uk_130 + 96800*uk_131 + 2698300*uk_132 + 2722500*uk_133 + 1331000*uk_134 + 7040*uk_135 + 196240*uk_136 + 198000*uk_137 + 96800*uk_138 + 5470190*uk_139 + 11310337*uk_14 + 5519250*uk_140 + 2698300*uk_141 + 5568750*uk_142 + 2722500*uk_143 + 1331000*uk_144 + 512*uk_145 + 14272*uk_146 + 14400*uk_147 + 7040*uk_148 + 397832*uk_149 + 11411775*uk_15 + 401400*uk_150 + 196240*uk_151 + 405000*uk_152 + 198000*uk_153 + 96800*uk_154 + 11089567*uk_155 + 11189025*uk_156 + 5470190*uk_157 + 11289375*uk_158 + 5519250*uk_159 + 5579090*uk_16 + 2698300*uk_160 + 11390625*uk_161 + 5568750*uk_162 + 2722500*uk_163 + 1331000*uk_164 + 3025*uk_17 + 5390*uk_18 + 6050*uk_19 + 55*uk_2 + 440*uk_20 + 12265*uk_21 + 12375*uk_22 + 6050*uk_23 + 9604*uk_24 + 10780*uk_25 + 784*uk_26 + 21854*uk_27 + 22050*uk_28 + 10780*uk_29 + 98*uk_3 + 12100*uk_30 + 880*uk_31 + 24530*uk_32 + 24750*uk_33 + 12100*uk_34 + 64*uk_35 + 1784*uk_36 + 1800*uk_37 + 880*uk_38 + 49729*uk_39 + 110*uk_4 + 50175*uk_40 + 24530*uk_41 + 50625*uk_42 + 24750*uk_43 + 12100*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 252096862178*uk_47 + 282965865710*uk_48 + 20579335688*uk_49 + 8*uk_5 + 573648982303*uk_50 + 578793816225*uk_51 + 282965865710*uk_52 + 153424975*uk_53 + 273375410*uk_54 + 306849950*uk_55 + 22316360*uk_56 + 622068535*uk_57 + 627647625*uk_58 + 306849950*uk_59 + 223*uk_6 + 487105276*uk_60 + 546750820*uk_61 + 39763696*uk_62 + 1108413026*uk_63 + 1118353950*uk_64 + 546750820*uk_65 + 613699900*uk_66 + 44632720*uk_67 + 1244137070*uk_68 + 1255295250*uk_69 + 225*uk_7 + 613699900*uk_70 + 3246016*uk_71 + 90482696*uk_72 + 91294200*uk_73 + 44632720*uk_74 + 2522205151*uk_75 + 2544825825*uk_76 + 1244137070*uk_77 + 2567649375*uk_78 + 1255295250*uk_79 + 110*uk_8 + 613699900*uk_80 + 166375*uk_81 + 296450*uk_82 + 332750*uk_83 + 24200*uk_84 + 674575*uk_85 + 680625*uk_86 + 332750*uk_87 + 528220*uk_88 + 592900*uk_89 + 2572416961*uk_9 + 43120*uk_90 + 1201970*uk_91 + 1212750*uk_92 + 592900*uk_93 + 665500*uk_94 + 48400*uk_95 + 1349150*uk_96 + 1361250*uk_97 + 665500*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 99000*uk_100 + 99000*uk_101 + 43120*uk_102 + 2784375*uk_103 + 2784375*uk_104 + 1212750*uk_105 + 2784375*uk_106 + 1212750*uk_107 + 528220*uk_108 + 830584*uk_109 + 4767586*uk_11 + 865928*uk_110 + 70688*uk_111 + 1988100*uk_112 + 1988100*uk_113 + 865928*uk_114 + 902776*uk_115 + 73696*uk_116 + 2072700*uk_117 + 2072700*uk_118 + 902776*uk_119 + 4970462*uk_12 + 6016*uk_120 + 169200*uk_121 + 169200*uk_122 + 73696*uk_123 + 4758750*uk_124 + 4758750*uk_125 + 2072700*uk_126 + 4758750*uk_127 + 2072700*uk_128 + 902776*uk_129 + 405752*uk_13 + 941192*uk_130 + 76832*uk_131 + 2160900*uk_132 + 2160900*uk_133 + 941192*uk_134 + 6272*uk_135 + 176400*uk_136 + 176400*uk_137 + 76832*uk_138 + 4961250*uk_139 + 11411775*uk_14 + 4961250*uk_140 + 2160900*uk_141 + 4961250*uk_142 + 2160900*uk_143 + 941192*uk_144 + 512*uk_145 + 14400*uk_146 + 14400*uk_147 + 6272*uk_148 + 405000*uk_149 + 11411775*uk_15 + 405000*uk_150 + 176400*uk_151 + 405000*uk_152 + 176400*uk_153 + 76832*uk_154 + 11390625*uk_155 + 11390625*uk_156 + 4961250*uk_157 + 11390625*uk_158 + 4961250*uk_159 + 4970462*uk_16 + 2160900*uk_160 + 11390625*uk_161 + 4961250*uk_162 + 2160900*uk_163 + 941192*uk_164 + 3025*uk_17 + 5170*uk_18 + 5390*uk_19 + 55*uk_2 + 440*uk_20 + 12375*uk_21 + 12375*uk_22 + 5390*uk_23 + 8836*uk_24 + 9212*uk_25 + 752*uk_26 + 21150*uk_27 + 21150*uk_28 + 9212*uk_29 + 94*uk_3 + 9604*uk_30 + 784*uk_31 + 22050*uk_32 + 22050*uk_33 + 9604*uk_34 + 64*uk_35 + 1800*uk_36 + 1800*uk_37 + 784*uk_38 + 50625*uk_39 + 98*uk_4 + 50625*uk_40 + 22050*uk_41 + 50625*uk_42 + 22050*uk_43 + 9604*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 241807194334*uk_47 + 252096862178*uk_48 + 20579335688*uk_49 + 8*uk_5 + 578793816225*uk_50 + 578793816225*uk_51 + 252096862178*uk_52 + 153424975*uk_53 + 262217230*uk_54 + 273375410*uk_55 + 22316360*uk_56 + 627647625*uk_57 + 627647625*uk_58 + 273375410*uk_59 + 225*uk_6 + 448153084*uk_60 + 467223428*uk_61 + 38140688*uk_62 + 1072706850*uk_63 + 1072706850*uk_64 + 467223428*uk_65 + 487105276*uk_66 + 39763696*uk_67 + 1118353950*uk_68 + 1118353950*uk_69 + 225*uk_7 + 487105276*uk_70 + 3246016*uk_71 + 91294200*uk_72 + 91294200*uk_73 + 39763696*uk_74 + 2567649375*uk_75 + 2567649375*uk_76 + 1118353950*uk_77 + 2567649375*uk_78 + 1118353950*uk_79 + 98*uk_8 + 487105276*uk_80 + 166375*uk_81 + 284350*uk_82 + 296450*uk_83 + 24200*uk_84 + 680625*uk_85 + 680625*uk_86 + 296450*uk_87 + 485980*uk_88 + 506660*uk_89 + 2572416961*uk_9 + 41360*uk_90 + 1163250*uk_91 + 1163250*uk_92 + 506660*uk_93 + 528220*uk_94 + 43120*uk_95 + 1212750*uk_96 + 1212750*uk_97 + 528220*uk_98 + 3520*uk_99,
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uk_0 + 50719*uk_1 + 2789545*uk_10 + 99880*uk_100 + 99000*uk_101 + 41360*uk_102 + 2834095*uk_103 + 2809125*uk_104 + 1173590*uk_105 + 2784375*uk_106 + 1163250*uk_107 + 485980*uk_108 + 941192*uk_109 + 4970462*uk_11 + 902776*uk_110 + 76832*uk_111 + 2180108*uk_112 + 2160900*uk_113 + 902776*uk_114 + 865928*uk_115 + 73696*uk_116 + 2091124*uk_117 + 2072700*uk_118 + 865928*uk_119 + 4767586*uk_12 + 6272*uk_120 + 177968*uk_121 + 176400*uk_122 + 73696*uk_123 + 5049842*uk_124 + 5005350*uk_125 + 2091124*uk_126 + 4961250*uk_127 + 2072700*uk_128 + 865928*uk_129 + 405752*uk_13 + 830584*uk_130 + 70688*uk_131 + 2005772*uk_132 + 1988100*uk_133 + 830584*uk_134 + 6016*uk_135 + 170704*uk_136 + 169200*uk_137 + 70688*uk_138 + 4843726*uk_139 + 11513213*uk_14 + 4801050*uk_140 + 2005772*uk_141 + 4758750*uk_142 + 1988100*uk_143 + 830584*uk_144 + 512*uk_145 + 14528*uk_146 + 14400*uk_147 + 6016*uk_148 + 412232*uk_149 + 11411775*uk_15 + 408600*uk_150 + 170704*uk_151 + 405000*uk_152 + 169200*uk_153 + 70688*uk_154 + 11697083*uk_155 + 11594025*uk_156 + 4843726*uk_157 + 11491875*uk_158 + 4801050*uk_159 + 4767586*uk_16 + 2005772*uk_160 + 11390625*uk_161 + 4758750*uk_162 + 1988100*uk_163 + 830584*uk_164 + 3025*uk_17 + 5390*uk_18 + 5170*uk_19 + 55*uk_2 + 440*uk_20 + 12485*uk_21 + 12375*uk_22 + 5170*uk_23 + 9604*uk_24 + 9212*uk_25 + 784*uk_26 + 22246*uk_27 + 22050*uk_28 + 9212*uk_29 + 98*uk_3 + 8836*uk_30 + 752*uk_31 + 21338*uk_32 + 21150*uk_33 + 8836*uk_34 + 64*uk_35 + 1816*uk_36 + 1800*uk_37 + 752*uk_38 + 51529*uk_39 + 94*uk_4 + 51075*uk_40 + 21338*uk_41 + 50625*uk_42 + 21150*uk_43 + 8836*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 252096862178*uk_47 + 241807194334*uk_48 + 20579335688*uk_49 + 8*uk_5 + 583938650147*uk_50 + 578793816225*uk_51 + 241807194334*uk_52 + 153424975*uk_53 + 273375410*uk_54 + 262217230*uk_55 + 22316360*uk_56 + 633226715*uk_57 + 627647625*uk_58 + 262217230*uk_59 + 227*uk_6 + 487105276*uk_60 + 467223428*uk_61 + 39763696*uk_62 + 1128294874*uk_63 + 1118353950*uk_64 + 467223428*uk_65 + 448153084*uk_66 + 38140688*uk_67 + 1082242022*uk_68 + 1072706850*uk_69 + 225*uk_7 + 448153084*uk_70 + 3246016*uk_71 + 92105704*uk_72 + 91294200*uk_73 + 38140688*uk_74 + 2613499351*uk_75 + 2590472925*uk_76 + 1082242022*uk_77 + 2567649375*uk_78 + 1072706850*uk_79 + 94*uk_8 + 448153084*uk_80 + 166375*uk_81 + 296450*uk_82 + 284350*uk_83 + 24200*uk_84 + 686675*uk_85 + 680625*uk_86 + 284350*uk_87 + 528220*uk_88 + 506660*uk_89 + 2572416961*uk_9 + 43120*uk_90 + 1223530*uk_91 + 1212750*uk_92 + 506660*uk_93 + 485980*uk_94 + 41360*uk_95 + 1173590*uk_96 + 1163250*uk_97 + 485980*uk_98 + 3520*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 396900*uk_100 + 1367100*uk_101 + 250047*uk_103 + 861273*uk_104 + 2966607*uk_106 + 64000*uk_109 + 1894120*uk_11 + 27200*uk_110 + 160000*uk_111 + 100800*uk_112 + 347200*uk_113 + 11560*uk_115 + 68000*uk_116 + 42840*uk_117 + 147560*uk_118 + 805001*uk_12 + 400000*uk_120 + 252000*uk_121 + 868000*uk_122 + 158760*uk_124 + 546840*uk_125 + 1883560*uk_127 + 4735300*uk_13 + 4913*uk_130 + 28900*uk_131 + 18207*uk_132 + 62713*uk_133 + 170000*uk_135 + 107100*uk_136 + 368900*uk_137 + 67473*uk_139 + 2983239*uk_14 + 232407*uk_140 + 800513*uk_142 + 1000000*uk_145 + 630000*uk_146 + 2170000*uk_147 + 396900*uk_149 + 10275601*uk_15 + 1367100*uk_150 + 4708900*uk_152 + 250047*uk_155 + 861273*uk_156 + 2966607*uk_158 + 10218313*uk_161 + 3969*uk_17 + 2520*uk_18 + 1071*uk_19 + 63*uk_2 + 6300*uk_20 + 3969*uk_21 + 13671*uk_22 + 1600*uk_24 + 680*uk_25 + 4000*uk_26 + 2520*uk_27 + 8680*uk_28 + 40*uk_3 + 289*uk_30 + 1700*uk_31 + 1071*uk_32 + 3689*uk_33 + 10000*uk_35 + 6300*uk_36 + 21700*uk_37 + 3969*uk_39 + 17*uk_4 + 13671*uk_40 + 47089*uk_42 + 106179944855977*uk_45 + 141265316367*uk_46 + 89692264360*uk_47 + 38119212353*uk_48 + 224230660900*uk_49 + 100*uk_5 + 141265316367*uk_50 + 486580534153*uk_51 + 187944057*uk_53 + 119329560*uk_54 + 50715063*uk_55 + 298323900*uk_56 + 187944057*uk_57 + 647362863*uk_58 + 63*uk_6 + 75764800*uk_60 + 32200040*uk_61 + 189412000*uk_62 + 119329560*uk_63 + 411024040*uk_64 + 13685017*uk_66 + 80500100*uk_67 + 50715063*uk_68 + 174685217*uk_69 + 217*uk_7 + 473530000*uk_71 + 298323900*uk_72 + 1027560100*uk_73 + 187944057*uk_75 + 647362863*uk_76 + 2229805417*uk_78 + 250047*uk_81 + 158760*uk_82 + 67473*uk_83 + 396900*uk_84 + 250047*uk_85 + 861273*uk_86 + 100800*uk_88 + 42840*uk_89 + 2242306609*uk_9 + 252000*uk_90 + 158760*uk_91 + 546840*uk_92 + 18207*uk_94 + 107100*uk_95 + 67473*uk_96 + 232407*uk_97 + 630000*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 376740*uk_100 + 1257732*uk_101 + 231840*uk_102 + 266175*uk_103 + 888615*uk_104 + 163800*uk_105 + 2966607*uk_106 + 546840*uk_107 + 100800*uk_108 + 35937*uk_109 + 1562649*uk_11 + 43560*uk_110 + 100188*uk_111 + 70785*uk_112 + 236313*uk_113 + 43560*uk_114 + 52800*uk_115 + 121440*uk_116 + 85800*uk_117 + 286440*uk_118 + 52800*uk_119 + 1894120*uk_12 + 279312*uk_120 + 197340*uk_121 + 658812*uk_122 + 121440*uk_123 + 139425*uk_124 + 465465*uk_125 + 85800*uk_126 + 1553937*uk_127 + 286440*uk_128 + 52800*uk_129 + 4356476*uk_13 + 64000*uk_130 + 147200*uk_131 + 104000*uk_132 + 347200*uk_133 + 64000*uk_134 + 338560*uk_135 + 239200*uk_136 + 798560*uk_137 + 147200*uk_138 + 169000*uk_139 + 3077945*uk_14 + 564200*uk_140 + 104000*uk_141 + 1883560*uk_142 + 347200*uk_143 + 64000*uk_144 + 778688*uk_145 + 550160*uk_146 + 1836688*uk_147 + 338560*uk_148 + 388700*uk_149 + 10275601*uk_15 + 1297660*uk_150 + 239200*uk_151 + 4332188*uk_152 + 798560*uk_153 + 147200*uk_154 + 274625*uk_155 + 916825*uk_156 + 169000*uk_157 + 3060785*uk_158 + 564200*uk_159 + 1894120*uk_16 + 104000*uk_160 + 10218313*uk_161 + 1883560*uk_162 + 347200*uk_163 + 64000*uk_164 + 3969*uk_17 + 2079*uk_18 + 2520*uk_19 + 63*uk_2 + 5796*uk_20 + 4095*uk_21 + 13671*uk_22 + 2520*uk_23 + 1089*uk_24 + 1320*uk_25 + 3036*uk_26 + 2145*uk_27 + 7161*uk_28 + 1320*uk_29 + 33*uk_3 + 1600*uk_30 + 3680*uk_31 + 2600*uk_32 + 8680*uk_33 + 1600*uk_34 + 8464*uk_35 + 5980*uk_36 + 19964*uk_37 + 3680*uk_38 + 4225*uk_39 + 40*uk_4 + 14105*uk_40 + 2600*uk_41 + 47089*uk_42 + 8680*uk_43 + 1600*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 73996118097*uk_47 + 89692264360*uk_48 + 206292208028*uk_49 + 92*uk_5 + 145749929585*uk_50 + 486580534153*uk_51 + 89692264360*uk_52 + 187944057*uk_53 + 98446887*uk_54 + 119329560*uk_55 + 274457988*uk_56 + 193910535*uk_57 + 647362863*uk_58 + 119329560*uk_59 + 65*uk_6 + 51567417*uk_60 + 62505960*uk_61 + 143763708*uk_62 + 101572185*uk_63 + 339094833*uk_64 + 62505960*uk_65 + 75764800*uk_66 + 174259040*uk_67 + 123117800*uk_68 + 411024040*uk_69 + 217*uk_7 + 75764800*uk_70 + 400795792*uk_71 + 283170940*uk_72 + 945355292*uk_73 + 174259040*uk_74 + 200066425*uk_75 + 667914065*uk_76 + 123117800*uk_77 + 2229805417*uk_78 + 411024040*uk_79 + 40*uk_8 + 75764800*uk_80 + 250047*uk_81 + 130977*uk_82 + 158760*uk_83 + 365148*uk_84 + 257985*uk_85 + 861273*uk_86 + 158760*uk_87 + 68607*uk_88 + 83160*uk_89 + 2242306609*uk_9 + 191268*uk_90 + 135135*uk_91 + 451143*uk_92 + 83160*uk_93 + 100800*uk_94 + 231840*uk_95 + 163800*uk_96 + 546840*uk_97 + 100800*uk_98 + 533232*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 306180*uk_100 + 820260*uk_101 + 120960*uk_102 + 413343*uk_103 + 1107351*uk_104 + 163296*uk_105 + 2966607*uk_106 + 437472*uk_107 + 64512*uk_108 + 117649*uk_109 + 2320297*uk_11 + 76832*uk_110 + 144060*uk_111 + 194481*uk_112 + 521017*uk_113 + 76832*uk_114 + 50176*uk_115 + 94080*uk_116 + 127008*uk_117 + 340256*uk_118 + 50176*uk_119 + 1515296*uk_12 + 176400*uk_120 + 238140*uk_121 + 637980*uk_122 + 94080*uk_123 + 321489*uk_124 + 861273*uk_125 + 127008*uk_126 + 2307361*uk_127 + 340256*uk_128 + 50176*uk_129 + 2841180*uk_13 + 32768*uk_130 + 61440*uk_131 + 82944*uk_132 + 222208*uk_133 + 32768*uk_134 + 115200*uk_135 + 155520*uk_136 + 416640*uk_137 + 61440*uk_138 + 209952*uk_139 + 3835593*uk_14 + 562464*uk_140 + 82944*uk_141 + 1506848*uk_142 + 222208*uk_143 + 32768*uk_144 + 216000*uk_145 + 291600*uk_146 + 781200*uk_147 + 115200*uk_148 + 393660*uk_149 + 10275601*uk_15 + 1054620*uk_150 + 155520*uk_151 + 2825340*uk_152 + 416640*uk_153 + 61440*uk_154 + 531441*uk_155 + 1423737*uk_156 + 209952*uk_157 + 3814209*uk_158 + 562464*uk_159 + 1515296*uk_16 + 82944*uk_160 + 10218313*uk_161 + 1506848*uk_162 + 222208*uk_163 + 32768*uk_164 + 3969*uk_17 + 3087*uk_18 + 2016*uk_19 + 63*uk_2 + 3780*uk_20 + 5103*uk_21 + 13671*uk_22 + 2016*uk_23 + 2401*uk_24 + 1568*uk_25 + 2940*uk_26 + 3969*uk_27 + 10633*uk_28 + 1568*uk_29 + 49*uk_3 + 1024*uk_30 + 1920*uk_31 + 2592*uk_32 + 6944*uk_33 + 1024*uk_34 + 3600*uk_35 + 4860*uk_36 + 13020*uk_37 + 1920*uk_38 + 6561*uk_39 + 32*uk_4 + 17577*uk_40 + 2592*uk_41 + 47089*uk_42 + 6944*uk_43 + 1024*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 109873023841*uk_47 + 71753811488*uk_48 + 134538396540*uk_49 + 60*uk_5 + 181626835329*uk_50 + 486580534153*uk_51 + 71753811488*uk_52 + 187944057*uk_53 + 146178711*uk_54 + 95463648*uk_55 + 178994340*uk_56 + 241642359*uk_57 + 647362863*uk_58 + 95463648*uk_59 + 81*uk_6 + 113694553*uk_60 + 74249504*uk_61 + 139217820*uk_62 + 187944057*uk_63 + 503504449*uk_64 + 74249504*uk_65 + 48489472*uk_66 + 90917760*uk_67 + 122738976*uk_68 + 328819232*uk_69 + 217*uk_7 + 48489472*uk_70 + 170470800*uk_71 + 230135580*uk_72 + 616536060*uk_73 + 90917760*uk_74 + 310683033*uk_75 + 832323681*uk_76 + 122738976*uk_77 + 2229805417*uk_78 + 328819232*uk_79 + 32*uk_8 + 48489472*uk_80 + 250047*uk_81 + 194481*uk_82 + 127008*uk_83 + 238140*uk_84 + 321489*uk_85 + 861273*uk_86 + 127008*uk_87 + 151263*uk_88 + 98784*uk_89 + 2242306609*uk_9 + 185220*uk_90 + 250047*uk_91 + 669879*uk_92 + 98784*uk_93 + 64512*uk_94 + 120960*uk_95 + 163296*uk_96 + 437472*uk_97 + 64512*uk_98 + 226800*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 292824*uk_100 + 765576*uk_101 + 172872*uk_102 + 434007*uk_103 + 1134693*uk_104 + 256221*uk_105 + 2966607*uk_106 + 669879*uk_107 + 151263*uk_108 + 79507*uk_109 + 2036179*uk_11 + 90601*uk_110 + 103544*uk_111 + 153467*uk_112 + 401233*uk_113 + 90601*uk_114 + 103243*uk_115 + 117992*uk_116 + 174881*uk_117 + 457219*uk_118 + 103243*uk_119 + 2320297*uk_12 + 134848*uk_120 + 199864*uk_121 + 522536*uk_122 + 117992*uk_123 + 296227*uk_124 + 774473*uk_125 + 174881*uk_126 + 2024827*uk_127 + 457219*uk_128 + 103243*uk_129 + 2651768*uk_13 + 117649*uk_130 + 134456*uk_131 + 199283*uk_132 + 521017*uk_133 + 117649*uk_134 + 153664*uk_135 + 227752*uk_136 + 595448*uk_137 + 134456*uk_138 + 337561*uk_139 + 3930299*uk_14 + 882539*uk_140 + 199283*uk_141 + 2307361*uk_142 + 521017*uk_143 + 117649*uk_144 + 175616*uk_145 + 260288*uk_146 + 680512*uk_147 + 153664*uk_148 + 385784*uk_149 + 