P={('B', 'a'): -4.762305214596967,
 ('B', 'ad'): -6.680066036784177,
 ('B', 'ag'): -3.14e+100,
 ('B', 'an'): -8.697083223018778,
 ('B', 'b'): -5.018374362109218,
 ('B', 'bg'): -3.14e+100,
 ('B', 'c'): -3.423880184954888,
 ('B', 'd'): -3.9750475297585357,
 ('B', 'df'): -8.888974230828882,
 ('B', 'dg'): -3.14e+100,
 ('B', 'e'): -8.563551830394255,
 ('B', 'en'): -3.14e+100,
 ('B', 'f'): -5.491630418482717,
 ('B', 'g'): -3.14e+100,
 ('B', 'h'): -13.533365129970255,
 ('B', 'i'): -6.1157847275557105,
 ('B', 'in'): -3.14e+100,
 ('B', 'j'): -5.0576191284681915,
 ('B', 'jn'): -3.14e+100,
 ('B', 'k'): -3.14e+100,
 ('B', 'l'): -4.905883584659895,
 ('B', 'ln'): -3.14e+100,
 ('B', 'm'): -3.6524299819046386,
 ('B', 'mg'): -3.14e+100,
 ('B', 'mq'): -6.78695300139688,
 ('B', 'n'): -1.6966257797548328,
 ('B', 'ng'): -3.14e+100,
 ('B', 'nr'): -2.2310495913769506,
 ('B', 'nrfg'): -5.873722175405573,
 ('B', 'nrt'): -4.985642733519195,
 ('B', 'ns'): -2.8228438314969213,
 ('B', 'nt'): -4.846091668182416,
 ('B', 'nz'): -3.94698846057672,
 ('B', 'o'): -8.433498702146057,
 ('B', 'p'): -4.200984132085048,
 ('B', 'q'): -6.998123858956596,
 ('B', 'qe'): -3.14e+100,
 ('B', 'qg'): -3.14e+100,
 ('B', 'r'): -3.4098187790818413,
 ('B', 'rg'): -3.14e+100,
 ('B', 'rr'): -12.434752841302146,
 ('B', 'rz'): -7.946116471570005,
 ('B', 's'): -5.522673590839954,
 ('B', 't'): -3.3647479094528574,
 ('B', 'tg'): -3.14e+100,
 ('B', 'u'): -9.163917277503234,
 ('B', 'ud'): -3.14e+100,
 ('B', 'ug'): -3.14e+100,
 ('B', 'uj'): -3.14e+100,
 ('B', 'ul'): -3.14e+100,
 ('B', 'uv'): -3.14e+100,
 ('B', 'uz'): -3.14e+100,
 ('B', 'v'): -2.6740584874265685,
 ('B', 'vd'): -9.044728760238115,
 ('B', 'vg'): -3.14e+100,
 ('B', 'vi'): -12.434752841302146,
 ('B', 'vn'): -4.3315610890163585,
 ('B', 'vq'): -12.147070768850364,
 ('B', 'w'): -3.14e+100,
 ('B', 'x'): -3.14e+100,
 ('B', 'y'): -9.844485675856319,
 ('B', 'yg'): -3.14e+100,
 ('B', 'z'): -7.045681111485645,
 ('B', 'zg'): -3.14e+100,
 ('E', 'a'): -3.14e+100,
 ('E', 'ad'): -3.14e+100,
 ('E', 'ag'): -3.14e+100,
 ('E', 'an'): -3.14e+100,
 ('E', 'b'): -3.14e+100,
 ('E', 'bg'): -3.14e+100,
 ('E', 'c'): -3.14e+100,
 ('E', 'd'): -3.14e+100,
 ('E', 'df'): -3.14e+100,
 ('E', 'dg'): -3.14e+100,
 ('E', 'e'): -3.14e+100,
 ('E', 'en'): -3.14e+100,
 ('E', 'f'): -3.14e+100,
 ('E', 'g'): -3.14e+100,
 ('E', 'h'): -3.14e+100,
 ('E', 'i'): -3.14e+100,