10275601*uk_15 + 1008616*uk_150 + 227752*uk_151 + 2636984*uk_152 + 595448*uk_153 + 134456*uk_154 + 571787*uk_155 + 1494913*uk_156 + 337561*uk_157 + 3908387*uk_158 + 882539*uk_159 + 2320297*uk_16 + 199283*uk_160 + 10218313*uk_161 + 2307361*uk_162 + 521017*uk_163 + 117649*uk_164 + 3969*uk_17 + 2709*uk_18 + 3087*uk_19 + 63*uk_2 + 3528*uk_20 + 5229*uk_21 + 13671*uk_22 + 3087*uk_23 + 1849*uk_24 + 2107*uk_25 + 2408*uk_26 + 3569*uk_27 + 9331*uk_28 + 2107*uk_29 + 43*uk_3 + 2401*uk_30 + 2744*uk_31 + 4067*uk_32 + 10633*uk_33 + 2401*uk_34 + 3136*uk_35 + 4648*uk_36 + 12152*uk_37 + 2744*uk_38 + 6889*uk_39 + 49*uk_4 + 18011*uk_40 + 4067*uk_41 + 47089*uk_42 + 10633*uk_43 + 2401*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 96419184187*uk_47 + 109873023841*uk_48 + 125569170104*uk_49 + 56*uk_5 + 186111448547*uk_50 + 486580534153*uk_51 + 109873023841*uk_52 + 187944057*uk_53 + 128279277*uk_54 + 146178711*uk_55 + 167061384*uk_56 + 247608837*uk_57 + 647362863*uk_58 + 146178711*uk_59 + 83*uk_6 + 87555697*uk_60 + 99772771*uk_61 + 114026024*uk_62 + 169002857*uk_63 + 441850843*uk_64 + 99772771*uk_65 + 113694553*uk_66 + 129936632*uk_67 + 192584651*uk_68 + 503504449*uk_69 + 217*uk_7 + 113694553*uk_70 + 148499008*uk_71 + 220096744*uk_72 + 575433656*uk_73 + 129936632*uk_74 + 326214817*uk_75 + 852874883*uk_76 + 192584651*uk_77 + 2229805417*uk_78 + 503504449*uk_79 + 49*uk_8 + 113694553*uk_80 + 250047*uk_81 + 170667*uk_82 + 194481*uk_83 + 222264*uk_84 + 329427*uk_85 + 861273*uk_86 + 194481*uk_87 + 116487*uk_88 + 132741*uk_89 + 2242306609*uk_9 + 151704*uk_90 + 224847*uk_91 + 587853*uk_92 + 132741*uk_93 + 151263*uk_94 + 172872*uk_95 + 256221*uk_96 + 669879*uk_97 + 151263*uk_98 + 197568*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 278460*uk_100 + 710892*uk_101 + 140868*uk_102 + 455175*uk_103 + 1162035*uk_104 + 230265*uk_105 + 2966607*uk_106 + 587853*uk_107 + 116487*uk_108 + 512*uk_109 + 378824*uk_11 + 2752*uk_110 + 3328*uk_111 + 5440*uk_112 + 13888*uk_113 + 2752*uk_114 + 14792*uk_115 + 17888*uk_116 + 29240*uk_117 + 74648*uk_118 + 14792*uk_119 + 2036179*uk_12 + 21632*uk_120 + 35360*uk_121 + 90272*uk_122 + 17888*uk_123 + 57800*uk_124 + 147560*uk_125 + 29240*uk_126 + 376712*uk_127 + 74648*uk_128 + 14792*uk_129 + 2462356*uk_13 + 79507*uk_130 + 96148*uk_131 + 157165*uk_132 + 401233*uk_133 + 79507*uk_134 + 116272*uk_135 + 190060*uk_136 + 485212*uk_137 + 96148*uk_138 + 310675*uk_139 + 4025005*uk_14 + 793135*uk_140 + 157165*uk_141 + 2024827*uk_142 + 401233*uk_143 + 79507*uk_144 + 140608*uk_145 + 229840*uk_146 + 586768*uk_147 + 116272*uk_148 + 375700*uk_149 + 10275601*uk_15 + 959140*uk_150 + 190060*uk_151 + 2448628*uk_152 + 485212*uk_153 + 96148*uk_154 + 614125*uk_155 + 1567825*uk_156 + 310675*uk_157 + 4002565*uk_158 + 793135*uk_159 + 2036179*uk_16 + 157165*uk_160 + 10218313*uk_161 + 2024827*uk_162 + 401233*uk_163 + 79507*uk_164 + 3969*uk_17 + 504*uk_18 + 2709*uk_19 + 63*uk_2 + 3276*uk_20 + 5355*uk_21 + 13671*uk_22 + 2709*uk_23 + 64*uk_24 + 344*uk_25 + 416*uk_26 + 680*uk_27 + 1736*uk_28 + 344*uk_29 + 8*uk_3 + 1849*uk_30 + 2236*uk_31 + 3655*uk_32 + 9331*uk_33 + 1849*uk_34 + 2704*uk_35 + 4420*uk_36 + 11284*uk_37 + 2236*uk_38 + 7225*uk_39 + 43*uk_4 + 18445*uk_40 + 3655*uk_41 + 47089*uk_42 + 9331*uk_43 + 1849*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 17938452872*uk_47 + 96419184187*uk_48 + 116599943668*uk_49 + 52*uk_5 + 190596061765*uk_50 + 486580534153*uk_51 + 96419184187*uk_52 + 187944057*uk_53 + 23865912*uk_54 + 128279277*uk_55 + 155128428*uk_56 + 253575315*uk_57 + 647362863*uk_58 + 128279277*uk_59 + 85*uk_6 + 3030592*uk_60 + 16289432*uk_61 + 19698848*uk_62 + 32200040*uk_63 + 82204808*uk_64 + 16289432*uk_65 + 87555697*uk_66 + 105881308*uk_67 + 173075215*uk_68 + 441850843*uk_69 + 217*uk_7 + 87555697*uk_70 + 128042512*uk_71 + 209300260*uk_72 + 534331252*uk_73 + 105881308*uk_74 + 342125425*uk_75 + 873426085*uk_76 + 173075215*uk_77 + 2229805417*uk_78 + 441850843*uk_79 + 43*uk_8 + 87555697*uk_80 + 250047*uk_81 + 31752*uk_82 + 170667*uk_83 + 206388*uk_84 + 337365*uk_85 + 861273*uk_86 + 170667*uk_87 + 4032*uk_88 + 21672*uk_89 + 2242306609*uk_9 + 26208*uk_90 + 42840*uk_91 + 109368*uk_92 + 21672*uk_93 + 116487*uk_94 + 140868*uk_95 + 230265*uk_96 + 587853*uk_97 + 116487*uk_98 + 170352*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 285012*uk_100 + 710892*uk_101 + 26208*uk_102 + 476847*uk_103 + 1189377*uk_104 + 43848*uk_105 + 2966607*uk_106 + 109368*uk_107 + 4032*uk_108 + 15625*uk_109 + 1183825*uk_11 + 5000*uk_110 + 32500*uk_111 + 54375*uk_112 + 135625*uk_113 + 5000*uk_114 + 1600*uk_115 + 10400*uk_116 + 17400*uk_117 + 43400*uk_118 + 1600*uk_119 + 378824*uk_12 + 67600*uk_120 + 113100*uk_121 + 282100*uk_122 + 10400*uk_123 + 189225*uk_124 + 471975*uk_125 + 17400*uk_126 + 1177225*uk_127 + 43400*uk_128 + 1600*uk_129 + 2462356*uk_13 + 512*uk_130 + 3328*uk_131 + 5568*uk_132 + 13888*uk_133 + 512*uk_134 + 21632*uk_135 + 36192*uk_136 + 90272*uk_137 + 3328*uk_138 + 60552*uk_139 + 4119711*uk_14 + 151032*uk_140 + 5568*uk_141 + 376712*uk_142 + 13888*uk_143 + 512*uk_144 + 140608*uk_145 + 235248*uk_146 + 586768*uk_147 + 21632*uk_148 + 393588*uk_149 + 10275601*uk_15 + 981708*uk_150 + 36192*uk_151 + 2448628*uk_152 + 90272*uk_153 + 3328*uk_154 + 658503*uk_155 + 1642473*uk_156 + 60552*uk_157 + 4096743*uk_158 + 151032*uk_159 + 378824*uk_16 + 5568*uk_160 + 10218313*uk_161 + 376712*uk_162 + 13888*uk_163 + 512*uk_164 + 3969*uk_17 + 1575*uk_18 + 504*uk_19 + 63*uk_2 + 3276*uk_20 + 5481*uk_21 + 13671*uk_22 + 504*uk_23 + 625*uk_24 + 200*uk_25 + 1300*uk_26 + 2175*uk_27 + 5425*uk_28 + 200*uk_29 + 25*uk_3 + 64*uk_30 + 416*uk_31 + 696*uk_32 + 1736*uk_33 + 64*uk_34 + 2704*uk_35 + 4524*uk_36 + 11284*uk_37 + 416*uk_38 + 7569*uk_39 + 8*uk_4 + 18879*uk_40 + 696*uk_41 + 47089*uk_42 + 1736*uk_43 + 64*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 56057665225*uk_47 + 17938452872*uk_48 + 116599943668*uk_49 + 52*uk_5 + 195080674983*uk_50 + 486580534153*uk_51 + 17938452872*uk_52 + 187944057*uk_53 + 74580975*uk_54 + 23865912*uk_55 + 155128428*uk_56 + 259541793*uk_57 + 647362863*uk_58 + 23865912*uk_59 + 87*uk_6 + 29595625*uk_60 + 9470600*uk_61 + 61558900*uk_62 + 102992775*uk_63 + 256890025*uk_64 + 9470600*uk_65 + 3030592*uk_66 + 19698848*uk_67 + 32957688*uk_68 + 82204808*uk_69 + 217*uk_7 + 3030592*uk_70 + 128042512*uk_71 + 214224972*uk_72 + 534331252*uk_73 + 19698848*uk_74 + 358414857*uk_75 + 893977287*uk_76 + 32957688*uk_77 + 2229805417*uk_78 + 82204808*uk_79 + 8*uk_8 + 3030592*uk_80 + 250047*uk_81 + 99225*uk_82 + 31752*uk_83 + 206388*uk_84 + 345303*uk_85 + 861273*uk_86 + 31752*uk_87 + 39375*uk_88 + 12600*uk_89 + 2242306609*uk_9 + 81900*uk_90 + 137025*uk_91 + 341775*uk_92 + 12600*uk_93 + 4032*uk_94 + 26208*uk_95 + 43848*uk_96 + 109368*uk_97 + 4032*uk_98 + 170352*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 269136*uk_100 + 656208*uk_101 + 75600*uk_102 + 499023*uk_103 + 1216719*uk_104 + 140175*uk_105 + 2966607*uk_106 + 341775*uk_107 + 39375*uk_108 + 125*uk_109 + 236765*uk_11 + 625*uk_110 + 1200*uk_111 + 2225*uk_112 + 5425*uk_113 + 625*uk_114 + 3125*uk_115 + 6000*uk_116 + 11125*uk_117 + 27125*uk_118 + 3125*uk_119 + 1183825*uk_12 + 11520*uk_120 + 21360*uk_121 + 52080*uk_122 + 6000*uk_123 + 39605*uk_124 + 96565*uk_125 + 11125*uk_126 + 235445*uk_127 + 27125*uk_128 + 3125*uk_129 + 2272944*uk_13 + 15625*uk_130 + 30000*uk_131 + 55625*uk_132 + 135625*uk_133 + 15625*uk_134 + 57600*uk_135 + 106800*uk_136 + 260400*uk_137 + 30000*uk_138 + 198025*uk_139 + 4214417*uk_14 + 482825*uk_140 + 55625*uk_141 + 1177225*uk_142 + 135625*uk_143 + 15625*uk_144 + 110592*uk_145 + 205056*uk_146 + 499968*uk_147 + 57600*uk_148 + 380208*uk_149 + 10275601*uk_15 + 927024*uk_150 + 106800*uk_151 + 2260272*uk_152 + 260400*uk_153 + 30000*uk_154 + 704969*uk_155 + 1718857*uk_156 + 198025*uk_157 + 4190921*uk_158 + 482825*uk_159 + 1183825*uk_16 + 55625*uk_160 + 10218313*uk_161 + 1177225*uk_162 + 135625*uk_163 + 15625*uk_164 + 3969*uk_17 + 315*uk_18 + 1575*uk_19 + 63*uk_2 + 3024*uk_20 + 5607*uk_21 + 13671*uk_22 + 1575*uk_23 + 25*uk_24 + 125*uk_25 + 240*uk_26 + 445*uk_27 + 1085*uk_28 + 125*uk_29 + 5*uk_3 + 625*uk_30 + 1200*uk_31 + 2225*uk_32 + 5425*uk_33 + 625*uk_34 + 2304*uk_35 + 4272*uk_36 + 10416*uk_37 + 1200*uk_38 + 7921*uk_39 + 25*uk_4 + 19313*uk_40 + 2225*uk_41 + 47089*uk_42 + 5425*uk_43 + 625*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 11211533045*uk_47 + 56057665225*uk_48 + 107630717232*uk_49 + 48*uk_5 + 199565288201*uk_50 + 486580534153*uk_51 + 56057665225*uk_52 + 187944057*uk_53 + 14916195*uk_54 + 74580975*uk_55 + 143195472*uk_56 + 265508271*uk_57 + 647362863*uk_58 + 74580975*uk_59 + 89*uk_6 + 1183825*uk_60 + 5919125*uk_61 + 11364720*uk_62 + 21072085*uk_63 + 51378005*uk_64 + 5919125*uk_65 + 29595625*uk_66 + 56823600*uk_67 + 105360425*uk_68 + 256890025*uk_69 + 217*uk_7 + 29595625*uk_70 + 109101312*uk_71 + 202292016*uk_72 + 493228848*uk_73 + 56823600*uk_74 + 375083113*uk_75 + 914528489*uk_76 + 105360425*uk_77 + 2229805417*uk_78 + 256890025*uk_79 + 25*uk_8 + 29595625*uk_80 + 250047*uk_81 + 19845*uk_82 + 99225*uk_83 + 190512*uk_84 + 353241*uk_85 + 861273*uk_86 + 99225*uk_87 + 1575*uk_88 + 7875*uk_89 + 2242306609*uk_9 + 15120*uk_90 + 28035*uk_91 + 68355*uk_92 + 7875*uk_93 + 39375*uk_94 + 75600*uk_95 + 140175*uk_96 + 341775*uk_97 + 39375*uk_98 + 145152*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 257796*uk_100 + 601524*uk_101 + 91476*uk_102 + 544887*uk_103 + 1271403*uk_104 + 193347*uk_105 + 2966607*uk_106 + 451143*uk_107 + 68607*uk_108 + 4096*uk_109 + 757648*uk_11 + 8448*uk_110 + 11264*uk_111 + 23808*uk_112 + 55552*uk_113 + 8448*uk_114 + 17424*uk_115 + 23232*uk_116 + 49104*uk_117 + 114576*uk_118 + 17424*uk_119 + 1562649*uk_12 + 30976*uk_120 + 65472*uk_121 + 152768*uk_122 + 23232*uk_123 + 138384*uk_124 + 322896*uk_125 + 49104*uk_126 + 753424*uk_127 + 114576*uk_128 + 17424*uk_129 + 2083532*uk_13 + 35937*uk_130 + 47916*uk_131 + 101277*uk_132 + 236313*uk_133 + 35937*uk_134 + 63888*uk_135 + 135036*uk_136 + 315084*uk_137 + 47916*uk_138 + 285417*uk_139 + 4403829*uk_14 + 665973*uk_140 + 101277*uk_141 + 1553937*uk_142 + 236313*uk_143 + 35937*uk_144 + 85184*uk_145 + 180048*uk_146 + 420112*uk_147 + 63888*uk_148 + 380556*uk_149 + 10275601*uk_15 + 887964*uk_150 + 135036*uk_151 + 2071916*uk_152 + 315084*uk_153 + 47916*uk_154 + 804357*uk_155 + 1876833*uk_156 + 285417*uk_157 + 4379277*uk_158 + 665973*uk_159 + 1562649*uk_16 + 101277*uk_160 + 10218313*uk_161 + 1553937*uk_162 + 236313*uk_163 + 35937*uk_164 + 3969*uk_17 + 1008*uk_18 + 2079*uk_19 + 63*uk_2 + 2772*uk_20 + 5859*uk_21 + 13671*uk_22 + 2079*uk_23 + 256*uk_24 + 528*uk_25 + 704*uk_26 + 1488*uk_27 + 3472*uk_28 + 528*uk_29 + 16*uk_3 + 1089*uk_30 + 1452*uk_31 + 3069*uk_32 + 7161*uk_33 + 1089*uk_34 + 1936*uk_35 + 4092*uk_36 + 9548*uk_37 + 1452*uk_38 + 8649*uk_39 + 33*uk_4 + 20181*uk_40 + 3069*uk_41 + 47089*uk_42 + 7161*uk_43 + 1089*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 35876905744*uk_47 + 73996118097*uk_48 + 98661490796*uk_49 + 44*uk_5 + 208534514637*uk_50 + 486580534153*uk_51 + 73996118097*uk_52 + 187944057*uk_53 + 47731824*uk_54 + 98446887*uk_55 + 131262516*uk_56 + 277441227*uk_57 + 647362863*uk_58 + 98446887*uk_59 + 93*uk_6 + 12122368*uk_60 + 25002384*uk_61 + 33336512*uk_62 + 70461264*uk_63 + 164409616*uk_64 + 25002384*uk_65 + 51567417*uk_66 + 68756556*uk_67 + 145326357*uk_68 + 339094833*uk_69 + 217*uk_7 + 51567417*uk_70 + 91675408*uk_71 + 193768476*uk_72 + 452126444*uk_73 + 68756556*uk_74 + 409556097*uk_75 + 955630893*uk_76 + 145326357*uk_77 + 2229805417*uk_78 + 339094833*uk_79 + 33*uk_8 + 51567417*uk_80 + 250047*uk_81 + 63504*uk_82 + 130977*uk_83 + 174636*uk_84 + 369117*uk_85 + 861273*uk_86 + 130977*uk_87 + 16128*uk_88 + 33264*uk_89 + 2242306609*uk_9 + 44352*uk_90 + 93744*uk_91 + 218736*uk_92 + 33264*uk_93 + 68607*uk_94 + 91476*uk_95 + 193347*uk_96 + 451143*uk_97 + 68607*uk_98 + 121968*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 263340*uk_100 + 601524*uk_101 + 44352*uk_102 + 568575*uk_103 + 1298745*uk_104 + 95760*uk_105 + 2966607*uk_106 + 218736*uk_107 + 16128*uk_108 + 79507*uk_109 + 2036179*uk_11 + 29584*uk_110 + 81356*uk_111 + 175655*uk_112 + 401233*uk_113 + 29584*uk_114 + 11008*uk_115 + 30272*uk_116 + 65360*uk_117 + 149296*uk_118 + 11008*uk_119 + 757648*uk_12 + 83248*uk_120 + 179740*uk_121 + 410564*uk_122 + 30272*uk_123 + 388075*uk_124 + 886445*uk_125 + 65360*uk_126 + 2024827*uk_127 + 149296*uk_128 + 11008*uk_129 + 2083532*uk_13 + 4096*uk_130 + 11264*uk_131 + 24320*uk_132 + 55552*uk_133 + 4096*uk_134 + 30976*uk_135 + 66880*uk_136 + 152768*uk_137 + 11264*uk_138 + 144400*uk_139 + 4498535*uk_14 + 329840*uk_140 + 24320*uk_141 + 753424*uk_142 + 55552*uk_143 + 4096*uk_144 + 85184*uk_145 + 183920*uk_146 + 420112*uk_147 + 30976*uk_148 + 397100*uk_149 + 10275601*uk_15 + 907060*uk_150 + 66880*uk_151 + 2071916*uk_152 + 152768*uk_153 + 11264*uk_154 + 857375*uk_155 + 1958425*uk_156 + 144400*uk_157 + 4473455*uk_158 + 329840*uk_159 + 757648*uk_16 + 24320*uk_160 + 10218313*uk_161 + 753424*uk_162 + 55552*uk_163 + 4096*uk_164 + 3969*uk_17 + 2709*uk_18 + 1008*uk_19 + 63*uk_2 + 2772*uk_20 + 5985*uk_21 + 13671*uk_22 + 1008*uk_23 + 1849*uk_24 + 688*uk_25 + 1892*uk_26 + 4085*uk_27 + 9331*uk_28 + 688*uk_29 + 43*uk_3 + 256*uk_30 + 704*uk_31 + 1520*uk_32 + 3472*uk_33 + 256*uk_34 + 1936*uk_35 + 4180*uk_36 + 9548*uk_37 + 704*uk_38 + 9025*uk_39 + 16*uk_4 + 20615*uk_40 + 1520*uk_41 + 47089*uk_42 + 3472*uk_43 + 256*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 96419184187*uk_47 + 35876905744*uk_48 + 98661490796*uk_49 + 44*uk_5 + 213019127855*uk_50 + 486580534153*uk_51 + 35876905744*uk_52 + 187944057*uk_53 + 128279277*uk_54 + 47731824*uk_55 + 131262516*uk_56 + 283407705*uk_57 + 647362863*uk_58 + 47731824*uk_59 + 95*uk_6 + 87555697*uk_60 + 32578864*uk_61 + 89591876*uk_62 + 193437005*uk_63 + 441850843*uk_64 + 32578864*uk_65 + 12122368*uk_66 + 33336512*uk_67 + 71976560*uk_68 + 164409616*uk_69 + 217*uk_7 + 12122368*uk_70 + 91675408*uk_71 + 197935540*uk_72 + 452126444*uk_73 + 33336512*uk_74 + 427360825*uk_75 + 976182095*uk_76 + 71976560*uk_77 + 2229805417*uk_78 + 164409616*uk_79 + 16*uk_8 + 12122368*uk_80 + 250047*uk_81 + 170667*uk_82 + 63504*uk_83 + 174636*uk_84 + 377055*uk_85 + 861273*uk_86 + 63504*uk_87 + 116487*uk_88 + 43344*uk_89 + 2242306609*uk_9 + 119196*uk_90 + 257355*uk_91 + 587853*uk_92 + 43344*uk_93 + 16128*uk_94 + 44352*uk_95 + 95760*uk_96 + 218736*uk_97 + 16128*uk_98 + 121968*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 244440*uk_100 + 546840*uk_101 + 108360*uk_102 + 592767*uk_103 + 1326087*uk_104 + 262773*uk_105 + 2966607*uk_106 + 587853*uk_107 + 116487*uk_108 + 4913*uk_109 + 805001*uk_11 + 12427*uk_110 + 11560*uk_111 + 28033*uk_112 + 62713*uk_113 + 12427*uk_114 + 31433*uk_115 + 29240*uk_116 + 70907*uk_117 + 158627*uk_118 + 31433*uk_119 + 2036179*uk_12 + 27200*uk_120 + 65960*uk_121 + 147560*uk_122 + 29240*uk_123 + 159953*uk_124 + 357833*uk_125 + 70907*uk_126 + 800513*uk_127 + 158627*uk_128 + 31433*uk_129 + 1894120*uk_13 + 79507*uk_130 + 73960*uk_131 + 179353*uk_132 + 401233*uk_133 + 79507*uk_134 + 68800*uk_135 + 166840*uk_136 + 373240*uk_137 + 73960*uk_138 + 404587*uk_139 + 4593241*uk_14 + 905107*uk_140 + 179353*uk_141 + 2024827*uk_142 + 401233*uk_143 + 79507*uk_144 + 64000*uk_145 + 155200*uk_146 + 347200*uk_147 + 68800*uk_148 + 376360*uk_149 + 10275601*uk_15 + 841960*uk_150 + 166840*uk_151 + 1883560*uk_152 + 373240*uk_153 + 73960*uk_154 + 912673*uk_155 + 2041753*uk_156 + 404587*uk_157 + 4567633*uk_158 + 905107*uk_159 + 2036179*uk_16 + 179353*uk_160 + 10218313*uk_161 + 2024827*uk_162 + 401233*uk_163 + 79507*uk_164 + 3969*uk_17 + 1071*uk_18 + 2709*uk_19 + 63*uk_2 + 2520*uk_20 + 6111*uk_21 + 13671*uk_22 + 2709*uk_23 + 289*uk_24 + 731*uk_25 + 680*uk_26 + 1649*uk_27 + 3689*uk_28 + 731*uk_29 + 17*uk_3 + 1849*uk_30 + 1720*uk_31 + 4171*uk_32 + 9331*uk_33 + 1849*uk_34 + 1600*uk_35 + 3880*uk_36 + 8680*uk_37 + 1720*uk_38 + 9409*uk_39 + 43*uk_4 + 21049*uk_40 + 4171*uk_41 + 47089*uk_42 + 9331*uk_43 + 1849*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 38119212353*uk_47 + 96419184187*uk_48 + 89692264360*uk_49 + 40*uk_5 + 217503741073*uk_50 + 486580534153*uk_51 + 96419184187*uk_52 + 187944057*uk_53 + 50715063*uk_54 + 128279277*uk_55 + 119329560*uk_56 + 289374183*uk_57 + 647362863*uk_58 + 128279277*uk_59 + 97*uk_6 + 13685017*uk_60 + 34615043*uk_61 + 32200040*uk_62 + 78085097*uk_63 + 174685217*uk_64 + 34615043*uk_65 + 87555697*uk_66 + 81447160*uk_67 + 197509363*uk_68 + 441850843*uk_69 + 217*uk_7 + 87555697*uk_70 + 75764800*uk_71 + 183729640*uk_72 + 411024040*uk_73 + 81447160*uk_74 + 445544377*uk_75 + 996733297*uk_76 + 197509363*uk_77 + 2229805417*uk_78 + 441850843*uk_79 + 43*uk_8 + 87555697*uk_80 + 250047*uk_81 + 67473*uk_82 + 170667*uk_83 + 158760*uk_84 + 384993*uk_85 + 861273*uk_86 + 170667*uk_87 + 18207*uk_88 + 46053*uk_89 + 2242306609*uk_9 + 42840*uk_90 + 103887*uk_91 + 232407*uk_92 + 46053*uk_93 + 116487*uk_94 + 108360*uk_95 + 262773*uk_96 + 587853*uk_97 + 116487*uk_98 + 100800*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 249480*uk_100 + 546840*uk_101 + 42840*uk_102 + 617463*uk_103 + 1353429*uk_104 + 106029*uk_105 + 2966607*uk_106 + 232407*uk_107 + 18207*uk_108 + 29791*uk_109 + 1467943*uk_11 + 16337*uk_110 + 38440*uk_111 + 95139*uk_112 + 208537*uk_113 + 16337*uk_114 + 8959*uk_115 + 21080*uk_116 + 52173*uk_117 + 114359*uk_118 + 8959*uk_119 + 805001*uk_12 + 49600*uk_120 + 122760*uk_121 + 269080*uk_122 + 21080*uk_123 + 303831*uk_124 + 665973*uk_125 + 52173*uk_126 + 1459759*uk_127 + 114359*uk_128 + 8959*uk_129 + 1894120*uk_13 + 4913*uk_130 + 11560*uk_131 + 28611*uk_132 + 62713*uk_133 + 4913*uk_134 + 27200*uk_135 + 67320*uk_136 + 147560*uk_137 + 11560*uk_138 + 166617*uk_139 + 4687947*uk_14 + 365211*uk_140 + 28611*uk_141 + 800513*uk_142 + 62713*uk_143 + 4913*uk_144 + 64000*uk_145 + 158400*uk_146 + 347200*uk_147 + 27200*uk_148 + 392040*uk_149 + 10275601*uk_15 + 859320*uk_150 + 67320*uk_151 + 1883560*uk_152 + 147560*uk_153 + 11560*uk_154 + 970299*uk_155 + 2126817*uk_156 + 166617*uk_157 + 4661811*uk_158 + 365211*uk_159 + 805001*uk_16 + 28611*uk_160 + 10218313*uk_161 + 800513*uk_162 + 62713*uk_163 + 4913*uk_164 + 3969*uk_17 + 1953*uk_18 + 1071*uk_19 + 63*uk_2 + 2520*uk_20 + 6237*uk_21 + 13671*uk_22 + 1071*uk_23 + 961*uk_24 + 527*uk_25 + 1240*uk_26 + 3069*uk_27 + 6727*uk_28 + 527*uk_29 + 31*uk_3 + 289*uk_30 + 680*uk_31 + 1683*uk_32 + 3689*uk_33 + 289*uk_34 + 1600*uk_35 + 3960*uk_36 + 8680*uk_37 + 680*uk_38 + 9801*uk_39 + 17*uk_4 + 21483*uk_40 + 1683*uk_41 + 47089*uk_42 + 3689*uk_43 + 289*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 69511504879*uk_47 + 38119212353*uk_48 + 89692264360*uk_49 + 40*uk_5 + 221988354291*uk_50 + 486580534153*uk_51 + 38119212353*uk_52 + 187944057*uk_53 + 92480409*uk_54 + 50715063*uk_55 + 119329560*uk_56 + 295340661*uk_57 + 647362863*uk_58 + 50715063*uk_59 + 99*uk_6 + 45506233*uk_60 + 24955031*uk_61 + 58717720*uk_62 + 145326357*uk_63 + 318543631*uk_64 + 24955031*uk_65 + 13685017*uk_66 + 32200040*uk_67 + 79695099*uk_68 + 174685217*uk_69 + 217*uk_7 + 13685017*uk_70 + 75764800*uk_71 + 187517880*uk_72 + 411024040*uk_73 + 32200040*uk_74 + 464106753*uk_75 + 1017284499*uk_76 + 79695099*uk_77 + 2229805417*uk_78 + 174685217*uk_79 + 17*uk_8 + 13685017*uk_80 + 250047*uk_81 + 123039*uk_82 + 67473*uk_83 + 158760*uk_84 + 392931*uk_85 + 861273*uk_86 + 67473*uk_87 + 60543*uk_88 + 33201*uk_89 + 2242306609*uk_9 + 78120*uk_90 + 193347*uk_91 + 423801*uk_92 + 33201*uk_93 + 18207*uk_94 + 42840*uk_95 + 106029*uk_96 + 232407*uk_97 + 18207*uk_98 + 100800*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 254520*uk_100 + 546840*uk_101 + 78120*uk_102 + 642663*uk_103 + 1380771*uk_104 + 197253*uk_105 + 2966607*uk_106 + 423801*uk_107 + 60543*uk_108 + 614125*uk_109 + 4025005*uk_11 + 223975*uk_110 + 289000*uk_111 + 729725*uk_112 + 1567825*uk_113 + 223975*uk_114 + 81685*uk_115 + 105400*uk_116 + 266135*uk_117 + 571795*uk_118 + 81685*uk_119 + 1467943*uk_12 + 136000*uk_120 + 343400*uk_121 + 737800*uk_122 + 105400*uk_123 + 867085*uk_124 + 1862945*uk_125 + 266135*uk_126 + 4002565*uk_127 + 571795*uk_128 + 81685*uk_129 + 1894120*uk_13 + 29791*uk_130 + 38440*uk_131 + 97061*uk_132 + 208537*uk_133 + 29791*uk_134 + 49600*uk_135 + 125240*uk_136 + 269080*uk_137 + 38440*uk_138 + 316231*uk_139 + 4782653*uk_14 + 679427*uk_140 + 97061*uk_141 + 1459759*uk_142 + 208537*uk_143 + 29791*uk_144 + 64000*uk_145 + 161600*uk_146 + 347200*uk_147 + 49600*uk_148 + 408040*uk_149 + 10275601*uk_15 + 876680*uk_150 + 125240*uk_151 + 1883560*uk_152 + 269080*uk_153 + 38440*uk_154 + 1030301*uk_155 + 2213617*uk_156 + 316231*uk_157 + 4755989*uk_158 + 679427*uk_159 + 1467943*uk_16 + 97061*uk_160 + 10218313*uk_161 + 1459759*uk_162 + 208537*uk_163 + 29791*uk_164 + 3969*uk_17 + 5355*uk_18 + 1953*uk_19 + 63*uk_2 + 2520*uk_20 + 6363*uk_21 + 13671*uk_22 + 1953*uk_23 + 7225*uk_24 + 2635*uk_25 + 3400*uk_26 + 8585*uk_27 + 18445*uk_28 + 2635*uk_29 + 85*uk_3 + 961*uk_30 + 1240*uk_31 + 3131*uk_32 + 6727*uk_33 + 961*uk_34 + 1600*uk_35 + 4040*uk_36 + 8680*uk_37 + 1240*uk_38 + 10201*uk_39 + 31*uk_4 + 21917*uk_40 + 3131*uk_41 + 47089*uk_42 + 6727*uk_43 + 961*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 190596061765*uk_47 + 69511504879*uk_48 + 89692264360*uk_49 + 40*uk_5 + 226472967509*uk_50 + 486580534153*uk_51 + 69511504879*uk_52 + 187944057*uk_53 + 253575315*uk_54 + 92480409*uk_55 + 119329560*uk_56 + 301307139*uk_57 + 647362863*uk_58 + 92480409*uk_59 + 101*uk_6 + 342125425*uk_60 + 124775155*uk_61 + 161000200*uk_62 + 406525505*uk_63 + 873426085*uk_64 + 124775155*uk_65 + 45506233*uk_66 + 58717720*uk_67 + 148262243*uk_68 + 318543631*uk_69 + 217*uk_7 + 45506233*uk_70 + 75764800*uk_71 + 191306120*uk_72 + 411024040*uk_73 + 58717720*uk_74 + 483047953*uk_75 + 1037835701*uk_76 + 148262243*uk_77 + 2229805417*uk_78 + 318543631*uk_79 + 31*uk_8 + 45506233*uk_80 + 250047*uk_81 + 337365*uk_82 + 123039*uk_83 + 158760*uk_84 + 400869*uk_85 + 861273*uk_86 + 123039*uk_87 + 455175*uk_88 + 166005*uk_89 + 2242306609*uk_9 + 214200*uk_90 + 540855*uk_91 + 1162035*uk_92 + 166005*uk_93 + 60543*uk_94 + 78120*uk_95 + 197253*uk_96 + 423801*uk_97 + 60543*uk_98 + 100800*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 238140*uk_100 + 492156*uk_101 + 172368*uk_102 + 694575*uk_103 + 1435455*uk_104 + 502740*uk_105 + 2966607*uk_106 + 1038996*uk_107 + 363888*uk_108 + 1092727*uk_109 + 4877359*uk_11 + 806284*uk_110 + 381924*uk_111 + 1113945*uk_112 + 2302153*uk_113 + 806284*uk_114 + 594928*uk_115 + 281808*uk_116 + 821940*uk_117 + 1698676*uk_118 + 594928*uk_119 + 3598828*uk_12 + 133488*uk_120 + 389340*uk_121 + 804636*uk_122 + 281808*uk_123 + 1135575*uk_124 + 2346855*uk_125 + 821940*uk_126 + 4850167*uk_127 + 1698676*uk_128 + 594928*uk_129 + 1704708*uk_13 + 438976*uk_130 + 207936*uk_131 + 606480*uk_132 + 1253392*uk_133 + 438976*uk_134 + 98496*uk_135 + 287280*uk_136 + 593712*uk_137 + 207936*uk_138 + 837900*uk_139 + 4972065*uk_14 + 1731660*uk_140 + 606480*uk_141 + 3578764*uk_142 + 1253392*uk_143 + 438976*uk_144 + 46656*uk_145 + 136080*uk_146 + 281232*uk_147 + 98496*uk_148 + 396900*uk_149 + 10275601*uk_15 + 820260*uk_150 + 287280*uk_151 + 1695204*uk_152 + 593712*uk_153 + 207936*uk_154 + 1157625*uk_155 + 2392425*uk_156 + 837900*uk_157 + 4944345*uk_158 + 1731660*uk_159 + 3598828*uk_16 + 606480*uk_160 + 10218313*uk_161 + 3578764*uk_162 + 1253392*uk_163 + 438976*uk_164 + 3969*uk_17 + 6489*uk_18 + 4788*uk_19 + 63*uk_2 + 2268*uk_20 + 6615*uk_21 + 13671*uk_22 + 4788*uk_23 + 10609*uk_24 + 7828*uk_25 + 3708*uk_26 + 10815*uk_27 + 22351*uk_28 + 7828*uk_29 + 103*uk_3 + 5776*uk_30 + 2736*uk_31 + 7980*uk_32 + 16492*uk_33 + 5776*uk_34 + 1296*uk_35 + 3780*uk_36 + 7812*uk_37 + 2736*uk_38 + 11025*uk_39 + 76*uk_4 + 22785*uk_40 + 7980*uk_41 + 47089*uk_42 + 16492*uk_43 + 5776*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 230957580727*uk_47 + 170415302284*uk_48 + 80723037924*uk_49 + 36*uk_5 + 235442193945*uk_50 + 486580534153*uk_51 + 170415302284*uk_52 + 187944057*uk_53 + 307273617*uk_54 + 226726164*uk_55 + 107396604*uk_56 + 313240095*uk_57 + 647362863*uk_58 + 226726164*uk_59 + 105*uk_6 + 502367977*uk_60 + 370679284*uk_61 + 175584924*uk_62 + 512122695*uk_63 + 1058386903*uk_64 + 370679284*uk_65 + 273510928*uk_66 + 129557808*uk_67 + 377876940*uk_68 + 780945676*uk_69 + 217*uk_7 + 273510928*uk_70 + 61369488*uk_71 + 178994340*uk_72 + 369921636*uk_73 + 129557808*uk_74 + 522066825*uk_75 + 1078938105*uk_76 + 377876940*uk_77 + 2229805417*uk_78 + 780945676*uk_79 + 76*uk_8 + 273510928*uk_80 + 250047*uk_81 + 408807*uk_82 + 301644*uk_83 + 142884*uk_84 + 416745*uk_85 + 861273*uk_86 + 301644*uk_87 + 668367*uk_88 + 493164*uk_89 + 2242306609*uk_9 + 233604*uk_90 + 681345*uk_91 + 1408113*uk_92 + 493164*uk_93 + 363888*uk_94 + 172368*uk_95 + 502740*uk_96 + 1038996*uk_97 + 363888*uk_98 + 81648*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 215712*uk_100 + 437472*uk_101 + 207648*uk_102 + 721287*uk_103 + 1462797*uk_104 + 694323*uk_105 + 2966607*uk_106 + 1408113*uk_107 + 668367*uk_108 + 205379*uk_109 + 2793827*uk_11 + 358543*uk_110 + 111392*uk_111 + 372467*uk_112 + 755377*uk_113 + 358543*uk_114 + 625931*uk_115 + 194464*uk_116 + 650239*uk_117 + 1318709*uk_118 + 625931*uk_119 + 4877359*uk_12 + 60416*uk_120 + 202016*uk_121 + 409696*uk_122 + 194464*uk_123 + 675491*uk_124 + 1369921*uk_125 + 650239*uk_126 + 2778251*uk_127 + 1318709*uk_128 + 625931*uk_129 + 1515296*uk_13 + 1092727*uk_130 + 339488*uk_131 + 1135163*uk_132 + 2302153*uk_133 + 1092727*uk_134 + 105472*uk_135 + 352672*uk_136 + 715232*uk_137 + 339488*uk_138 + 1179247*uk_139 + 5066771*uk_14 + 2391557*uk_140 + 1135163*uk_141 + 4850167*uk_142 + 2302153*uk_143 + 1092727*uk_144 + 32768*uk_145 + 109568*uk_146 + 222208*uk_147 + 105472*uk_148 + 366368*uk_149 + 10275601*uk_15 + 743008*uk_150 + 352672*uk_151 + 1506848*uk_152 + 715232*uk_153 + 339488*uk_154 + 1225043*uk_155 + 2484433*uk_156 + 1179247*uk_157 + 5038523*uk_158 + 2391557*uk_159 + 4877359*uk_16 + 1135163*uk_160 + 10218313*uk_161 + 4850167*uk_162 + 2302153*uk_163 + 1092727*uk_164 + 3969*uk_17 + 3717*uk_18 + 6489*uk_19 + 63*uk_2 + 2016*uk_20 + 6741*uk_21 + 13671*uk_22 + 6489*uk_23 + 3481*uk_24 + 6077*uk_25 + 1888*uk_26 + 6313*uk_27 + 12803*uk_28 + 6077*uk_29 + 59*uk_3 + 10609*uk_30 + 3296*uk_31 + 11021*uk_32 + 22351*uk_33 + 10609*uk_34 + 1024*uk_35 + 3424*uk_36 + 6944*uk_37 + 3296*uk_38 + 11449*uk_39 + 103*uk_4 + 23219*uk_40 + 11021*uk_41 + 47089*uk_42 + 22351*uk_43 + 10609*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 132296089931*uk_47 + 230957580727*uk_48 + 71753811488*uk_49 + 32*uk_5 + 239926807163*uk_50 + 486580534153*uk_51 + 230957580727*uk_52 + 187944057*uk_53 + 176011101*uk_54 + 307273617*uk_55 + 95463648*uk_56 + 319206573*uk_57 + 647362863*uk_58 + 307273617*uk_59 + 107*uk_6 + 164835793*uk_60 + 287764181*uk_61 + 89402464*uk_62 + 298939489*uk_63 + 606260459*uk_64 + 287764181*uk_65 + 502367977*uk_66 + 156075488*uk_67 + 521877413*uk_68 + 1058386903*uk_69 + 217*uk_7 + 502367977*uk_70 + 48489472*uk_71 + 162136672*uk_72 + 328819232*uk_73 + 156075488*uk_74 + 542144497*uk_75 + 1099489307*uk_76 + 521877413*uk_77 + 2229805417*uk_78 + 1058386903*uk_79 + 103*uk_8 + 502367977*uk_80 + 250047*uk_81 + 234171*uk_82 + 408807*uk_83 + 127008*uk_84 + 424683*uk_85 + 861273*uk_86 + 408807*uk_87 + 219303*uk_88 + 382851*uk_89 + 2242306609*uk_9 + 118944*uk_90 + 397719*uk_91 + 806589*uk_92 + 382851*uk_93 + 668367*uk_94 + 207648*uk_95 + 694323*uk_96 + 1408113*uk_97 + 668367*uk_98 + 64512*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 223776*uk_100 + 437472*uk_101 + 94752*uk_102 + 776223*uk_103 + 1517481*uk_104 + 328671*uk_105 + 2966607*uk_106 + 642537*uk_107 + 139167*uk_108 + 300763*uk_109 + 3172651*uk_11 + 210983*uk_110 + 143648*uk_111 + 498279*uk_112 + 974113*uk_113 + 210983*uk_114 + 148003*uk_115 + 100768*uk_116 + 349539*uk_117 + 683333*uk_118 + 148003*uk_119 + 2225591*uk_12 + 68608*uk_120 + 237984*uk_121 + 465248*uk_122 + 100768*uk_123 + 825507*uk_124 + 1613829*uk_125 + 349539*uk_126 + 3154963*uk_127 + 683333*uk_128 + 148003*uk_129 + 1515296*uk_13 + 103823*uk_130 + 70688*uk_131 + 245199*uk_132 + 479353*uk_133 + 103823*uk_134 + 48128*uk_135 + 166944*uk_136 + 326368*uk_137 + 70688*uk_138 + 579087*uk_139 + 5256183*uk_14 + 1132089*uk_140 + 245199*uk_141 + 2213183*uk_142 + 479353*uk_143 + 103823*uk_144 + 32768*uk_145 + 113664*uk_146 + 222208*uk_147 + 48128*uk_148 + 394272*uk_149 + 10275601*uk_15 + 770784*uk_150 + 166944*uk_151 + 1506848*uk_152 + 326368*uk_153 + 70688*uk_154 + 1367631*uk_155 + 2673657*uk_156 + 579087*uk_157 + 5226879*uk_158 + 1132089*uk_159 + 2225591*uk_16 + 245199*uk_160 + 10218313*uk_161 + 2213183*uk_162 + 479353*uk_163 + 103823*uk_164 + 3969*uk_17 + 4221*uk_18 + 2961*uk_19 + 63*uk_2 + 2016*uk_20 + 6993*uk_21 + 13671*uk_22 + 2961*uk_23 + 4489*uk_24 + 3149*uk_25 + 2144*uk_26 + 7437*uk_27 + 14539*uk_28 + 3149*uk_29 + 67*uk_3 + 2209*uk_30 + 1504*uk_31 + 5217*uk_32 + 10199*uk_33 + 2209*uk_34 + 1024*uk_35 + 3552*uk_36 + 6944*uk_37 + 1504*uk_38 + 12321*uk_39 + 47*uk_4 + 24087*uk_40 + 5217*uk_41 + 47089*uk_42 + 10199*uk_43 + 2209*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 150234542803*uk_47 + 105388410623*uk_48 + 71753811488*uk_49 + 32*uk_5 + 248896033599*uk_50 + 486580534153*uk_51 + 105388410623*uk_52 + 187944057*uk_53 + 199877013*uk_54 + 140212233*uk_55 + 95463648*uk_56 + 331139529*uk_57 + 647362863*uk_58 + 140212233*uk_59 + 111*uk_6 + 212567617*uk_60 + 149114597*uk_61 + 101524832*uk_62 + 352164261*uk_63 + 688465267*uk_64 + 149114597*uk_65 + 104602777*uk_66 + 71218912*uk_67 + 247040601*uk_68 + 482953247*uk_69 + 217*uk_7 + 104602777*uk_70 + 48489472*uk_71 + 168197856*uk_72 + 328819232*uk_73 + 71218912*uk_74 + 583436313*uk_75 + 1140591711*uk_76 + 247040601*uk_77 + 2229805417*uk_78 + 482953247*uk_79 + 47*uk_8 + 104602777*uk_80 + 250047*uk_81 + 265923*uk_82 + 186543*uk_83 + 127008*uk_84 + 440559*uk_85 + 861273*uk_86 + 186543*uk_87 + 282807*uk_88 + 198387*uk_89 + 2242306609*uk_9 + 135072*uk_90 + 468531*uk_91 + 915957*uk_92 + 198387*uk_93 + 139167*uk_94 + 94752*uk_95 + 328671*uk_96 + 642537*uk_97 + 139167*uk_98 + 64512*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 206388*uk_100 + 382788*uk_101 + 155232*uk_102 + 862407*uk_103 + 1599507*uk_104 + 648648*uk_105 + 2966607*uk_106 + 1203048*uk_107 + 487872*uk_108 + 614125*uk_109 + 4025005*uk_11 + 635800*uk_110 + 202300*uk_111 + 845325*uk_112 + 1567825*uk_113 + 635800*uk_114 + 658240*uk_115 + 209440*uk_116 + 875160*uk_117 + 1623160*uk_118 + 658240*uk_119 + 4167064*uk_12 + 66640*uk_120 + 278460*uk_121 + 516460*uk_122 + 209440*uk_123 + 1163565*uk_124 + 2158065*uk_125 + 875160*uk_126 + 4002565*uk_127 + 1623160*uk_128 + 658240*uk_129 + 1325884*uk_13 + 681472*uk_130 + 216832*uk_131 + 906048*uk_132 + 1680448*uk_133 + 681472*uk_134 + 68992*uk_135 + 288288*uk_136 + 534688*uk_137 + 216832*uk_138 + 1204632*uk_139 + 5540301*uk_14 + 2234232*uk_140 + 906048*uk_141 + 4143832*uk_142 + 1680448*uk_143 + 681472*uk_144 + 21952*uk_145 + 91728*uk_146 + 170128*uk_147 + 68992*uk_148 + 383292*uk_149 + 10275601*uk_15 + 710892*uk_150 + 288288*uk_151 + 1318492*uk_152 + 534688*uk_153 + 216832*uk_154 + 1601613*uk_155 + 2970513*uk_156 + 1204632*uk_157 + 5509413*uk_158 + 2234232*uk_159 + 4167064*uk_16 + 906048*uk_160 + 10218313*uk_161 + 4143832*uk_162 + 1680448*uk_163 + 681472*uk_164 + 3969*uk_17 + 5355*uk_18 + 5544*uk_19 + 63*uk_2 + 1764*uk_20 + 7371*uk_21 + 13671*uk_22 + 5544*uk_23 + 7225*uk_24 + 7480*uk_25 + 2380*uk_26 + 9945*uk_27 + 18445*uk_28 + 7480*uk_29 + 85*uk_3 + 7744*uk_30 + 2464*uk_31 + 10296*uk_32 + 19096*uk_33 + 7744*uk_34 + 784*uk_35 + 3276*uk_36 + 6076*uk_37 + 2464*uk_38 + 13689*uk_39 + 88*uk_4 + 25389*uk_40 + 10296*uk_41 + 47089*uk_42 + 19096*uk_43 + 7744*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 190596061765*uk_47 + 197322981592*uk_48 + 62784585052*uk_49 + 28*uk_5 + 262349873253*uk_50 + 486580534153*uk_51 + 197322981592*uk_52 + 187944057*uk_53 + 253575315*uk_54 + 262525032*uk_55 + 83530692*uk_56 + 349038963*uk_57 + 647362863*uk_58 + 262525032*uk_59 + 117*uk_6 + 342125425*uk_60 + 354200440*uk_61 + 112700140*uk_62 + 470925585*uk_63 + 873426085*uk_64 + 354200440*uk_65 + 366701632*uk_66 + 116677792*uk_67 + 487546488*uk_68 + 904252888*uk_69 + 217*uk_7 + 366701632*uk_70 + 37124752*uk_71 + 155128428*uk_72 + 287716828*uk_73 + 116677792*uk_74 + 648215217*uk_75 + 1202245317*uk_76 + 487546488*uk_77 + 2229805417*uk_78 + 904252888*uk_79 + 88*uk_8 + 366701632*uk_80 + 250047*uk_81 + 337365*uk_82 + 349272*uk_83 + 111132*uk_84 + 464373*uk_85 + 861273*uk_86 + 349272*uk_87 + 455175*uk_88 + 471240*uk_89 + 2242306609*uk_9 + 149940*uk_90 + 626535*uk_91 + 1162035*uk_92 + 471240*uk_93 + 487872*uk_94 + 155232*uk_95 + 648648*uk_96 + 1203048*uk_97 + 487872*uk_98 + 49392*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 209916*uk_100 + 382788*uk_101 + 149940*uk_102 + 892143*uk_103 + 1626849*uk_104 + 637245*uk_105 + 2966607*uk_106 + 1162035*uk_107 + 455175*uk_108 + 1331000*uk_109 + 5208830*uk_11 + 1028500*uk_110 + 338800*uk_111 + 1439900*uk_112 + 2625700*uk_113 + 1028500*uk_114 + 794750*uk_115 + 261800*uk_116 + 1112650*uk_117 + 2028950*uk_118 + 794750*uk_119 + 4025005*uk_12 + 86240*uk_120 + 366520*uk_121 + 668360*uk_122 + 261800*uk_123 + 1557710*uk_124 + 2840530*uk_125 + 1112650*uk_126 + 5179790*uk_127 + 2028950*uk_128 + 794750*uk_129 + 1325884*uk_13 + 614125*uk_130 + 202300*uk_131 + 859775*uk_132 + 1567825*uk_133 + 614125*uk_134 + 66640*uk_135 + 283220*uk_136 + 516460*uk_137 + 202300*uk_138 + 1203685*uk_139 + 5635007*uk_14 + 2194955*uk_140 + 859775*uk_141 + 4002565*uk_142 + 1567825*uk_143 + 614125*uk_144 + 21952*uk_145 + 93296*uk_146 + 170128*uk_147 + 66640*uk_148 + 396508*uk_149 + 10275601*uk_15 + 723044*uk_150 + 283220*uk_151 + 1318492*uk_152 + 516460*uk_153 + 202300*uk_154 + 1685159*uk_155 + 3072937*uk_156 + 1203685*uk_157 + 5603591*uk_158 + 2194955*uk_159 + 4025005*uk_16 + 859775*uk_160 + 10218313*uk_161 + 4002565*uk_162 + 1567825*uk_163 + 614125*uk_164 + 3969*uk_17 + 6930*uk_18 + 5355*uk_19 + 63*uk_2 + 1764*uk_20 + 7497*uk_21 + 13671*uk_22 + 5355*uk_23 + 12100*uk_24 + 9350*uk_25 + 3080*uk_26 + 13090*uk_27 + 23870*uk_28 + 9350*uk_29 + 110*uk_3 + 7225*uk_30 + 2380*uk_31 + 10115*uk_32 + 18445*uk_33 + 7225*uk_34 + 784*uk_35 + 3332*uk_36 + 6076*uk_37 + 2380*uk_38 + 14161*uk_39 + 85*uk_4 + 25823*uk_40 + 10115*uk_41 + 47089*uk_42 + 18445*uk_43 + 7225*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 246653726990*uk_47 + 190596061765*uk_48 + 62784585052*uk_49 + 28*uk_5 + 266834486471*uk_50 + 486580534153*uk_51 + 190596061765*uk_52 + 187944057*uk_53 + 328156290*uk_54 + 253575315*uk_55 + 83530692*uk_56 + 355005441*uk_57 + 647362863*uk_58 + 253575315*uk_59 + 119*uk_6 + 572971300*uk_60 + 442750550*uk_61 + 145847240*uk_62 + 619850770*uk_63 + 1130316110*uk_64 + 442750550*uk_65 + 342125425*uk_66 + 112700140*uk_67 + 478975595*uk_68 + 873426085*uk_69 + 217*uk_7 + 342125425*uk_70 + 37124752*uk_71 + 157780196*uk_72 + 287716828*uk_73 + 112700140*uk_74 + 670565833*uk_75 + 1222796519*uk_76 + 478975595*uk_77 + 2229805417*uk_78 + 873426085*uk_79 + 85*uk_8 + 342125425*uk_80 + 250047*uk_81 + 436590*uk_82 + 337365*uk_83 + 111132*uk_84 + 472311*uk_85 + 861273*uk_86 + 337365*uk_87 + 762300*uk_88 + 589050*uk_89 + 2242306609*uk_9 + 194040*uk_90 + 824670*uk_91 + 1503810*uk_92 + 589050*uk_93 + 455175*uk_94 + 149940*uk_95 + 637245*uk_96 + 1162035*uk_97 + 455175*uk_98 + 49392*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 182952*uk_100 + 328104*uk_101 + 166320*uk_102 + 922383*uk_103 + 1654191*uk_104 + 838530*uk_105 + 2966607*uk_106 + 1503810*uk_107 + 762300*uk_108 + 74088*uk_109 + 1988826*uk_11 + 194040*uk_110 + 42336*uk_111 + 213444*uk_112 + 382788*uk_113 + 194040*uk_114 + 508200*uk_115 + 110880*uk_116 + 559020*uk_117 + 1002540*uk_118 + 508200*uk_119 + 5208830*uk_12 + 24192*uk_120 + 121968*uk_121 + 218736*uk_122 + 110880*uk_123 + 614922*uk_124 + 1102794*uk_125 + 559020*uk_126 + 1977738*uk_127 + 1002540*uk_128 + 508200*uk_129 + 1136472*uk_13 + 1331000*uk_130 + 290400*uk_131 + 1464100*uk_132 + 2625700*uk_133 + 1331000*uk_134 + 63360*uk_135 + 319440*uk_136 + 572880*uk_137 + 290400*uk_138 + 1610510*uk_139 + 5729713*uk_14 + 2888270*uk_140 + 1464100*uk_141 + 5179790*uk_142 + 2625700*uk_143 + 1331000*uk_144 + 13824*uk_145 + 69696*uk_146 + 124992*uk_147 + 63360*uk_148 + 351384*uk_149 + 10275601*uk_15 + 630168*uk_150 + 319440*uk_151 + 1130136*uk_152 + 572880*uk_153 + 290400*uk_154 + 1771561*uk_155 + 3177097*uk_156 + 1610510*uk_157 + 5697769*uk_158 + 2888270*uk_159 + 5208830*uk_16 + 1464100*uk_160 + 10218313*uk_161 + 5179790*uk_162 + 2625700*uk_163 + 1331000*uk_164 + 3969*uk_17 + 2646*uk_18 + 6930*uk_19 + 63*uk_2 + 1512*uk_20 + 7623*uk_21 + 13671*uk_22 + 6930*uk_23 + 1764*uk_24 + 4620*uk_25 + 1008*uk_26 + 5082*uk_27 + 9114*uk_28 + 4620*uk_29 + 42*uk_3 + 12100*uk_30 + 2640*uk_31 + 13310*uk_32 + 23870*uk_33 + 12100*uk_34 + 576*uk_35 + 2904*uk_36 + 5208*uk_37 + 2640*uk_38 + 14641*uk_39 + 110*uk_4 + 26257*uk_40 + 13310*uk_41 + 47089*uk_42 + 23870*uk_43 + 12100*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 94176877578*uk_47 + 246653726990*uk_48 + 53815358616*uk_49 + 24*uk_5 + 271319099689*uk_50 + 486580534153*uk_51 + 246653726990*uk_52 + 187944057*uk_53 + 125296038*uk_54 + 328156290*uk_55 + 71597736*uk_56 + 360971919*uk_57 + 647362863*uk_58 + 328156290*uk_59 + 121*uk_6 + 83530692*uk_60 + 218770860*uk_61 + 47731824*uk_62 + 240647946*uk_63 + 431575242*uk_64 + 218770860*uk_65 + 572971300*uk_66 + 125011920*uk_67 + 630268430*uk_68 + 1130316110*uk_69 + 217*uk_7 + 572971300*uk_70 + 27275328*uk_71 + 137513112*uk_72 + 246614424*uk_73 + 125011920*uk_74 + 693295273*uk_75 + 1243347721*uk_76 + 630268430*uk_77 + 2229805417*uk_78 + 1130316110*uk_79 + 110*uk_8 + 572971300*uk_80 + 250047*uk_81 + 166698*uk_82 + 436590*uk_83 + 95256*uk_84 + 480249*uk_85 + 861273*uk_86 + 436590*uk_87 + 111132*uk_88 + 291060*uk_89 + 2242306609*uk_9 + 63504*uk_90 + 320166*uk_91 + 574182*uk_92 + 291060*uk_93 + 762300*uk_94 + 166320*uk_95 + 838530*uk_96 + 1503810*uk_97 + 762300*uk_98 + 36288*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 162540*uk_100 + 273420*uk_101 + 137340*uk_102 + 1048383*uk_103 + 1763559*uk_104 + 885843*uk_105 + 2966607*uk_106 + 1490139*uk_107 + 748503*uk_108 + 1000*uk_109 + 473530*uk_11 + 10900*uk_110 + 2000*uk_111 + 12900*uk_112 + 21700*uk_113 + 10900*uk_114 + 118810*uk_115 + 21800*uk_116 + 140610*uk_117 + 236530*uk_118 + 118810*uk_119 + 5161477*uk_12 + 4000*uk_120 + 25800*uk_121 + 43400*uk_122 + 21800*uk_123 + 166410*uk_124 + 279930*uk_125 + 140610*uk_126 + 470890*uk_127 + 236530*uk_128 + 118810*uk_129 + 947060*uk_13 + 1295029*uk_130 + 237620*uk_131 + 1532649*uk_132 + 2578177*uk_133 + 1295029*uk_134 + 43600*uk_135 + 281220*uk_136 + 473060*uk_137 + 237620*uk_138 + 1813869*uk_139 + 6108537*uk_14 + 3051237*uk_140 + 1532649*uk_141 + 5132701*uk_142 + 2578177*uk_143 + 1295029*uk_144 + 8000*uk_145 + 51600*uk_146 + 86800*uk_147 + 43600*uk_148 + 332820*uk_149 + 10275601*uk_15 + 559860*uk_150 + 281220*uk_151 + 941780*uk_152 + 473060*uk_153 + 237620*uk_154 + 2146689*uk_155 + 3611097*uk_156 + 1813869*uk_157 + 6074481*uk_158 + 3051237*uk_159 + 5161477*uk_16 + 1532649*uk_160 + 10218313*uk_161 + 5132701*uk_162 + 2578177*uk_163 + 1295029*uk_164 + 3969*uk_17 + 630*uk_18 + 6867*uk_19 + 63*uk_2 + 1260*uk_20 + 8127*uk_21 + 13671*uk_22 + 6867*uk_23 + 100*uk_24 + 1090*uk_25 + 200*uk_26 + 1290*uk_27 + 2170*uk_28 + 1090*uk_29 + 10*uk_3 + 11881*uk_30 + 2180*uk_31 + 14061*uk_32 + 23653*uk_33 + 11881*uk_34 + 400*uk_35 + 2580*uk_36 + 4340*uk_37 + 2180*uk_38 + 16641*uk_39 + 109*uk_4 + 27993*uk_40 + 14061*uk_41 + 47089*uk_42 + 23653*uk_43 + 11881*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 22423066090*uk_47 + 244411420381*uk_48 + 44846132180*uk_49 + 20*uk_5 + 289257552561*uk_50 + 486580534153*uk_51 + 244411420381*uk_52 + 187944057*uk_53 + 29832390*uk_54 + 325173051*uk_55 + 59664780*uk_56 + 384837831*uk_57 + 647362863*uk_58 + 325173051*uk_59 + 129*uk_6 + 4735300*uk_60 + 51614770*uk_61 + 9470600*uk_62 + 61085370*uk_63 + 102756010*uk_64 + 51614770*uk_65 + 562600993*uk_66 + 103229540*uk_67 + 665830533*uk_68 + 1120040509*uk_69 + 217*uk_7 + 562600993*uk_70 + 18941200*uk_71 + 122170740*uk_72 + 205512020*uk_73 + 103229540*uk_74 + 788001273*uk_75 + 1325552529*uk_76 + 665830533*uk_77 + 2229805417*uk_78 + 1120040509*uk_79 + 109*uk_8 + 562600993*uk_80 + 250047*uk_81 + 39690*uk_82 + 432621*uk_83 + 79380*uk_84 + 512001*uk_85 + 861273*uk_86 + 432621*uk_87 + 6300*uk_88 + 68670*uk_89 + 2242306609*uk_9 + 12600*uk_90 + 81270*uk_91 + 136710*uk_92 + 68670*uk_93 + 748503*uk_94 + 137340*uk_95 + 885843*uk_96 + 1490139*uk_97 + 748503*uk_98 + 25200*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 198072*uk_100 + 328104*uk_101 + 15120*uk_102 + 1081143*uk_103 + 1790901*uk_104 + 82530*uk_105 + 2966607*uk_106 + 136710*uk_107 + 6300*uk_108 + 238328*uk_109 + 2935886*uk_11 + 38440*uk_110 + 92256*uk_111 + 503564*uk_112 + 834148*uk_113 + 38440*uk_114 + 6200*uk_115 + 14880*uk_116 + 81220*uk_117 + 134540*uk_118 + 6200*uk_119 + 473530*uk_12 + 35712*uk_120 + 194928*uk_121 + 322896*uk_122 + 14880*uk_123 + 1063982*uk_124 + 1762474*uk_125 + 81220*uk_126 + 2919518*uk_127 + 134540*uk_128 + 6200*uk_129 + 1136472*uk_13 + 1000*uk_130 + 2400*uk_131 + 13100*uk_132 + 21700*uk_133 + 1000*uk_134 + 5760*uk_135 + 31440*uk_136 + 52080*uk_137 + 2400*uk_138 + 171610*uk_139 + 6203243*uk_14 + 284270*uk_140 + 13100*uk_141 + 470890*uk_142 + 21700*uk_143 + 1000*uk_144 + 13824*uk_145 + 75456*uk_146 + 124992*uk_147 + 5760*uk_148 + 411864*uk_149 + 10275601*uk_15 + 682248*uk_150 + 31440*uk_151 + 1130136*uk_152 + 52080*uk_153 + 2400*uk_154 + 2248091*uk_155 + 3723937*uk_156 + 171610*uk_157 + 6168659*uk_158 + 284270*uk_159 + 473530*uk_16 + 13100*uk_160 + 10218313*uk_161 + 470890*uk_162 + 21700*uk_163 + 1000*uk_164 + 3969*uk_17 + 3906*uk_18 + 630*uk_19 + 63*uk_2 + 1512*uk_20 + 8253*uk_21 + 13671*uk_22 + 630*uk_23 + 3844*uk_24 + 620*uk_25 + 1488*uk_26 + 8122*uk_27 + 13454*uk_28 + 620*uk_29 + 62*uk_3 + 100*uk_30 + 240*uk_31 + 1310*uk_32 + 2170*uk_33 + 100*uk_34 + 576*uk_35 + 3144*uk_36 + 5208*uk_37 + 240*uk_38 + 17161*uk_39 + 10*uk_4 + 28427*uk_40 + 1310*uk_41 + 47089*uk_42 + 2170*uk_43 + 100*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 139023009758*uk_47 + 22423066090*uk_48 + 53815358616*uk_49 + 24*uk_5 + 293742165779*uk_50 + 486580534153*uk_51 + 22423066090*uk_52 + 187944057*uk_53 + 184960818*uk_54 + 29832390*uk_55 + 71597736*uk_56 + 390804309*uk_57 + 647362863*uk_58 + 29832390*uk_59 + 131*uk_6 + 182024932*uk_60 + 29358860*uk_61 + 70461264*uk_62 + 384601066*uk_63 + 637087262*uk_64 + 29358860*uk_65 + 4735300*uk_66 + 11364720*uk_67 + 62032430*uk_68 + 102756010*uk_69 + 217*uk_7 + 4735300*uk_70 + 27275328*uk_71 + 148877832*uk_72 + 246614424*uk_73 + 11364720*uk_74 + 812624833*uk_75 + 1346103731*uk_76 + 62032430*uk_77 + 2229805417*uk_78 + 102756010*uk_79 + 10*uk_8 + 4735300*uk_80 + 250047*uk_81 + 246078*uk_82 + 39690*uk_83 + 95256*uk_84 + 519939*uk_85 + 861273*uk_86 + 39690*uk_87 + 242172*uk_88 + 39060*uk_89 + 2242306609*uk_9 + 93744*uk_90 + 511686*uk_91 + 847602*uk_92 + 39060*uk_93 + 6300*uk_94 + 15120*uk_95 + 82530*uk_96 + 136710*uk_97 + 6300*uk_98 + 36288*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 167580*uk_100 + 273420*uk_101 + 78120*uk_102 + 1114407*uk_103 + 1818243*uk_104 + 519498*uk_105 + 2966607*uk_106 + 847602*uk_107 + 242172*uk_108 + 125*uk_109 + 236765*uk_11 + 1550*uk_110 + 500*uk_111 + 3325*uk_112 + 5425*uk_113 + 1550*uk_114 + 19220*uk_115 + 6200*uk_116 + 41230*uk_117 + 67270*uk_118 + 19220*uk_119 + 2935886*uk_12 + 2000*uk_120 + 13300*uk_121 + 21700*uk_122 + 6200*uk_123 + 88445*uk_124 + 144305*uk_125 + 41230*uk_126 + 235445*uk_127 + 67270*uk_128 + 19220*uk_129 + 947060*uk_13 + 238328*uk_130 + 76880*uk_131 + 511252*uk_132 + 834148*uk_133 + 238328*uk_134 + 24800*uk_135 + 164920*uk_136 + 269080*uk_137 + 76880*uk_138 + 1096718*uk_139 + 6297949*uk_14 + 1789382*uk_140 + 511252*uk_141 + 2919518*uk_142 + 834148*uk_143 + 238328*uk_144 + 8000*uk_145 + 53200*uk_146 + 86800*uk_147 + 24800*uk_148 + 353780*uk_149 + 10275601*uk_15 + 577220*uk_150 + 164920*uk_151 + 941780*uk_152 + 269080*uk_153 + 76880*uk_154 + 2352637*uk_155 + 3838513*uk_156 + 1096718*uk_157 + 6262837*uk_158 + 1789382*uk_159 + 2935886*uk_16 + 511252*uk_160 + 10218313*uk_161 + 2919518*uk_162 + 834148*uk_163 + 238328*uk_164 + 3969*uk_17 + 315*uk_18 + 3906*uk_19 + 63*uk_2 + 1260*uk_20 + 8379*uk_21 + 13671*uk_22 + 3906*uk_23 + 25*uk_24 + 310*uk_25 + 100*uk_26 + 665*uk_27 + 1085*uk_28 + 310*uk_29 + 5*uk_3 + 3844*uk_30 + 1240*uk_31 + 8246*uk_32 + 13454*uk_33 + 3844*uk_34 + 400*uk_35 + 2660*uk_36 + 4340*uk_37 + 1240*uk_38 + 17689*uk_39 + 62*uk_4 + 28861*uk_40 + 8246*uk_41 + 47089*uk_42 + 13454*uk_43 + 3844*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 11211533045*uk_47 + 139023009758*uk_48 + 44846132180*uk_49 + 20*uk_5 + 298226778997*uk_50 + 486580534153*uk_51 + 139023009758*uk_52 + 187944057*uk_53 + 14916195*uk_54 + 184960818*uk_55 + 59664780*uk_56 + 396770787*uk_57 + 647362863*uk_58 + 184960818*uk_59 + 133*uk_6 + 1183825*uk_60 + 14679430*uk_61 + 4735300*uk_62 + 31489745*uk_63 + 51378005*uk_64 + 14679430*uk_65 + 182024932*uk_66 + 58717720*uk_67 + 390472838*uk_68 + 637087262*uk_69 + 217*uk_7 + 182024932*uk_70 + 18941200*uk_71 + 125958980*uk_72 + 205512020*uk_73 + 58717720*uk_74 + 837627217*uk_75 + 1366654933*uk_76 + 390472838*uk_77 + 2229805417*uk_78 + 637087262*uk_79 + 62*uk_8 + 182024932*uk_80 + 250047*uk_81 + 19845*uk_82 + 246078*uk_83 + 79380*uk_84 + 527877*uk_85 + 861273*uk_86 + 246078*uk_87 + 1575*uk_88 + 19530*uk_89 + 2242306609*uk_9 + 6300*uk_90 + 41895*uk_91 + 68355*uk_92 + 19530*uk_93 + 242172*uk_94 + 78120*uk_95 + 519498*uk_96 + 847602*uk_97 + 242172*uk_98 + 25200*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 204120*uk_100 + 328104*uk_101 + 7560*uk_102 + 1148175*uk_103 + 1845585*uk_104 + 42525*uk_105 + 2966607*uk_106 + 68355*uk_107 + 1575*uk_108 + 1092727*uk_109 + 4877359*uk_11 + 53045*uk_110 + 254616*uk_111 + 1432215*uk_112 + 2302153*uk_113 + 53045*uk_114 + 2575*uk_115 + 12360*uk_116 + 69525*uk_117 + 111755*uk_118 + 2575*uk_119 + 236765*uk_12 + 59328*uk_120 + 333720*uk_121 + 536424*uk_122 + 12360*uk_123 + 1877175*uk_124 + 3017385*uk_125 + 69525*uk_126 + 4850167*uk_127 + 111755*uk_128 + 2575*uk_129 + 1136472*uk_13 + 125*uk_130 + 600*uk_131 + 3375*uk_132 + 5425*uk_133 + 125*uk_134 + 2880*uk_135 + 16200*uk_136 + 26040*uk_137 + 600*uk_138 + 91125*uk_139 + 6392655*uk_14 + 146475*uk_140 + 3375*uk_141 + 235445*uk_142 + 5425*uk_143 + 125*uk_144 + 13824*uk_145 + 77760*uk_146 + 124992*uk_147 + 2880*uk_148 + 437400*uk_149 + 10275601*uk_15 + 703080*uk_150 + 16200*uk_151 + 1130136*uk_152 + 26040*uk_153 + 600*uk_154 + 2460375*uk_155 + 3954825*uk_156 + 91125*uk_157 + 6357015*uk_158 + 146475*uk_159 + 236765*uk_16 + 3375*uk_160 + 10218313*uk_161 + 235445*uk_162 + 5425*uk_163 + 125*uk_164 + 3969*uk_17 + 6489*uk_18 + 315*uk_19 + 63*uk_2 + 1512*uk_20 + 8505*uk_21 + 13671*uk_22 + 315*uk_23 + 10609*uk_24 + 515*uk_25 + 2472*uk_26 + 13905*uk_27 + 22351*uk_28 + 515*uk_29 + 103*uk_3 + 25*uk_30 + 120*uk_31 + 675*uk_32 + 1085*uk_33 + 25*uk_34 + 576*uk_35 + 3240*uk_36 + 5208*uk_37 + 120*uk_38 + 18225*uk_39 + 5*uk_4 + 29295*uk_40 + 675*uk_41 + 47089*uk_42 + 1085*uk_43 + 25*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 230957580727*uk_47 + 11211533045*uk_48 + 53815358616*uk_49 + 24*uk_5 + 302711392215*uk_50 + 486580534153*uk_51 + 11211533045*uk_52 + 187944057*uk_53 + 307273617*uk_54 + 14916195*uk_55 + 71597736*uk_56 + 402737265*uk_57 + 647362863*uk_58 + 14916195*uk_59 + 135*uk_6 + 502367977*uk_60 + 24386795*uk_61 + 117056616*uk_62 + 658443465*uk_63 + 1058386903*uk_64 + 24386795*uk_65 + 1183825*uk_66 + 5682360*uk_67 + 31963275*uk_68 + 51378005*uk_69 + 217*uk_7 + 1183825*uk_70 + 27275328*uk_71 + 153423720*uk_72 + 246614424*uk_73 + 5682360*uk_74 + 863008425*uk_75 + 1387206135*uk_76 + 31963275*uk_77 + 2229805417*uk_78 + 51378005*uk_79 + 5*uk_8 + 1183825*uk_80 + 250047*uk_81 + 408807*uk_82 + 19845*uk_83 + 95256*uk_84 + 535815*uk_85 + 861273*uk_86 + 19845*uk_87 + 668367*uk_88 + 32445*uk_89 + 2242306609*uk_9 + 155736*uk_90 + 876015*uk_91 + 1408113*uk_92 + 32445*uk_93 + 1575*uk_94 + 7560*uk_95 + 42525*uk_96 + 68355*uk_97 + 1575*uk_98 + 36288*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 172620*uk_100 + 273420*uk_101 + 129780*uk_102 + 1182447*uk_103 + 1872927*uk_104 + 888993*uk_105 + 2966607*uk_106 + 1408113*uk_107 + 668367*uk_108 + 681472*uk_109 + 4167064*uk_11 + 797632*uk_110 + 154880*uk_111 + 1060928*uk_112 + 1680448*uk_113 + 797632*uk_114 + 933592*uk_115 + 181280*uk_116 + 1241768*uk_117 + 1966888*uk_118 + 933592*uk_119 + 4877359*uk_12 + 35200*uk_120 + 241120*uk_121 + 381920*uk_122 + 181280*uk_123 + 1651672*uk_124 + 2616152*uk_125 + 1241768*uk_126 + 4143832*uk_127 + 1966888*uk_128 + 933592*uk_129 + 947060*uk_13 + 1092727*uk_130 + 212180*uk_131 + 1453433*uk_132 + 2302153*uk_133 + 1092727*uk_134 + 41200*uk_135 + 282220*uk_136 + 447020*uk_137 + 212180*uk_138 + 1933207*uk_139 + 6487361*uk_14 + 3062087*uk_140 + 1453433*uk_141 + 4850167*uk_142 + 2302153*uk_143 + 1092727*uk_144 + 8000*uk_145 + 54800*uk_146 + 86800*uk_147 + 41200*uk_148 + 375380*uk_149 + 10275601*uk_15 + 594580*uk_150 + 282220*uk_151 + 941780*uk_152 + 447020*uk_153 + 212180*uk_154 + 2571353*uk_155 + 4072873*uk_156 + 1933207*uk_157 + 6451193*uk_158 + 3062087*uk_159 + 4877359*uk_16 + 1453433*uk_160 + 10218313*uk_161 + 4850167*uk_162 + 2302153*uk_163 + 1092727*uk_164 + 3969*uk_17 + 5544*uk_18 + 6489*uk_19 + 63*uk_2 + 1260*uk_20 + 8631*uk_21 + 13671*uk_22 + 6489*uk_23 + 7744*uk_24 + 9064*uk_25 + 1760*uk_26 + 12056*uk_27 + 19096*uk_28 + 9064*uk_29 + 88*uk_3 + 10609*uk_30 + 2060*uk_31 + 14111*uk_32 + 22351*uk_33 + 10609*uk_34 + 400*uk_35 + 2740*uk_36 + 4340*uk_37 + 2060*uk_38 + 18769*uk_39 + 103*uk_4 + 29729*uk_40 + 14111*uk_41 + 47089*uk_42 + 22351*uk_43 + 10609*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 197322981592*uk_47 + 230957580727*uk_48 + 44846132180*uk_49 + 20*uk_5 + 307196005433*uk_50 + 486580534153*uk_51 + 230957580727*uk_52 + 187944057*uk_53 + 262525032*uk_54 + 307273617*uk_55 + 59664780*uk_56 + 408703743*uk_57 + 647362863*uk_58 + 307273617*uk_59 + 137*uk_6 + 366701632*uk_60 + 429207592*uk_61 + 83341280*uk_62 + 570887768*uk_63 + 904252888*uk_64 + 429207592*uk_65 + 502367977*uk_66 + 97547180*uk_67 + 668198183*uk_68 + 1058386903*uk_69 + 217*uk_7 + 502367977*uk_70 + 18941200*uk_71 + 129747220*uk_72 + 205512020*uk_73 + 97547180*uk_74 + 888768457*uk_75 + 1407757337*uk_76 + 668198183*uk_77 + 2229805417*uk_78 + 1058386903*uk_79 + 103*uk_8 + 502367977*uk_80 + 250047*uk_81 + 349272*uk_82 + 408807*uk_83 + 79380*uk_84 + 543753*uk_85 + 861273*uk_86 + 408807*uk_87 + 487872*uk_88 + 571032*uk_89 + 2242306609*uk_9 + 110880*uk_90 + 759528*uk_91 + 1203048*uk_92 + 571032*uk_93 + 668367*uk_94 + 129780*uk_95 + 888993*uk_96 + 1408113*uk_97 + 668367*uk_98 + 25200*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 154224*uk_100 + 218736*uk_101 + 90720*uk_102 + 1474767*uk_103 + 2091663*uk_104 + 867510*uk_105 + 2966607*uk_106 + 1230390*uk_107 + 510300*uk_108 + 438976*uk_109 + 3598828*uk_11 + 519840*uk_110 + 92416*uk_111 + 883728*uk_112 + 1253392*uk_113 + 519840*uk_114 + 615600*uk_115 + 109440*uk_116 + 1046520*uk_117 + 1484280*uk_118 + 615600*uk_119 + 4261770*uk_12 + 19456*uk_120 + 186048*uk_121 + 263872*uk_122 + 109440*uk_123 + 1779084*uk_124 + 2523276*uk_125 + 1046520*uk_126 + 3578764*uk_127 + 1484280*uk_128 + 615600*uk_129 + 757648*uk_13 + 729000*uk_130 + 129600*uk_131 + 1239300*uk_132 + 1757700*uk_133 + 729000*uk_134 + 23040*uk_135 + 220320*uk_136 + 312480*uk_137 + 129600*uk_138 + 2106810*uk_139 + 7245009*uk_14 + 2988090*uk_140 + 1239300*uk_141 + 4238010*uk_142 + 1757700*uk_143 + 729000*uk_144 + 4096*uk_145 + 39168*uk_146 + 55552*uk_147 + 23040*uk_148 + 374544*uk_149 + 10275601*uk_15 + 531216*uk_150 + 220320*uk_151 + 753424*uk_152 + 312480*uk_153 + 129600*uk_154 + 3581577*uk_155 + 5079753*uk_156 + 2106810*uk_157 + 7204617*uk_158 + 2988090*uk_159 + 4261770*uk_16 + 1239300*uk_160 + 10218313*uk_161 + 4238010*uk_162 + 1757700*uk_163 + 729000*uk_164 + 3969*uk_17 + 4788*uk_18 + 5670*uk_19 + 63*uk_2 + 1008*uk_20 + 9639*uk_21 + 13671*uk_22 + 5670*uk_23 + 5776*uk_24 + 6840*uk_25 + 1216*uk_26 + 11628*uk_27 + 16492*uk_28 + 6840*uk_29 + 76*uk_3 + 8100*uk_30 + 1440*uk_31 + 13770*uk_32 + 19530*uk_33 + 8100*uk_34 + 256*uk_35 + 2448*uk_36 + 3472*uk_37 + 1440*uk_38 + 23409*uk_39 + 90*uk_4 + 33201*uk_40 + 13770*uk_41 + 47089*uk_42 + 19530*uk_43 + 8100*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 170415302284*uk_47 + 201807594810*uk_48 + 35876905744*uk_49 + 16*uk_5 + 343072911177*uk_50 + 486580534153*uk_51 + 201807594810*uk_52 + 187944057*uk_53 + 226726164*uk_54 + 268491510*uk_55 + 47731824*uk_56 + 456435567*uk_57 + 647362863*uk_58 + 268491510*uk_59 + 153*uk_6 + 273510928*uk_60 + 323894520*uk_61 + 57581248*uk_62 + 550620684*uk_63 + 780945676*uk_64 + 323894520*uk_65 + 383559300*uk_66 + 68188320*uk_67 + 652050810*uk_68 + 924804090*uk_69 + 217*uk_7 + 383559300*uk_70 + 12122368*uk_71 + 115920144*uk_72 + 164409616*uk_73 + 68188320*uk_74 + 1108486377*uk_75 + 1572166953*uk_76 + 652050810*uk_77 + 2229805417*uk_78 + 924804090*uk_79 + 90*uk_8 + 383559300*uk_80 + 250047*uk_81 + 301644*uk_82 + 357210*uk_83 + 63504*uk_84 + 607257*uk_85 + 861273*uk_86 + 357210*uk_87 + 363888*uk_88 + 430920*uk_89 + 2242306609*uk_9 + 76608*uk_90 + 732564*uk_91 + 1038996*uk_92 + 430920*uk_93 + 510300*uk_94 + 90720*uk_95 + 867510*uk_96 + 1230390*uk_97 + 510300*uk_98 + 16128*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 156240*uk_100 + 218736*uk_101 + 76608*uk_102 + 1513575*uk_103 + 2119005*uk_104 + 742140*uk_105 + 2966607*uk_106 + 1038996*uk_107 + 363888*uk_108 + 474552*uk_109 + 3693534*uk_11 + 462384*uk_110 + 97344*uk_111 + 943020*uk_112 + 1320228*uk_113 + 462384*uk_114 + 450528*uk_115 + 94848*uk_116 + 918840*uk_117 + 1286376*uk_118 + 450528*uk_119 + 3598828*uk_12 + 19968*uk_120 + 193440*uk_121 + 270816*uk_122 + 94848*uk_123 + 1873950*uk_124 + 2623530*uk_125 + 918840*uk_126 + 3672942*uk_127 + 1286376*uk_128 + 450528*uk_129 + 757648*uk_13 + 438976*uk_130 + 92416*uk_131 + 895280*uk_132 + 1253392*uk_133 + 438976*uk_134 + 19456*uk_135 + 188480*uk_136 + 263872*uk_137 + 92416*uk_138 + 1825900*uk_139 + 7339715*uk_14 + 2556260*uk_140 + 895280*uk_141 + 3578764*uk_142 + 1253392*uk_143 + 438976*uk_144 + 4096*uk_145 + 39680*uk_146 + 55552*uk_147 + 19456*uk_148 + 384400*uk_149 + 10275601*uk_15 + 538160*uk_150 + 188480*uk_151 + 753424*uk_152 + 263872*uk_153 + 92416*uk_154 + 3723875*uk_155 + 5213425*uk_156 + 1825900*uk_157 + 7298795*uk_158 + 2556260*uk_159 + 3598828*uk_16 + 895280*uk_160 + 10218313*uk_161 + 3578764*uk_162 + 1253392*uk_163 + 438976*uk_164 + 3969*uk_17 + 4914*uk_18 + 4788*uk_19 + 63*uk_2 + 1008*uk_20 + 9765*uk_21 + 13671*uk_22 + 4788*uk_23 + 6084*uk_24 + 5928*uk_25 + 1248*uk_26 + 12090*uk_27 + 16926*uk_28 + 5928*uk_29 + 78*uk_3 + 5776*uk_30 + 1216*uk_31 + 11780*uk_32 + 16492*uk_33 + 5776*uk_34 + 256*uk_35 + 2480*uk_36 + 3472*uk_37 + 1216*uk_38 + 24025*uk_39 + 76*uk_4 + 33635*uk_40 + 11780*uk_41 + 47089*uk_42 + 16492*uk_43 + 5776*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 174899915502*uk_47 + 170415302284*uk_48 + 35876905744*uk_49 + 16*uk_5 + 347557524395*uk_50 + 486580534153*uk_51 + 170415302284*uk_52 + 187944057*uk_53 + 232692642*uk_54 + 226726164*uk_55 + 47731824*uk_56 + 462402045*uk_57 + 647362863*uk_58 + 226726164*uk_59 + 155*uk_6 + 288095652*uk_60 + 280708584*uk_61 + 59096544*uk_62 + 572497770*uk_63 + 801496878*uk_64 + 280708584*uk_65 + 273510928*uk_66 + 57581248*uk_67 + 557818340*uk_68 + 780945676*uk_69 + 217*uk_7 + 273510928*uk_70 + 12122368*uk_71 + 117435440*uk_72 + 164409616*uk_73 + 57581248*uk_74 + 1137655825*uk_75 + 1592718155*uk_76 + 557818340*uk_77 + 2229805417*uk_78 + 780945676*uk_79 + 76*uk_8 + 273510928*uk_80 + 250047*uk_81 + 309582*uk_82 + 301644*uk_83 + 63504*uk_84 + 615195*uk_85 + 861273*uk_86 + 301644*uk_87 + 383292*uk_88 + 373464*uk_89 + 2242306609*uk_9 + 78624*uk_90 + 761670*uk_91 + 1066338*uk_92 + 373464*uk_93 + 363888*uk_94 + 76608*uk_95 + 742140*uk_96 + 1038996*uk_97 + 363888*uk_98 + 16128*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 158256*uk_100 + 218736*uk_101 + 78624*uk_102 + 1552887*uk_103 + 2146347*uk_104 + 771498*uk_105 + 2966607*uk_106 + 1066338*uk_107 + 383292*uk_108 + 884736*uk_109 + 4545888*uk_11 + 718848*uk_110 + 147456*uk_111 + 1446912*uk_112 + 1999872*uk_113 + 718848*uk_114 + 584064*uk_115 + 119808*uk_116 + 1175616*uk_117 + 1624896*uk_118 + 584064*uk_119 + 3693534*uk_12 + 24576*uk_120 + 241152*uk_121 + 333312*uk_122 + 119808*uk_123 + 2366304*uk_124 + 3270624*uk_125 + 1175616*uk_126 + 4520544*uk_127 + 1624896*uk_128 + 584064*uk_129 + 757648*uk_13 + 474552*uk_130 + 97344*uk_131 + 955188*uk_132 + 1320228*uk_133 + 474552*uk_134 + 19968*uk_135 + 195936*uk_136 + 270816*uk_137 + 97344*uk_138 + 1922622*uk_139 + 7434421*uk_14 + 2657382*uk_140 + 955188*uk_141 + 3672942*uk_142 + 1320228*uk_143 + 474552*uk_144 + 4096*uk_145 + 40192*uk_146 + 55552*uk_147 + 19968*uk_148 + 394384*uk_149 + 10275601*uk_15 + 545104*uk_150 + 195936*uk_151 + 753424*uk_152 + 270816*uk_153 + 97344*uk_154 + 3869893*uk_155 + 5348833*uk_156 + 1922622*uk_157 + 7392973*uk_158 + 2657382*uk_159 + 3693534*uk_16 + 955188*uk_160 + 10218313*uk_161 + 3672942*uk_162 + 1320228*uk_163 + 474552*uk_164 + 3969*uk_17 + 6048*uk_18 + 4914*uk_19 + 63*uk_2 + 1008*uk_20 + 9891*uk_21 + 13671*uk_22 + 4914*uk_23 + 9216*uk_24 + 7488*uk_25 + 1536*uk_26 + 15072*uk_27 + 20832*uk_28 + 7488*uk_29 + 96*uk_3 + 6084*uk_30 + 1248*uk_31 + 12246*uk_32 + 16926*uk_33 + 6084*uk_34 + 256*uk_35 + 2512*uk_36 + 3472*uk_37 + 1248*uk_38 + 24649*uk_39 + 78*uk_4 + 34069*uk_40 + 12246*uk_41 + 47089*uk_42 + 16926*uk_43 + 6084*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 215261434464*uk_47 + 174899915502*uk_48 + 35876905744*uk_49 + 16*uk_5 + 352042137613*uk_50 + 486580534153*uk_51 + 174899915502*uk_52 + 187944057*uk_53 + 286390944*uk_54 + 232692642*uk_55 + 47731824*uk_56 + 468368523*uk_57 + 647362863*uk_58 + 232692642*uk_59 + 157*uk_6 + 436405248*uk_60 + 354579264*uk_61 + 72734208*uk_62 + 713704416*uk_63 + 986457696*uk_64 + 354579264*uk_65 + 288095652*uk_66 + 59096544*uk_67 + 579884838*uk_68 + 801496878*uk_69 + 217*uk_7 + 288095652*uk_70 + 12122368*uk_71 + 118950736*uk_72 + 164409616*uk_73 + 59096544*uk_74 + 1167204097*uk_75 + 1613269357*uk_76 + 579884838*uk_77 + 2229805417*uk_78 + 801496878*uk_79 + 78*uk_8 + 288095652*uk_80 + 250047*uk_81 + 381024*uk_82 + 309582*uk_83 + 63504*uk_84 + 623133*uk_85 + 861273*uk_86 + 309582*uk_87 + 580608*uk_88 + 471744*uk_89 + 2242306609*uk_9 + 96768*uk_90 + 949536*uk_91 + 1312416*uk_92 + 471744*uk_93 + 383292*uk_94 + 78624*uk_95 + 771498*uk_96 + 1066338*uk_97 + 383292*uk_98 + 16128*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 160272*uk_100 + 218736*uk_101 + 96768*uk_102 + 1592703*uk_103 + 2173689*uk_104 + 961632*uk_105 + 2966607*uk_106 + 1312416*uk_107 + 580608*uk_108 + 2197000*uk_109 + 6155890*uk_11 + 1622400*uk_110 + 270400*uk_111 + 2687100*uk_112 + 3667300*uk_113 + 1622400*uk_114 + 1198080*uk_115 + 199680*uk_116 + 1984320*uk_117 + 2708160*uk_118 + 1198080*uk_119 + 4545888*uk_12 + 33280*uk_120 + 330720*uk_121 + 451360*uk_122 + 199680*uk_123 + 3286530*uk_124 + 4485390*uk_125 + 1984320*uk_126 + 6121570*uk_127 + 2708160*uk_128 + 1198080*uk_129 + 757648*uk_13 + 884736*uk_130 + 147456*uk_131 + 1465344*uk_132 + 1999872*uk_133 + 884736*uk_134 + 24576*uk_135 + 244224*uk_136 + 333312*uk_137 + 147456*uk_138 + 2426976*uk_139 + 7529127*uk_14 + 3312288*uk_140 + 1465344*uk_141 + 4520544*uk_142 + 1999872*uk_143 + 884736*uk_144 + 4096*uk_145 + 40704*uk_146 + 55552*uk_147 + 24576*uk_148 + 404496*uk_149 + 10275601*uk_15 + 552048*uk_150 + 244224*uk_151 + 753424*uk_152 + 333312*uk_153 + 147456*uk_154 + 4019679*uk_155 + 5485977*uk_156 + 2426976*uk_157 + 7487151*uk_158 + 3312288*uk_159 + 4545888*uk_16 + 1465344*uk_160 + 10218313*uk_161 + 4520544*uk_162 + 1999872*uk_163 + 884736*uk_164 + 3969*uk_17 + 8190*uk_18 + 6048*uk_19 + 63*uk_2 + 1008*uk_20 + 10017*uk_21 + 13671*uk_22 + 6048*uk_23 + 16900*uk_24 + 12480*uk_25 + 2080*uk_26 + 20670*uk_27 + 28210*uk_28 + 12480*uk_29 + 130*uk_3 + 9216*uk_30 + 1536*uk_31 + 15264*uk_32 + 20832*uk_33 + 9216*uk_34 + 256*uk_35 + 2544*uk_36 + 3472*uk_37 + 1536*uk_38 + 25281*uk_39 + 96*uk_4 + 34503*uk_40 + 15264*uk_41 + 47089*uk_42 + 20832*uk_43 + 9216*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 291499859170*uk_47 + 215261434464*uk_48 + 35876905744*uk_49 + 16*uk_5 + 356526750831*uk_50 + 486580534153*uk_51 + 215261434464*uk_52 + 187944057*uk_53 + 387821070*uk_54 + 286390944*uk_55 + 47731824*uk_56 + 474335001*uk_57 + 647362863*uk_58 + 286390944*uk_59 + 159*uk_6 + 800265700*uk_60 + 590965440*uk_61 + 98494240*uk_62 + 978786510*uk_63 + 1335828130*uk_64 + 590965440*uk_65 + 436405248*uk_66 + 72734208*uk_67 + 722796192*uk_68 + 986457696*uk_69 + 217*uk_7 + 436405248*uk_70 + 12122368*uk_71 + 120466032*uk_72 + 164409616*uk_73 + 72734208*uk_74 + 1197131193*uk_75 + 1633820559*uk_76 + 722796192*uk_77 + 2229805417*uk_78 + 986457696*uk_79 + 96*uk_8 + 436405248*uk_80 + 250047*uk_81 + 515970*uk_82 + 381024*uk_83 + 63504*uk_84 + 631071*uk_85 + 861273*uk_86 + 381024*uk_87 + 1064700*uk_88 + 786240*uk_89 + 2242306609*uk_9 + 131040*uk_90 + 1302210*uk_91 + 1777230*uk_92 + 786240*uk_93 + 580608*uk_94 + 96768*uk_95 + 961632*uk_96 + 1312416*uk_97 + 580608*uk_98 + 16128*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 126252*uk_100 + 164052*uk_101 + 123228*uk_102 + 1757007*uk_103 + 2283057*uk_104 + 1714923*uk_105 + 2966607*uk_106 + 2228373*uk_107 + 1673847*uk_108 + 778688*uk_109 + 4356476*uk_11 + 1379632*uk_110 + 101568*uk_111 + 1413488*uk_112 + 1836688*uk_113 + 1379632*uk_114 + 2444348*uk_115 + 179952*uk_116 + 2504332*uk_117 + 3254132*uk_118 + 2444348*uk_119 + 7718539*uk_12 + 13248*uk_120 + 184368*uk_121 + 239568*uk_122 + 179952*uk_123 + 2565788*uk_124 + 3333988*uk_125 + 2504332*uk_126 + 4332188*uk_127 + 3254132*uk_128 + 2444348*uk_129 + 568236*uk_13 + 4330747*uk_130 + 318828*uk_131 + 4437023*uk_132 + 5765473*uk_133 + 4330747*uk_134 + 23472*uk_135 + 326652*uk_136 + 424452*uk_137 + 318828*uk_138 + 4545907*uk_139 + 7907951*uk_14 + 5906957*uk_140 + 4437023*uk_141 + 7675507*uk_142 + 5765473*uk_143 + 4330747*uk_144 + 1728*uk_145 + 24048*uk_146 + 31248*uk_147 + 23472*uk_148 + 334668*uk_149 + 10275601*uk_15 + 434868*uk_150 + 326652*uk_151 + 565068*uk_152 + 424452*uk_153 + 318828*uk_154 + 4657463*uk_155 + 6051913*uk_156 + 4545907*uk_157 + 7863863*uk_158 + 5906957*uk_159 + 7718539*uk_16 + 4437023*uk_160 + 10218313*uk_161 + 7675507*uk_162 + 5765473*uk_163 + 4330747*uk_164 + 3969*uk_17 + 5796*uk_18 + 10269*uk_19 + 63*uk_2 + 756*uk_20 + 10521*uk_21 + 13671*uk_22 + 10269*uk_23 + 8464*uk_24 + 14996*uk_25 + 1104*uk_26 + 15364*uk_27 + 19964*uk_28 + 14996*uk_29 + 92*uk_3 + 26569*uk_30 + 1956*uk_31 + 27221*uk_32 + 35371*uk_33 + 26569*uk_34 + 144*uk_35 + 2004*uk_36 + 2604*uk_37 + 1956*uk_38 + 27889*uk_39 + 163*uk_4 + 36239*uk_40 + 27221*uk_41 + 47089*uk_42 + 35371*uk_43 + 26569*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 206292208028*uk_47 + 365495977267*uk_48 + 26907679308*uk_49 + 12*uk_5 + 374465203703*uk_50 + 486580534153*uk_51 + 365495977267*uk_52 + 187944057*uk_53 + 274457988*uk_54 + 486267957*uk_55 + 35798868*uk_56 + 498200913*uk_57 + 647362863*uk_58 + 486267957*uk_59 + 167*uk_6 + 400795792*uk_60 + 710105588*uk_61 + 52277712*uk_62 + 727531492*uk_63 + 945355292*uk_64 + 710105588*uk_65 + 1258121857*uk_66 + 92622468*uk_67 + 1288996013*uk_68 + 1674922963*uk_69 + 217*uk_7 + 1258121857*uk_70 + 6818832*uk_71 + 94895412*uk_72 + 123307212*uk_73 + 92622468*uk_74 + 1320627817*uk_75 + 1716025367*uk_76 + 1288996013*uk_77 + 2229805417*uk_78 + 1674922963*uk_79 + 163*uk_8 + 1258121857*uk_80 + 250047*uk_81 + 365148*uk_82 + 646947*uk_83 + 47628*uk_84 + 662823*uk_85 + 861273*uk_86 + 646947*uk_87 + 533232*uk_88 + 944748*uk_89 + 2242306609*uk_9 + 69552*uk_90 + 967932*uk_91 + 1257732*uk_92 + 944748*uk_93 + 1673847*uk_94 + 123228*uk_95 + 1714923*uk_96 + 2228373*uk_97 + 1673847*uk_98 + 9072*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 133812*uk_100 + 164052*uk_101 + 77868*uk_102 + 1973727*uk_103 + 2419767*uk_104 + 1148553*uk_105 + 2966607*uk_106 + 1408113*uk_107 + 668367*uk_108 + 830584*uk_109 + 4451182*uk_11 + 910108*uk_110 + 106032*uk_111 + 1563972*uk_112 + 1917412*uk_113 + 910108*uk_114 + 997246*uk_115 + 116184*uk_116 + 1713714*uk_117 + 2100994*uk_118 + 997246*uk_119 + 4877359*uk_12 + 13536*uk_120 + 199656*uk_121 + 244776*uk_122 + 116184*uk_123 + 2944926*uk_124 + 3610446*uk_125 + 1713714*uk_126 + 4426366*uk_127 + 2100994*uk_128 + 997246*uk_129 + 568236*uk_13 + 1092727*uk_130 + 127308*uk_131 + 1877793*uk_132 + 2302153*uk_133 + 1092727*uk_134 + 14832*uk_135 + 218772*uk_136 + 268212*uk_137 + 127308*uk_138 + 3226887*uk_139 + 8381481*uk_14 + 3956127*uk_140 + 1877793*uk_141 + 4850167*uk_142 + 2302153*uk_143 + 1092727*uk_144 + 1728*uk_145 + 25488*uk_146 + 31248*uk_147 + 14832*uk_148 + 375948*uk_149 + 10275601*uk_15 + 460908*uk_150 + 218772*uk_151 + 565068*uk_152 + 268212*uk_153 + 127308*uk_154 + 5545233*uk_155 + 6798393*uk_156 + 3226887*uk_157 + 8334753*uk_158 + 3956127*uk_159 + 4877359*uk_16 + 1877793*uk_160 + 10218313*uk_161 + 4850167*uk_162 + 2302153*uk_163 + 1092727*uk_164 + 3969*uk_17 + 5922*uk_18 + 6489*uk_19 + 63*uk_2 + 756*uk_20 + 11151*uk_21 + 13671*uk_22 + 6489*uk_23 + 8836*uk_24 + 9682*uk_25 + 1128*uk_26 + 16638*uk_27 + 20398*uk_28 + 9682*uk_29 + 94*uk_3 + 10609*uk_30 + 1236*uk_31 + 18231*uk_32 + 22351*uk_33 + 10609*uk_34 + 144*uk_35 + 2124*uk_36 + 2604*uk_37 + 1236*uk_38 + 31329*uk_39 + 103*uk_4 + 38409*uk_40 + 18231*uk_41 + 47089*uk_42 + 22351*uk_43 + 10609*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 210776821246*uk_47 + 230957580727*uk_48 + 26907679308*uk_49 + 12*uk_5 + 396888269793*uk_50 + 486580534153*uk_51 + 230957580727*uk_52 + 187944057*uk_53 + 280424466*uk_54 + 307273617*uk_55 + 35798868*uk_56 + 528033303*uk_57 + 647362863*uk_58 + 307273617*uk_59 + 177*uk_6 + 418411108*uk_60 + 458471746*uk_61 + 53414184*uk_62 + 787859214*uk_63 + 965906494*uk_64 + 458471746*uk_65 + 502367977*uk_66 + 58528308*uk_67 + 863292543*uk_68 + 1058386903*uk_69 + 217*uk_7 + 502367977*uk_70 + 6818832*uk_71 + 100577772*uk_72 + 123307212*uk_73 + 58528308*uk_74 + 1483522137*uk_75 + 1818781377*uk_76 + 863292543*uk_77 + 2229805417*uk_78 + 1058386903*uk_79 + 103*uk_8 + 502367977*uk_80 + 250047*uk_81 + 373086*uk_82 + 408807*uk_83 + 47628*uk_84 + 702513*uk_85 + 861273*uk_86 + 408807*uk_87 + 556668*uk_88 + 609966*uk_89 + 2242306609*uk_9 + 71064*uk_90 + 1048194*uk_91 + 1285074*uk_92 + 609966*uk_93 + 668367*uk_94 + 77868*uk_95 + 1148553*uk_96 + 1408113*uk_97 + 668367*uk_98 + 9072*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 135324*uk_100 + 164052*uk_101 + 71064*uk_102 + 2018583*uk_103 + 2447109*uk_104 + 1060038*uk_105 + 2966607*uk_106 + 1285074*uk_107 + 556668*uk_108 + 912673*uk_109 + 4593241*uk_11 + 884446*uk_110 + 112908*uk_111 + 1684211*uk_112 + 2041753*uk_113 + 884446*uk_114 + 857092*uk_115 + 109416*uk_116 + 1632122*uk_117 + 1978606*uk_118 + 857092*uk_119 + 4451182*uk_12 + 13968*uk_120 + 208356*uk_121 + 252588*uk_122 + 109416*uk_123 + 3107977*uk_124 + 3767771*uk_125 + 1632122*uk_126 + 4567633*uk_127 + 1978606*uk_128 + 857092*uk_129 + 568236*uk_13 + 830584*uk_130 + 106032*uk_131 + 1581644*uk_132 + 1917412*uk_133 + 830584*uk_134 + 13536*uk_135 + 201912*uk_136 + 244776*uk_137 + 106032*uk_138 + 3011854*uk_139 + 8476187*uk_14 + 3651242*uk_140 + 1581644*uk_141 + 4426366*uk_142 + 1917412*uk_143 + 830584*uk_144 + 1728*uk_145 + 25776*uk_146 + 31248*uk_147 + 13536*uk_148 + 384492*uk_149 + 10275601*uk_15 + 466116*uk_150 + 201912*uk_151 + 565068*uk_152 + 244776*uk_153 + 106032*uk_154 + 5735339*uk_155 + 6952897*uk_156 + 3011854*uk_157 + 8428931*uk_158 + 3651242*uk_159 + 4451182*uk_16 + 1581644*uk_160 + 10218313*uk_161 + 4426366*uk_162 + 1917412*uk_163 + 830584*uk_164 + 3969*uk_17 + 6111*uk_18 + 5922*uk_19 + 63*uk_2 + 756*uk_20 + 11277*uk_21 + 13671*uk_22 + 5922*uk_23 + 9409*uk_24 + 9118*uk_25 + 1164*uk_26 + 17363*uk_27 + 21049*uk_28 + 9118*uk_29 + 97*uk_3 + 8836*uk_30 + 1128*uk_31 + 16826*uk_32 + 20398*uk_33 + 8836*uk_34 + 144*uk_35 + 2148*uk_36 + 2604*uk_37 + 1128*uk_38 + 32041*uk_39 + 94*uk_4 + 38843*uk_40 + 16826*uk_41 + 47089*uk_42 + 20398*uk_43 + 8836*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 217503741073*uk_47 + 210776821246*uk_48 + 26907679308*uk_49 + 12*uk_5 + 401372883011*uk_50 + 486580534153*uk_51 + 210776821246*uk_52 + 187944057*uk_53 + 289374183*uk_54 + 280424466*uk_55 + 35798868*uk_56 + 533999781*uk_57 + 647362863*uk_58 + 280424466*uk_59 + 179*uk_6 + 445544377*uk_60 + 431764654*uk_61 + 55118892*uk_62 + 822190139*uk_63 + 996733297*uk_64 + 431764654*uk_65 + 418411108*uk_66 + 53414184*uk_67 + 796761578*uk_68 + 965906494*uk_69 + 217*uk_7 + 418411108*uk_70 + 6818832*uk_71 + 101714244*uk_72 + 123307212*uk_73 + 53414184*uk_74 + 1517237473*uk_75 + 1839332579*uk_76 + 796761578*uk_77 + 2229805417*uk_78 + 965906494*uk_79 + 94*uk_8 + 418411108*uk_80 + 250047*uk_81 + 384993*uk_82 + 373086*uk_83 + 47628*uk_84 + 710451*uk_85 + 861273*uk_86 + 373086*uk_87 + 592767*uk_88 + 574434*uk_89 + 2242306609*uk_9 + 73332*uk_90 + 1093869*uk_91 + 1326087*uk_92 + 574434*uk_93 + 556668*uk_94 + 71064*uk_95 + 1060038*uk_96 + 1285074*uk_97 + 556668*uk_98 + 9072*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 136836*uk_100 + 164052*uk_101 + 73332*uk_102 + 2063943*uk_103 + 2474451*uk_104 + 1106091*uk_105 + 2966607*uk_106 + 1326087*uk_107 + 592767*uk_108 + 1404928*uk_109 + 5303536*uk_11 + 1216768*uk_110 + 150528*uk_111 + 2270464*uk_112 + 2722048*uk_113 + 1216768*uk_114 + 1053808*uk_115 + 130368*uk_116 + 1966384*uk_117 + 2357488*uk_118 + 1053808*uk_119 + 4593241*uk_12 + 16128*uk_120 + 243264*uk_121 + 291648*uk_122 + 130368*uk_123 + 3669232*uk_124 + 4399024*uk_125 + 1966384*uk_126 + 5273968*uk_127 + 2357488*uk_128 + 1053808*uk_129 + 568236*uk_13 + 912673*uk_130 + 112908*uk_131 + 1703029*uk_132 + 2041753*uk_133 + 912673*uk_134 + 13968*uk_135 + 210684*uk_136 + 252588*uk_137 + 112908*uk_138 + 3177817*uk_139 + 8570893*uk_14 + 3809869*uk_140 + 1703029*uk_141 + 4567633*uk_142 + 2041753*uk_143 + 912673*uk_144 + 1728*uk_145 + 26064*uk_146 + 31248*uk_147 + 13968*uk_148 + 393132*uk_149 + 10275601*uk_15 + 471324*uk_150 + 210684*uk_151 + 565068*uk_152 + 252588*uk_153 + 112908*uk_154 + 5929741*uk_155 + 7109137*uk_156 + 3177817*uk_157 + 8523109*uk_158 + 3809869*uk_159 + 4593241*uk_16 + 1703029*uk_160 + 10218313*uk_161 + 4567633*uk_162 + 2041753*uk_163 + 912673*uk_164 + 3969*uk_17 + 7056*uk_18 + 6111*uk_19 + 63*uk_2 + 756*uk_20 + 11403*uk_21 + 13671*uk_22 + 6111*uk_23 + 12544*uk_24 + 10864*uk_25 + 1344*uk_26 + 20272*uk_27 + 24304*uk_28 + 10864*uk_29 + 112*uk_3 + 9409*uk_30 + 1164*uk_31 + 17557*uk_32 + 21049*uk_33 + 9409*uk_34 + 144*uk_35 + 2172*uk_36 + 2604*uk_37 + 1164*uk_38 + 32761*uk_39 + 97*uk_4 + 39277*uk_40 + 17557*uk_41 + 47089*uk_42 + 21049*uk_43 + 9409*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 251138340208*uk_47 + 217503741073*uk_48 + 26907679308*uk_49 + 12*uk_5 + 405857496229*uk_50 + 486580534153*uk_51 + 217503741073*uk_52 + 187944057*uk_53 + 334122768*uk_54 + 289374183*uk_55 + 35798868*uk_56 + 539966259*uk_57 + 647362863*uk_58 + 289374183*uk_59 + 181*uk_6 + 593996032*uk_60 + 514442992*uk_61 + 63642432*uk_62 + 959940016*uk_63 + 1150867312*uk_64 + 514442992*uk_65 + 445544377*uk_66 + 55118892*uk_67 + 831376621*uk_68 + 996733297*uk_69 + 217*uk_7 + 445544377*uk_70 + 6818832*uk_71 + 102850716*uk_72 + 123307212*uk_73 + 55118892*uk_74 + 1551331633*uk_75 + 1859883781*uk_76 + 831376621*uk_77 + 2229805417*uk_78 + 996733297*uk_79 + 97*uk_8 + 445544377*uk_80 + 250047*uk_81 + 444528*uk_82 + 384993*uk_83 + 47628*uk_84 + 718389*uk_85 + 861273*uk_86 + 384993*uk_87 + 790272*uk_88 + 684432*uk_89 + 2242306609*uk_9 + 84672*uk_90 + 1277136*uk_91 + 1531152*uk_92 + 684432*uk_93 + 592767*uk_94 + 73332*uk_95 + 1106091*uk_96 + 1326087*uk_97 + 592767*uk_98 + 9072*uk_99,
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|
|
uk_0 + 47353*uk_1 + 2983239*uk_10 + 106344*uk_100 + 109368*uk_101 + 59976*uk_102 + 2804823*uk_103 + 2884581*uk_104 + 1581867*uk_105 + 2966607*uk_106 + 1626849*uk_107 + 892143*uk_108 + 704969*uk_109 + 4214417*uk_11 + 942599*uk_110 + 63368*uk_111 + 1671331*uk_112 + 1718857*uk_113 + 942599*uk_114 + 1260329*uk_115 + 84728*uk_116 + 2234701*uk_117 + 2298247*uk_118 + 1260329*uk_119 + 5635007*uk_12 + 5696*uk_120 + 150232*uk_121 + 154504*uk_122 + 84728*uk_123 + 3962369*uk_124 + 4075043*uk_125 + 2234701*uk_126 + 4190921*uk_127 + 2298247*uk_128 + 1260329*uk_129 + 378824*uk_13 + 1685159*uk_130 + 113288*uk_131 + 2987971*uk_132 + 3072937*uk_133 + 1685159*uk_134 + 7616*uk_135 + 200872*uk_136 + 206584*uk_137 + 113288*uk_138 + 5297999*uk_139 + 9991483*uk_14 + 5448653*uk_140 + 2987971*uk_141 + 5603591*uk_142 + 3072937*uk_143 + 1685159*uk_144 + 512*uk_145 + 13504*uk_146 + 13888*uk_147 + 7616*uk_148 + 356168*uk_149 + 10275601*uk_15 + 366296*uk_150 + 200872*uk_151 + 376712*uk_152 + 206584*uk_153 + 113288*uk_154 + 9393931*uk_155 + 9661057*uk_156 + 5297999*uk_157 + 9935779*uk_158 + 5448653*uk_159 + 5635007*uk_16 + 2987971*uk_160 + 10218313*uk_161 + 5603591*uk_162 + 3072937*uk_163 + 1685159*uk_164 + 3969*uk_17 + 5607*uk_18 + 7497*uk_19 + 63*uk_2 + 504*uk_20 + 13293*uk_21 + 13671*uk_22 + 7497*uk_23 + 7921*uk_24 + 10591*uk_25 + 712*uk_26 + 18779*uk_27 + 19313*uk_28 + 10591*uk_29 + 89*uk_3 + 14161*uk_30 + 952*uk_31 + 25109*uk_32 + 25823*uk_33 + 14161*uk_34 + 64*uk_35 + 1688*uk_36 + 1736*uk_37 + 952*uk_38 + 44521*uk_39 + 119*uk_4 + 45787*uk_40 + 25109*uk_41 + 47089*uk_42 + 25823*uk_43 + 14161*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 199565288201*uk_47 + 266834486471*uk_48 + 17938452872*uk_49 + 8*uk_5 + 473126694499*uk_50 + 486580534153*uk_51 + 266834486471*uk_52 + 187944057*uk_53 + 265508271*uk_54 + 355005441*uk_55 + 23865912*uk_56 + 629463429*uk_57 + 647362863*uk_58 + 355005441*uk_59 + 211*uk_6 + 375083113*uk_60 + 501515623*uk_61 + 33715336*uk_62 + 889241987*uk_63 + 914528489*uk_64 + 501515623*uk_65 + 670565833*uk_66 + 45080056*uk_67 + 1188986477*uk_68 + 1222796519*uk_69 + 217*uk_7 + 670565833*uk_70 + 3030592*uk_71 + 79931864*uk_72 + 82204808*uk_73 + 45080056*uk_74 + 2108202913*uk_75 + 2168151811*uk_76 + 1188986477*uk_77 + 2229805417*uk_78 + 1222796519*uk_79 + 119*uk_8 + 670565833*uk_80 + 250047*uk_81 + 353241*uk_82 + 472311*uk_83 + 31752*uk_84 + 837459*uk_85 + 861273*uk_86 + 472311*uk_87 + 499023*uk_88 + 667233*uk_89 + 2242306609*uk_9 + 44856*uk_90 + 1183077*uk_91 + 1216719*uk_92 + 667233*uk_93 + 892143*uk_94 + 59976*uk_95 + 1581867*uk_96 + 1626849*uk_97 + 892143*uk_98 + 4032*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 107352*uk_100 + 109368*uk_101 + 44856*uk_102 + 2858247*uk_103 + 2911923*uk_104 + 1194291*uk_105 + 2966607*uk_106 + 1216719*uk_107 + 499023*uk_108 + 300763*uk_109 + 3172651*uk_11 + 399521*uk_110 + 35912*uk_111 + 956157*uk_112 + 974113*uk_113 + 399521*uk_114 + 530707*uk_115 + 47704*uk_116 + 1270119*uk_117 + 1293971*uk_118 + 530707*uk_119 + 4214417*uk_12 + 4288*uk_120 + 114168*uk_121 + 116312*uk_122 + 47704*uk_123 + 3039723*uk_124 + 3096807*uk_125 + 1270119*uk_126 + 3154963*uk_127 + 1293971*uk_128 + 530707*uk_129 + 378824*uk_13 + 704969*uk_130 + 63368*uk_131 + 1687173*uk_132 + 1718857*uk_133 + 704969*uk_134 + 5696*uk_135 + 151656*uk_136 + 154504*uk_137 + 63368*uk_138 + 4037841*uk_139 + 10086189*uk_14 + 4113669*uk_140 + 1687173*uk_141 + 4190921*uk_142 + 1718857*uk_143 + 704969*uk_144 + 512*uk_145 + 13632*uk_146 + 13888*uk_147 + 5696*uk_148 + 362952*uk_149 + 10275601*uk_15 + 369768*uk_150 + 151656*uk_151 + 376712*uk_152 + 154504*uk_153 + 63368*uk_154 + 9663597*uk_155 + 9845073*uk_156 + 4037841*uk_157 + 10029957*uk_158 + 4113669*uk_159 + 4214417*uk_16 + 1687173*uk_160 + 10218313*uk_161 + 4190921*uk_162 + 1718857*uk_163 + 704969*uk_164 + 3969*uk_17 + 4221*uk_18 + 5607*uk_19 + 63*uk_2 + 504*uk_20 + 13419*uk_21 + 13671*uk_22 + 5607*uk_23 + 4489*uk_24 + 5963*uk_25 + 536*uk_26 + 14271*uk_27 + 14539*uk_28 + 5963*uk_29 + 67*uk_3 + 7921*uk_30 + 712*uk_31 + 18957*uk_32 + 19313*uk_33 + 7921*uk_34 + 64*uk_35 + 1704*uk_36 + 1736*uk_37 + 712*uk_38 + 45369*uk_39 + 89*uk_4 + 46221*uk_40 + 18957*uk_41 + 47089*uk_42 + 19313*uk_43 + 7921*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 150234542803*uk_47 + 199565288201*uk_48 + 17938452872*uk_49 + 8*uk_5 + 477611307717*uk_50 + 486580534153*uk_51 + 199565288201*uk_52 + 187944057*uk_53 + 199877013*uk_54 + 265508271*uk_55 + 23865912*uk_56 + 635429907*uk_57 + 647362863*uk_58 + 265508271*uk_59 + 213*uk_6 + 212567617*uk_60 + 282365939*uk_61 + 25381208*uk_62 + 675774663*uk_63 + 688465267*uk_64 + 282365939*uk_65 + 375083113*uk_66 + 33715336*uk_67 + 897670821*uk_68 + 914528489*uk_69 + 217*uk_7 + 375083113*uk_70 + 3030592*uk_71 + 80689512*uk_72 + 82204808*uk_73 + 33715336*uk_74 + 2148358257*uk_75 + 2188703013*uk_76 + 897670821*uk_77 + 2229805417*uk_78 + 914528489*uk_79 + 89*uk_8 + 375083113*uk_80 + 250047*uk_81 + 265923*uk_82 + 353241*uk_83 + 31752*uk_84 + 845397*uk_85 + 861273*uk_86 + 353241*uk_87 + 282807*uk_88 + 375669*uk_89 + 2242306609*uk_9 + 33768*uk_90 + 899073*uk_91 + 915957*uk_92 + 375669*uk_93 + 499023*uk_94 + 44856*uk_95 + 1194291*uk_96 + 1216719*uk_97 + 499023*uk_98 + 4032*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 108360*uk_100 + 109368*uk_101 + 33768*uk_102 + 2912175*uk_103 + 2939265*uk_104 + 907515*uk_105 + 2966607*uk_106 + 915957*uk_107 + 282807*uk_108 + 148877*uk_109 + 2509709*uk_11 + 188203*uk_110 + 22472*uk_111 + 603935*uk_112 + 609553*uk_113 + 188203*uk_114 + 237917*uk_115 + 28408*uk_116 + 763465*uk_117 + 770567*uk_118 + 237917*uk_119 + 3172651*uk_12 + 3392*uk_120 + 91160*uk_121 + 92008*uk_122 + 28408*uk_123 + 2449925*uk_124 + 2472715*uk_125 + 763465*uk_126 + 2495717*uk_127 + 770567*uk_128 + 237917*uk_129 + 378824*uk_13 + 300763*uk_130 + 35912*uk_131 + 965135*uk_132 + 974113*uk_133 + 300763*uk_134 + 4288*uk_135 + 115240*uk_136 + 116312*uk_137 + 35912*uk_138 + 3097075*uk_139 + 10180895*uk_14 + 3125885*uk_140 + 965135*uk_141 + 3154963*uk_142 + 974113*uk_143 + 300763*uk_144 + 512*uk_145 + 13760*uk_146 + 13888*uk_147 + 4288*uk_148 + 369800*uk_149 + 10275601*uk_15 + 373240*uk_150 + 115240*uk_151 + 376712*uk_152 + 116312*uk_153 + 35912*uk_154 + 9938375*uk_155 + 10030825*uk_156 + 3097075*uk_157 + 10124135*uk_158 + 3125885*uk_159 + 3172651*uk_16 + 965135*uk_160 + 10218313*uk_161 + 3154963*uk_162 + 974113*uk_163 + 300763*uk_164 + 3969*uk_17 + 3339*uk_18 + 4221*uk_19 + 63*uk_2 + 504*uk_20 + 13545*uk_21 + 13671*uk_22 + 4221*uk_23 + 2809*uk_24 + 3551*uk_25 + 424*uk_26 + 11395*uk_27 + 11501*uk_28 + 3551*uk_29 + 53*uk_3 + 4489*uk_30 + 536*uk_31 + 14405*uk_32 + 14539*uk_33 + 4489*uk_34 + 64*uk_35 + 1720*uk_36 + 1736*uk_37 + 536*uk_38 + 46225*uk_39 + 67*uk_4 + 46655*uk_40 + 14405*uk_41 + 47089*uk_42 + 14539*uk_43 + 4489*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 118842250277*uk_47 + 150234542803*uk_48 + 17938452872*uk_49 + 8*uk_5 + 482095920935*uk_50 + 486580534153*uk_51 + 150234542803*uk_52 + 187944057*uk_53 + 158111667*uk_54 + 199877013*uk_55 + 23865912*uk_56 + 641396385*uk_57 + 647362863*uk_58 + 199877013*uk_59 + 215*uk_6 + 133014577*uk_60 + 168150503*uk_61 + 20077672*uk_62 + 539587435*uk_63 + 544606853*uk_64 + 168150503*uk_65 + 212567617*uk_66 + 25381208*uk_67 + 682119965*uk_68 + 688465267*uk_69 + 217*uk_7 + 212567617*uk_70 + 3030592*uk_71 + 81447160*uk_72 + 82204808*uk_73 + 25381208*uk_74 + 2188892425*uk_75 + 2209254215*uk_76 + 682119965*uk_77 + 2229805417*uk_78 + 688465267*uk_79 + 67*uk_8 + 212567617*uk_80 + 250047*uk_81 + 210357*uk_82 + 265923*uk_83 + 31752*uk_84 + 853335*uk_85 + 861273*uk_86 + 265923*uk_87 + 176967*uk_88 + 223713*uk_89 + 2242306609*uk_9 + 26712*uk_90 + 717885*uk_91 + 724563*uk_92 + 223713*uk_93 + 282807*uk_94 + 33768*uk_95 + 907515*uk_96 + 915957*uk_97 + 282807*uk_98 + 4032*uk_99,
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uk_0 + 47353*uk_1 + 2983239*uk_10 + 109368*uk_100 + 109368*uk_101 + 26712*uk_102 + 2966607*uk_103 + 2966607*uk_104 + 724563*uk_105 + 2966607*uk_106 + 724563*uk_107 + 176967*uk_108 + 103823*uk_109 + 2225591*uk_11 + 117077*uk_110 + 17672*uk_111 + 479353*uk_112 + 479353*uk_113 + 117077*uk_114 + 132023*uk_115 + 19928*uk_116 + 540547*uk_117 + 540547*uk_118 + 132023*uk_119 + 2509709*uk_12 + 3008*uk_120 + 81592*uk_121 + 81592*uk_122 + 19928*uk_123 + 2213183*uk_124 + 2213183*uk_125 + 540547*uk_126 + 2213183*uk_127 + 540547*uk_128 + 132023*uk_129 + 378824*uk_13 + 148877*uk_130 + 22472*uk_131 + 609553*uk_132 + 609553*uk_133 + 148877*uk_134 + 3392*uk_135 + 92008*uk_136 + 92008*uk_137 + 22472*uk_138 + 2495717*uk_139 + 10275601*uk_14 + 2495717*uk_140 + 609553*uk_141 + 2495717*uk_142 + 609553*uk_143 + 148877*uk_144 + 512*uk_145 + 13888*uk_146 + 13888*uk_147 + 3392*uk_148 + 376712*uk_149 + 10275601*uk_15 + 376712*uk_150 + 92008*uk_151 + 376712*uk_152 + 92008*uk_153 + 22472*uk_154 + 10218313*uk_155 + 10218313*uk_156 + 2495717*uk_157 + 10218313*uk_158 + 2495717*uk_159 + 2509709*uk_16 + 609553*uk_160 + 10218313*uk_161 + 2495717*uk_162 + 609553*uk_163 + 148877*uk_164 + 3969*uk_17 + 2961*uk_18 + 3339*uk_19 + 63*uk_2 + 504*uk_20 + 13671*uk_21 + 13671*uk_22 + 3339*uk_23 + 2209*uk_24 + 2491*uk_25 + 376*uk_26 + 10199*uk_27 + 10199*uk_28 + 2491*uk_29 + 47*uk_3 + 2809*uk_30 + 424*uk_31 + 11501*uk_32 + 11501*uk_33 + 2809*uk_34 + 64*uk_35 + 1736*uk_36 + 1736*uk_37 + 424*uk_38 + 47089*uk_39 + 53*uk_4 + 47089*uk_40 + 11501*uk_41 + 47089*uk_42 + 11501*uk_43 + 2809*uk_44 + 106179944855977*uk_45 + 141265316367*uk_46 + 105388410623*uk_47 + 118842250277*uk_48 + 17938452872*uk_49 + 8*uk_5 + 486580534153*uk_50 + 486580534153*uk_51 + 118842250277*uk_52 + 187944057*uk_53 + 140212233*uk_54 + 158111667*uk_55 + 23865912*uk_56 + 647362863*uk_57 + 647362863*uk_58 + 158111667*uk_59 + 217*uk_6 + 104602777*uk_60 + 117956323*uk_61 + 17804728*uk_62 + 482953247*uk_63 + 482953247*uk_64 + 117956323*uk_65 + 133014577*uk_66 + 20077672*uk_67 + 544606853*uk_68 + 544606853*uk_69 + 217*uk_7 + 133014577*uk_70 + 3030592*uk_71 + 82204808*uk_72 + 82204808*uk_73 + 20077672*uk_74 + 2229805417*uk_75 + 2229805417*uk_76 + 544606853*uk_77 + 2229805417*uk_78 + 544606853*uk_79 + 53*uk_8 + 133014577*uk_80 + 250047*uk_81 + 186543*uk_82 + 210357*uk_83 + 31752*uk_84 + 861273*uk_85 + 861273*uk_86 + 210357*uk_87 + 139167*uk_88 + 156933*uk_89 + 2242306609*uk_9 + 23688*uk_90 + 642537*uk_91 + 642537*uk_92 + 156933*uk_93 + 176967*uk_94 + 26712*uk_95 + 724563*uk_96 + 724563*uk_97 + 176967*uk_98 + 4032*uk_99,
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]
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def sol_165x165():
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return {
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uk_0: -QQ(295441,1683)*uk_2 - QQ(175799,1683)*uk_7 + QQ(2401696807,1)*uk_9 - QQ(9606787228,1683)*uk_10 + QQ(9606787228,1683)*uk_15 - QQ(29030443,1683)*uk_17 - QQ(5965893,187)*uk_22 + QQ(262901,99)*uk_42 + QQ(235539209256104,1)*uk_45 - QQ(232597130667529,1683)*uk_46 + QQ(1364372733998209,1683)*uk_51 - QQ(1133600892904,1683)*uk_53 - QQ(172922170104,187)*uk_58 + QQ(249776467928,99)*uk_78 - QQ(2401889209,1683)*uk_81 - QQ(636292759,187)*uk_86 - QQ(1034157281,187)*uk_106 + QQ(10558824289,1683)*uk_161,
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uk_1: QQ(4,1683)*uk_2 - QQ(4,1683)*uk_7 - QQ(98072,1)*uk_9 + QQ(96847,1683)*uk_10 - QQ(568087,1683)*uk_15 + QQ(472,1683)*uk_17 + QQ(72,187)*uk_22 - QQ(104,99)*uk_42 - QQ(7216420377,1)*uk_45 - QQ(108808244,1683)*uk_46 - QQ(46106641036,1683)*uk_51 + QQ(17259541,1683)*uk_53 + QQ(1095291,187)*uk_58 - QQ(9936587,99)*uk_78 + QQ(41836,1683)*uk_81 + QQ(10036,187)*uk_86 + QQ(10124,187)*uk_106 - QQ(8,1)*uk_149 - QQ(586156,1683)*uk_161,
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uk_3: -QQ(295441,1683)*uk_18 - QQ(175799,1683)*uk_28 + QQ(2401696807,1)*uk_47 - QQ(9606787228,1683)*uk_54 + QQ(9606787228,1683)*uk_64 - QQ(29030443,1683)*uk_82 - QQ(5965893,187)*uk_92 + QQ(262901,99)*uk_127 + QQ(8,1)*uk_149,
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uk_4: -QQ(295441,1683)*uk_19 + QQ(1602583,3366)*uk_29 - QQ(175799,1683)*uk_33 - QQ(45670,99)*uk_34 - QQ(76006,187)*uk_38 + QQ(295441,1683)*uk_41 - QQ(45670,99)*uk_44 + QQ(2401696807,1)*uk_48 - QQ(9606787228,1683)*uk_55 + QQ(74452601017,3366)*uk_65 + QQ(9606787228,1683)*uk_69 - QQ(2401696807,99)*uk_70 - QQ(4803393614,187)*uk_74 + QQ(9606787228,1683)*uk_77 - QQ(2401696807,99)*uk_80 - QQ(29030443,1683)*uk_83 + QQ(11596905,374)*uk_93 - QQ(5965893,187)*uk_97 - QQ(769658,33)*uk_98 - QQ(17335370,1683)*uk_102 + QQ(29030443,1683)*uk_105 - QQ(769658,33)*uk_108 + QQ(77314807,3366)*uk_114 + QQ(750229,198)*uk_119 + QQ(72457964,1683)*uk_123 + QQ(11596905,374)*uk_126 + QQ(31304645,306)*uk_128 + QQ(750229,198)*uk_129 - QQ(3191393,99)*uk_134 - QQ(647642,9)*uk_138 - QQ(769658,33)*uk_141 + QQ(262901,99)*uk_142 - QQ(10478626,99)*uk_143 - QQ(3191393,99)*uk_144 - QQ(20480616,187)*uk_148 - QQ(17335370,1683)*uk_151 - QQ(174199750,1683)*uk_153 - QQ(647642,9)*uk_154 + QQ(29030443,1683)*uk_157 + QQ(5965893,187)*uk_159 - QQ(769658,33)*uk_160 - QQ(10478626,99)*uk_163 - QQ(3191393,99)*uk_164,
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uk_5: -QQ(295441,1683)*uk_20 - QQ(175799,1683)*uk_37 + QQ(2401696807,1)*uk_49 - QQ(9606787228,1683)*uk_56 + QQ(9606787228,1683)*uk_73 - QQ(29030443,1683)*uk_84 - QQ(5965893,187)*uk_101 + QQ(262901,99)*uk_152,
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uk_6: -QQ(295441,1683)*uk_21 - QQ(175799,1683)*uk_40 + QQ(2401696807,1)*uk_50 - QQ(9606787228,1683)*uk_57 + QQ(9606787228,1683)*uk_76 - QQ(29030443,1683)*uk_85 - QQ(5965893,187)*uk_104 + QQ(262901,99)*uk_158,
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uk_8: -QQ(295441,1683)*uk_23 - QQ(1602583,3366)*uk_29 + QQ(45670,99)*uk_34 + QQ(76006,187)*uk_38 - QQ(295441,1683)*uk_41 - QQ(175799,1683)*uk_43 + QQ(45670,99)*uk_44 + QQ(2401696807,1)*uk_52 - QQ(9606787228,1683)*uk_59 - QQ(74452601017,3366)*uk_65 + QQ(2401696807,99)*uk_70 + QQ(4803393614,187)*uk_74 - QQ(9606787228,1683)*uk_77 + QQ(9606787228,1683)*uk_79 + QQ(2401696807,99)*uk_80 - QQ(29030443,1683)*uk_87 - QQ(11596905,374)*uk_93 + QQ(769658,33)*uk_98 + QQ(17335370,1683)*uk_102 - QQ(29030443,1683)*uk_105 - QQ(5965893,187)*uk_107 + QQ(769658,33)*uk_108 - QQ(77314807,3366)*uk_114 - QQ(750229,198)*uk_119 - QQ(72457964,1683)*uk_123 - QQ(11596905,374)*uk_126 - QQ(31304645,306)*uk_128 - QQ(750229,198)*uk_129 + QQ(3191393,99)*uk_134 + QQ(647642,9)*uk_138 + QQ(769658,33)*uk_141 + QQ(10478626,99)*uk_143 + QQ(3191393,99)*uk_144 + QQ(20480616,187)*uk_148 + QQ(17335370,1683)*uk_151 + QQ(174199750,1683)*uk_153 + QQ(647642,9)*uk_154 - QQ(29030443,1683)*uk_157 - QQ(5965893,187)*uk_159 + QQ(769658,33)*uk_160 + QQ(262901,99)*uk_162 + QQ(10478626,99)*uk_163 + QQ(3191393,99)*uk_164,
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uk_11: QQ(4,1683)*uk_18 - QQ(4,1683)*uk_28 - QQ(98072,1)*uk_47 + QQ(96847,1683)*uk_54 - QQ(568087,1683)*uk_64 + QQ(472,1683)*uk_82 + QQ(72,187)*uk_92 - QQ(104,99)*uk_127,
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uk_12: QQ(4,1683)*uk_19 - QQ(31,3366)*uk_29 - QQ(4,1683)*uk_33 + QQ(1,99)*uk_34 + QQ(2,187)*uk_38 - QQ(4,1683)*uk_41 + QQ(1,99)*uk_44 - QQ(98072,1)*uk_48 + QQ(96847,1683)*uk_55 - QQ(1437649,3366)*uk_65 - QQ(568087,1683)*uk_69 + QQ(52402,99)*uk_70 + QQ(120138,187)*uk_74 - QQ(96847,1683)*uk_77 + QQ(52402,99)*uk_80 + QQ(472,1683)*uk_83 - QQ(225,374)*uk_93 + QQ(72,187)*uk_97 + QQ(17,33)*uk_98 + QQ(590,1683)*uk_102 - QQ(472,1683)*uk_105 + QQ(17,33)*uk_108 - QQ(1519,3366)*uk_114 - QQ(13,198)*uk_119 - QQ(1388,1683)*uk_123 - QQ(225,374)*uk_126 - QQ(605,306)*uk_128 - QQ(13,198)*uk_129 + QQ(68,99)*uk_134 + QQ(14,9)*uk_138 + QQ(17,33)*uk_141 - QQ(104,99)*uk_142 + QQ(229,99)*uk_143 + QQ(68,99)*uk_144 + QQ(472,187)*uk_148 + QQ(590,1683)*uk_151 + QQ(4450,1683)*uk_153 + QQ(14,9)*uk_154 - QQ(472,1683)*uk_157 - QQ(72,187)*uk_159 + QQ(17,33)*uk_160 + QQ(229,99)*uk_163 + QQ(68,99)*uk_164,
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uk_13: QQ(4,1683)*uk_20 - QQ(4,1683)*uk_37 - QQ(98072,1)*uk_49 + QQ(96847,1683)*uk_56 - QQ(568087,1683)*uk_73 + QQ(472,1683)*uk_84 + QQ(72,187)*uk_101 - QQ(104,99)*uk_152,
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uk_14: QQ(4,1683)*uk_21 - QQ(4,1683)*uk_40 - QQ(98072,1)*uk_50 + QQ(96847,1683)*uk_57 - QQ(568087,1683)*uk_76 + QQ(472,1683)*uk_85 + QQ(72,187)*uk_104 - QQ(104,99)*uk_158,
|
|
uk_16: QQ(4,1683)*uk_23 + QQ(31,3366)*uk_29 - QQ(1,99)*uk_34 - QQ(2,187)*uk_38 + QQ(4,1683)*uk_41 - QQ(4,1683)*uk_43 - QQ(1,99)*uk_44 - QQ(98072,1)*uk_52 + QQ(96847,1683)*uk_59 + QQ(1437649,3366)*uk_65 - QQ(52402,99)*uk_70 - QQ(120138,187)*uk_74 + QQ(96847,1683)*uk_77 - QQ(568087,1683)*uk_79 - QQ(52402,99)*uk_80 + QQ(472,1683)*uk_87 + QQ(225,374)*uk_93 - QQ(17,33)*uk_98 - QQ(590,1683)*uk_102 + QQ(472,1683)*uk_105 + QQ(72,187)*uk_107 - QQ(17,33)*uk_108 + QQ(1519,3366)*uk_114 + QQ(13,198)*uk_119 + QQ(1388,1683)*uk_123 + QQ(225,374)*uk_126 + QQ(605,306)*uk_128 + QQ(13,198)*uk_129 - QQ(68,99)*uk_134 - QQ(14,9)*uk_138 - QQ(17,33)*uk_141 - QQ(229,99)*uk_143 - QQ(68,99)*uk_144 - QQ(472,187)*uk_148 - QQ(590,1683)*uk_151 - QQ(4450,1683)*uk_153 - QQ(14,9)*uk_154 + QQ(472,1683)*uk_157 + QQ(72,187)*uk_159 - QQ(17,33)*uk_160 - QQ(104,99)*uk_162 - QQ(229,99)*uk_163 - QQ(68,99)*uk_164,
|
|
uk_24: -QQ(295441,1683)*uk_88 - QQ(175799,1683)*uk_113,
|
|
uk_26: -QQ(295441,1683)*uk_90 - QQ(175799,1683)*uk_122, uk_25: -uk_29 - QQ(295441,1683)*uk_89 - QQ(295441,1683)*uk_93 - QQ(175799,1683)*uk_118 - QQ(175799,1683)*uk_128,
|
|
uk_27: -QQ(295441,1683)*uk_91 - QQ(175799,1683)*uk_125 - QQ(4,1)*uk_149,
|
|
uk_30: -uk_34 - uk_44 - QQ(295441,1683)*uk_94 - QQ(295441,1683)*uk_98 - QQ(295441,1683)*uk_108 - QQ(175799,1683)*uk_133 - QQ(175799,1683)*uk_143 - QQ(175799,1683)*uk_163,
|
|
uk_31: -uk_38 - QQ(295441,1683)*uk_95 - QQ(295441,1683)*uk_102 - QQ(175799,1683)*uk_137 - QQ(175799,1683)*uk_153,
|
|
uk_32: -uk_41 - QQ(295441,1683)*uk_96 - QQ(295441,1683)*uk_105 - QQ(175799,1683)*uk_140 + QQ(4,1)*uk_149 - QQ(175799,1683)*uk_159,
|
|
uk_35: -QQ(295441,1683)*uk_99 - QQ(175799,1683)*uk_147,
|
|
uk_36: -QQ(295441,1683)*uk_100 - QQ(2,1)*uk_149 - QQ(175799,1683)*uk_150,
|
|
uk_39: -QQ(295441,1683)*uk_103 - QQ(175799,1683)*uk_156,
|
|
uk_60: QQ(4,1683)*uk_88 - QQ(4,1683)*uk_113,
|
|
uk_61: -uk_65 + QQ(4,1683)*uk_89 + QQ(4,1683)*uk_93 - QQ(4,1683)*uk_118 - QQ(4,1683)*uk_128,
|
|
uk_62: QQ(4,1683)*uk_90 - QQ(4,1683)*uk_122,
|
|
uk_63: QQ(4,1683)*uk_91 - QQ(4,1683)*uk_125,
|
|
uk_66: -uk_70 - uk_80 + QQ(4,1683)*uk_94 + QQ(4,1683)*uk_98 + QQ(4,1683)*uk_108 - QQ(4,1683)*uk_133 - QQ(4,1683)*uk_143 - QQ(4,1683)*uk_163,
|
|
uk_67: -uk_74 + QQ(4,1683)*uk_95 + QQ(4,1683)*uk_102 - QQ(4,1683)*uk_137 - QQ(4,1683)*uk_153,
|
|
uk_68: -uk_77 + QQ(4,1683)*uk_96 + QQ(4,1683)*uk_105 - QQ(4,1683)*uk_140 - QQ(4,1683)*uk_159,
|
|
uk_71: QQ(4,1683)*uk_99 - QQ(4,1683)*uk_147,
|
|
uk_72: QQ(4,1683)*uk_100 - QQ(4,1683)*uk_150,
|
|
uk_75: QQ(4,1683)*uk_103 - QQ(4,1683)*uk_156,
|
|
uk_109: 0,
|
|
uk_110: -uk_114,
|
|
uk_111: 0,
|
|
uk_112: 0,
|
|
uk_115: -uk_119 - uk_129,
|
|
uk_116: -uk_123,
|
|
uk_117: -uk_126,
|
|
uk_120: 0,
|
|
uk_121: 0,
|
|
uk_124: 0,
|
|
uk_130: -uk_134 - uk_144 - uk_164,
|
|
uk_131: -uk_138 - uk_154,
|
|
uk_132: -uk_141 - uk_160,
|
|
uk_135: -uk_148,
|
|
uk_136: -uk_151,
|
|
uk_139: -uk_157,
|
|
uk_145: 0,
|
|
uk_146: 0,
|
|
uk_155: 0,
|
|
}
|
|
|
|
def time_eqs_165x165():
|
|
if len(eqs_165x165()) != 165:
|
|
raise ValueError("length should be 165")
|
|
|
|
def time_solve_lin_sys_165x165():
|
|
eqs = eqs_165x165()
|
|
sol = solve_lin_sys(eqs, R_165)
|
|
if sol != sol_165x165():
|
|
raise ValueError("Value should be equal")
|
|
|
|
def time_verify_sol_165x165():
|
|
eqs = eqs_165x165()
|
|
sol = sol_165x165()
|
|
zeros = [ eq.compose(sol) for eq in eqs ]
|
|
if not all(zero == 0 for zero in zeros):
|
|
raise ValueError("All should be 0")
|
|
|
|
def time_to_expr_eqs_165x165():
|
|
eqs = eqs_165x165()
|
|
assert [ R_165.from_expr(eq.as_expr()) for eq in eqs ] == eqs
|
|
|
|
# Benchmark R_49: shows how fast are arithmetics in rational function fields.
|
|
F_abc, a, b, c = field("a,b,c", ZZ)
|
|
R_49, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, k12, k13, k14, k15, k16, k17, k18, k19, k20, k21, k22, k23, k24, k25, k26, k27, k28, k29, k30, k31, k32, k33, k34, k35, k36, k37, k38, k39, k40, k41, k42, k43, k44, k45, k46, k47, k48, k49 = ring("k1:50", F_abc)
|
|
|
|
def eqs_189x49():
|
|
return [
|
|
-b*k8/a+c*k8/a,
|
|
-b*k11/a+c*k11/a,
|
|
-b*k10/a+c*k10/a+k2,
|
|
-k3-b*k9/a+c*k9/a,
|
|
-b*k14/a+c*k14/a,
|
|
-b*k15/a+c*k15/a,
|
|
-b*k18/a+c*k18/a-k2,
|
|
-b*k17/a+c*k17/a,
|
|
-b*k16/a+c*k16/a+k4,
|
|
-b*k13/a+c*k13/a-b*k21/a+c*k21/a+b*k5/a-c*k5/a,
|
|
b*k44/a-c*k44/a,
|
|
-b*k45/a+c*k45/a,
|
|
-b*k20/a+c*k20/a,
|
|
-b*k44/a+c*k44/a,
|
|
b*k46/a-c*k46/a,
|
|
b**2*k47/a**2-2*b*c*k47/a**2+c**2*k47/a**2,
|
|
k3,
|
|
-k4,
|
|
-b*k12/a+c*k12/a-a*k6/b+c*k6/b,
|
|
-b*k19/a+c*k19/a+a*k7/c-b*k7/c,
|
|
b*k45/a-c*k45/a,
|
|
-b*k46/a+c*k46/a,
|
|
-k48+c*k48/a+c*k48/b-c**2*k48/(a*b),
|
|
-k49+b*k49/a+b*k49/c-b**2*k49/(a*c),
|
|
a*k1/b-c*k1/b,
|
|
a*k4/b-c*k4/b,
|
|
a*k3/b-c*k3/b+k9,
|
|
-k10+a*k2/b-c*k2/b,
|
|
a*k7/b-c*k7/b,
|
|
-k9,
|
|
k11,
|
|
b*k12/a-c*k12/a+a*k6/b-c*k6/b,
|
|
a*k15/b-c*k15/b,
|
|
k10+a*k18/b-c*k18/b,
|
|
-k11+a*k17/b-c*k17/b,
|
|
a*k16/b-c*k16/b,
|
|
-a*k13/b+c*k13/b+a*k21/b-c*k21/b+a*k5/b-c*k5/b,
|
|
-a*k44/b+c*k44/b,
|
|
a*k45/b-c*k45/b,
|
|
a*k14/c-b*k14/c+a*k20/b-c*k20/b,
|
|
a*k44/b-c*k44/b,
|
|
-a*k46/b+c*k46/b,
|
|
-k47+c*k47/a+c*k47/b-c**2*k47/(a*b),
|
|
a*k19/b-c*k19/b,
|
|
-a*k45/b+c*k45/b,
|
|
a*k46/b-c*k46/b,
|
|
a**2*k48/b**2-2*a*c*k48/b**2+c**2*k48/b**2,
|
|
-k49+a*k49/b+a*k49/c-a**2*k49/(b*c),
|
|
k16,
|
|
-k17,
|
|
-a*k1/c+b*k1/c,
|
|
-k16-a*k4/c+b*k4/c,
|
|
-a*k3/c+b*k3/c,
|
|
k18-a*k2/c+b*k2/c,
|
|
b*k19/a-c*k19/a-a*k7/c+b*k7/c,
|
|
-a*k6/c+b*k6/c,
|
|
-a*k8/c+b*k8/c,
|
|
-a*k11/c+b*k11/c+k17,
|
|
-a*k10/c+b*k10/c-k18,
|
|
-a*k9/c+b*k9/c,
|
|
-a*k14/c+b*k14/c-a*k20/b+c*k20/b,
|
|
-a*k13/c+b*k13/c+a*k21/c-b*k21/c-a*k5/c+b*k5/c,
|
|
a*k44/c-b*k44/c,
|
|
-a*k45/c+b*k45/c,
|
|
-a*k44/c+b*k44/c,
|
|
a*k46/c-b*k46/c,
|
|
-k47+b*k47/a+b*k47/c-b**2*k47/(a*c),
|
|
-a*k12/c+b*k12/c,
|
|
a*k45/c-b*k45/c,
|
|
-a*k46/c+b*k46/c,
|
|
-k48+a*k48/b+a*k48/c-a**2*k48/(b*c),
|
|
a**2*k49/c**2-2*a*b*k49/c**2+b**2*k49/c**2,
|
|
k8,
|
|
k11,
|
|
-k15,
|
|
k10-k18,
|
|
-k17,
|
|
k9,
|
|
-k16,
|
|
-k29,
|
|
k14-k32,
|
|
-k21+k23-k31,
|
|
-k24-k30,
|
|
-k35,
|
|
k44,
|
|
-k45,
|
|
k36,
|
|
k13-k23+k39,
|
|
-k20+k38,
|
|
k25+k37,
|
|
b*k26/a-c*k26/a-k34+k42,
|
|
-2*k44,
|
|
k45,
|
|
k46,
|
|
b*k47/a-c*k47/a,
|
|
k41,
|
|
k44,
|
|
-k46,
|
|
-b*k47/a+c*k47/a,
|
|
k12+k24,
|
|
-k19-k25,
|
|
-a*k27/b+c*k27/b-k33,
|
|
k45,
|
|
-k46,
|
|
-a*k48/b+c*k48/b,
|
|
a*k28/c-b*k28/c+k40,
|
|
-k45,
|
|
k46,
|
|
a*k48/b-c*k48/b,
|
|
a*k49/c-b*k49/c,
|
|
-a*k49/c+b*k49/c,
|
|
-k1,
|
|
-k4,
|
|
-k3,
|
|
k15,
|
|
k18-k2,
|
|
k17,
|
|
k16,
|
|
k22,
|
|
k25-k7,
|
|
k24+k30,
|
|
k21+k23-k31,
|
|
k28,
|
|
-k44,
|
|
k45,
|
|
-k30-k6,
|
|
k20+k32,
|
|
k27+b*k33/a-c*k33/a,
|
|
k44,
|
|
-k46,
|
|
-b*k47/a+c*k47/a,
|
|
-k36,
|
|
k31-k39-k5,
|
|
-k32-k38,
|
|
k19-k37,
|
|
k26-a*k34/b+c*k34/b-k42,
|
|
k44,
|
|
-2*k45,
|
|
k46,
|
|
a*k48/b-c*k48/b,
|
|
a*k35/c-b*k35/c-k41,
|
|
-k44,
|
|
k46,
|
|
b*k47/a-c*k47/a,
|
|
-a*k49/c+b*k49/c,
|
|
-k40,
|
|
k45,
|
|
-k46,
|
|
-a*k48/b+c*k48/b,
|
|
a*k49/c-b*k49/c,
|
|
k1,
|
|
k4,
|
|
k3,
|
|
-k8,
|
|
-k11,
|
|
-k10+k2,
|
|
-k9,
|
|
k37+k7,
|
|
-k14-k38,
|
|
-k22,
|
|
-k25-k37,
|
|
-k24+k6,
|
|
-k13-k23+k39,
|
|
-k28+b*k40/a-c*k40/a,
|
|
k44,
|
|
-k45,
|
|
-k27,
|
|
-k44,
|
|
k46,
|
|
b*k47/a-c*k47/a,
|
|
k29,
|
|
k32+k38,
|
|
k31-k39+k5,
|
|
-k12+k30,
|
|
k35-a*k41/b+c*k41/b,
|
|
-k44,
|
|
k45,
|
|
-k26+k34+a*k42/c-b*k42/c,
|
|
k44,
|
|
k45,
|
|
-2*k46,
|
|
-b*k47/a+c*k47/a,
|
|
-a*k48/b+c*k48/b,
|
|
a*k49/c-b*k49/c,
|
|
k33,
|
|
-k45,
|
|
k46,
|
|
a*k48/b-c*k48/b,
|
|
-a*k49/c+b*k49/c,
|
|
]
|
|
|
|
def sol_189x49():
|
|
return {
|
|
k49: 0, k48: 0, k47: 0, k46: 0, k45: 0, k44: 0, k41: 0, k40: 0,
|
|
k38: 0, k37: 0, k36: 0, k35: 0, k33: 0, k32: 0, k30: 0, k29: 0,
|
|
k28: 0, k27: 0, k25: 0, k24: 0, k22: 0, k21: 0, k20: 0, k19: 0,
|
|
k18: 0, k17: 0, k16: 0, k15: 0, k14: 0, k13: 0, k12: 0, k11: 0,
|
|
k10: 0, k9: 0, k8: 0, k7: 0, k6: 0, k5: 0, k4: 0, k3: 0,
|
|
k2: 0, k1: 0,
|
|
k34: b/c*k42,
|
|
k31: k39,
|
|
k26: a/c*k42,
|
|
k23: k39,
|
|
}
|
|
|
|
def time_eqs_189x49():
|
|
if len(eqs_189x49()) != 189:
|
|
raise ValueError("Length should be equal to 189")
|
|
|
|
def time_solve_lin_sys_189x49():
|
|
eqs = eqs_189x49()
|
|
sol = solve_lin_sys(eqs, R_49)
|
|
if sol != sol_189x49():
|
|
raise ValueError("Values should be equal")
|
|
|
|
def time_verify_sol_189x49():
|
|
eqs = eqs_189x49()
|
|
sol = sol_189x49()
|
|
zeros = [ eq.compose(sol) for eq in eqs ]
|
|
assert all(zero == 0 for zero in zeros)
|
|
|
|
def time_to_expr_eqs_189x49():
|
|
eqs = eqs_189x49()
|
|
assert [ R_49.from_expr(eq.as_expr()) for eq in eqs ] == eqs
|
|
|
|
# Benchmark R_8: shows how fast polynomial GCDs are computed.
|
|
|
|
F_a5_5, a_11, a_12, a_13, a_14, a_21, a_22, a_23, a_24, a_31, a_32, a_33, a_34, a_41, a_42, a_43, a_44 = field("a_(1:5)(1:5)", ZZ)
|
|
R_8, x0, x1, x2, x3, x4, x5, x6, x7 = ring("x:8", F_a5_5)
|
|
|
|
def eqs_10x8():
|
|
return [
|
|
(a_33*a_34 + a_33*a_44 + a_43*a_44)*x3 + (a_33*a_34 + a_33*a_44 + a_43*a_44)*x4 + (a_12*a_34 + a_12*a_44 + a_22*a_34 + a_22*a_44)*x5 + (a_12*a_44 + a_22*a_44)*x6 + (a_12*a_33 + a_22*a_33)*x7 - a_12*a_33 - a_12*a_43 - a_22*a_33 - a_22*a_43,
|
|
(a_33 + a_34 + a_43 + a_44)*x3 + (a_33 + a_34 + a_43 + a_44)*x4 + (a_12 + a_22 + a_34 + a_44)*x5 + (a_12 + a_22 + a_44)*x6 + (a_12 + a_22 + a_33)*x7 - a_12 - a_22 - a_33 - a_43,
|
|
x3 + x4 + x5 + x6 + x7 - 1,
|
|
(a_12*a_33*a_34 + a_12*a_33*a_44 + a_12*a_43*a_44 + a_22*a_33*a_34 + a_22*a_33*a_44 + a_22*a_43*a_44)*x0 + (a_22*a_33*a_34 + a_22*a_33*a_44 + a_22*a_43*a_44)*x1 + (a_12*a_33*a_34 + a_12*a_33*a_44 + a_12*a_43*a_44 + a_22*a_33*a_34 + a_22*a_33*a_44 + a_22*a_43*a_44)*x2 + (a_11*a_33*a_34 + a_11*a_33*a_44 + a_11*a_43*a_44 + a_31*a_33*a_34 + a_31*a_33*a_44 + a_31*a_43*a_44)*x3 + (a_11*a_33*a_34 + a_11*a_33*a_44 + a_11*a_43*a_44 + a_21*a_33*a_34 + a_21*a_33*a_44 + a_21*a_43*a_44 + a_31*a_33*a_34 + a_31*a_33*a_44 + a_31*a_43*a_44)*x4 + (a_11*a_12*a_34 + a_11*a_12*a_44 + a_11*a_22*a_34 + a_11*a_22*a_44 + a_12*a_31*a_34 + a_12*a_31*a_44 + a_21*a_22*a_34 + a_21*a_22*a_44 + a_22*a_31*a_34 + a_22*a_31*a_44)*x5 + (a_11*a_12*a_44 + a_11*a_22*a_44 + a_12*a_31*a_44 + a_21*a_22*a_44 + a_22*a_31*a_44)*x6 + (a_11*a_12*a_33 + a_11*a_22*a_33 + a_12*a_31*a_33 + a_21*a_22*a_33 + a_22*a_31*a_33)*x7 - a_11*a_12*a_33 - a_11*a_12*a_43 - a_11*a_22*a_33 - a_11*a_22*a_43 - a_12*a_31*a_33 - a_12*a_31*a_43 - a_21*a_22*a_33 - a_21*a_22*a_43 - a_22*a_31*a_33 - a_22*a_31*a_43,
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(a_12*a_33 + a_12*a_34 + a_12*a_43 + a_12*a_44 + a_22*a_33 + a_22*a_34 + a_22*a_43 + a_22*a_44 + a_33*a_34 + a_33*a_44 + a_43*a_44)*x0 + (a_22*a_33 + a_22*a_34 + a_22*a_43 + a_22*a_44 + a_33*a_34 + a_33*a_44 + a_43*a_44)*x1 + (a_12*a_33 + a_12*a_34 + a_12*a_43 + a_12*a_44 + a_22*a_33 + a_22*a_34 + a_22*a_43 + a_22*a_44 + a_33*a_34 + a_33*a_44 + a_43*a_44)*x2 + (a_11*a_33 + a_11*a_34 + a_11*a_43 + a_11*a_44 + a_31*a_33 + a_31*a_34 + a_31*a_43 + a_31*a_44 + a_33*a_34 + a_33*a_44 + a_43*a_44)*x3 + (a_11*a_33 + a_11*a_34 + a_11*a_43 + a_11*a_44 + a_21*a_33 + a_21*a_34 + a_21*a_43 + a_21*a_44 + a_31*a_33 + a_31*a_34 + a_31*a_43 + a_31*a_44 + a_33*a_34 + a_33*a_44 + a_43*a_44)*x4 + (a_11*a_12 + a_11*a_22 + a_11*a_34 + a_11*a_44 + a_12*a_31 + a_12*a_34 + a_12*a_44 + a_21*a_22 + a_21*a_34 + a_21*a_44 + a_22*a_31 + a_22*a_34 + a_22*a_44 + a_31*a_34 + a_31*a_44)*x5 + (a_11*a_12 + a_11*a_22 + a_11*a_44 + a_12*a_31 + a_12*a_44 + a_21*a_22 + a_21*a_44 + a_22*a_31 + a_22*a_44 + a_31*a_44)*x6 + (a_11*a_12 + a_11*a_22 + a_11*a_33 + a_12*a_31 + a_12*a_33 + a_21*a_22 + a_21*a_33 + a_22*a_31 + a_22*a_33 + a_31*a_33)*x7 - a_11*a_12 - a_11*a_22 - a_11*a_33 - a_11*a_43 - a_12*a_31 - a_12*a_33 - a_12*a_43 - a_21*a_22 - a_21*a_33 - a_21*a_43 - a_22*a_31 - a_22*a_33 - a_22*a_43 - a_31*a_33 - a_31*a_43,
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(a_12 + a_22 + a_33 + a_34 + a_43 + a_44)*x0 + (a_22 + a_33 + a_34 + a_43 + a_44)*x1 + (a_12 + a_22 + a_33 + a_34 + a_43 + a_44)*x2 + (a_11 + a_31 + a_33 + a_34 + a_43 + a_44)*x3 + (a_11 + a_21 + a_31 + a_33 + a_34 + a_43 + a_44)*x4 + (a_11 + a_12 + a_21 + a_22 + a_31 + a_34 + a_44)*x5 + (a_11 + a_12 + a_21 + a_22 + a_31 + a_44)*x6 + (a_11 + a_12 + a_21 + a_22 + a_31 + a_33)*x7 - a_11 - a_12 - a_21 - a_22 - a_31 - a_33 - a_43,
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x0 + x1 + x2 + x3 + x4 + x5 + x6 + x7 - 1,
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(a_12*a_34 + a_12*a_44 + a_22*a_34 + a_22*a_44)*x2 + (a_31*a_34 + a_31*a_44)*x3 + (a_31*a_34 + a_31*a_44)*x4 + (a_12*a_31 + a_22*a_31)*x7 - a_12*a_31 - a_22*a_31,
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(a_12 + a_22 + a_34 + a_44)*x2 + a_31*x3 + a_31*x4 + a_31*x7 - a_31,
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x2,
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]
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def sol_10x8():
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return {
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x0: -a_21/a_12*x4,
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x1: a_21/a_12*x4,
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x2: 0,
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x3: -x4,
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x5: a_43/a_34,
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x6: -a_43/a_34,
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x7: 1,
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}
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def time_eqs_10x8():
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if len(eqs_10x8()) != 10:
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raise ValueError("Value should be equal to 10")
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|
|
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def time_solve_lin_sys_10x8():
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eqs = eqs_10x8()
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sol = solve_lin_sys(eqs, R_8)
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if sol != sol_10x8():
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raise ValueError("Values should be equal")
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def time_verify_sol_10x8():
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eqs = eqs_10x8()
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sol = sol_10x8()
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zeros = [ eq.compose(sol) for eq in eqs ]
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if not all(zero == 0 for zero in zeros):
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raise ValueError("All values in zero should be 0")
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|
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def time_to_expr_eqs_10x8():
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eqs = eqs_10x8()
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assert [ R_8.from_expr(eq.as_expr()) for eq in eqs ] == eqs
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