 ('E', 'in'): -3.14e+100,
 ('E', 'j'): -3.14e+100,
 ('E', 'jn'): -3.14e+100,
 ('E', 'k'): -3.14e+100,
 ('E', 'l'): -3.14e+100,
 ('E', 'ln'): -3.14e+100,
 ('E', 'm'): -3.14e+100,
 ('E', 'mg'): -3.14e+100,
 ('E', 'mq'): -3.14e+100,
 ('E', 'n'): -3.14e+100,
 ('E', 'ng'): -3.14e+100,
 ('E', 'nr'): -3.14e+100,
 ('E', 'nrfg'): -3.14e+100,
 ('E', 'nrt'): -3.14e+100,
 ('E', 'ns'): -3.14e+100,
 ('E', 'nt'): -3.14e+100,
 ('E', 'nz'): -3.14e+100,
 ('E', 'o'): -3.14e+100,
 ('E', 'p'): -3.14e+100,
 ('E', 'q'): -3.14e+100,
 ('E', 'qe'): -3.14e+100,
 ('E', 'qg'): -3.14e+100,
 ('E', 'r'): -3.14e+100,
 ('E', 'rg'): -3.14e+100,
 ('E', 'rr'): -3.14e+100,
 ('E', 'rz'): -3.14e+100,
 ('E', 's'): -3.14e+100,
 ('E', 't'): -3.14e+100,
 ('E', 'tg'): -3.14e+100,
 ('E', 'u'): -3.14e+100,
 ('E', 'ud'): -3.14e+100,
 ('E', 'ug'): -3.14e+100,
 ('E', 'uj'): -3.14e+100,
 ('E', 'ul'): -3.14e+100,
 ('E', 'uv'): -3.14e+100,
 ('E', 'uz'): -3.14e+100,
 ('E', 'v'): -3.14e+100,
 ('E', 'vd'): -3.14e+100,
 ('E', 'vg'): -3.14e+100,
 ('E', 'vi'): -3.14e+100,
 ('E', 'vn'): -3.14e+100,
 ('E', 'vq'): -3.14e+100,
 ('E', 'w'): -3.14e+100,
 ('E', 'x'): -3.14e+100,
 ('E', 'y'): -3.14e+100,
 ('E', 'yg'): -3.14e+100,
 ('E', 'z'): -3.14e+100,
 ('E', 'zg'): -3.14e+100,
 ('M', 'a'): -3.14e+100,
 ('M', 'ad'): -3.14e+100,
 ('M', 'ag'): -3.14e+100,
 ('M', 'an'): -3.14e+100,
 ('M', 'b'): -3.14e+100,
 ('M', 'bg'): -3.14e+100,
 ('M', 'c'): -3.14e+100,
 ('M', 'd'): -3.14e+100,
 ('M', 'df'): -3.14e+100,
 ('M', 'dg'): -3.14e+100,
 ('M', 'e'): -3.14e+100,
 ('M', 'en'): -3.14e+100,
 ('M', 'f'): -3.14e+100,
 ('M', 'g'): -3.14e+100,
 ('M', 'h'): -3.14e+100,
 ('M', 'i'): -3.14e+100,
 ('M', 'in'): -3.14e+100,
 ('M', 'j'): -3.14e+100,
 ('M', 'jn'): -3.14e+100,
 ('M', 'k'): -3.14e+100,
 ('M', 'l'): -3.14e+100,
 ('M', 'ln'): -3.14e+100,
 ('M', 'm'): -3.14e+100,
 ('M', 'mg'): -3.14e+100,
 ('M', 'mq'): -3.14e+100,
 ('M', 'n'): -3.14e+100,
 ('M', 'ng'): -3.14e+100,
 ('M', 'nr'): -3.14e+100,
 ('M', 'nrfg'): -3.14e+100,
 ('M', 'nrt'): -3.14e+100,
 ('M', 'ns'): -3.14e+100,
 ('M', 'nt'): -3.14e+100,
 ('M', 'nz'): -3.14e+100,
 ('M', 'o'): -3.14e+100,
 ('M', 'p'): -3.14e+100,
 ('M', 'q'): -3.14e+100,
 ('M', 'qe'): -3.14e+100,
 ('M', 'qg'): -3.14e+100,
 ('M', 'r'): -3.14e+100,
 ('M', 'rg'): -3.14e+100,
 ('M', 'rr'): -3.14e+100,
 ('M', 'rz'): -3.14e+100,
 ('M', 's'): -3.14e+100,
 ('M', 't'): -3.14e+100,
 ('M', 'tg'): -3.14e+100,
 ('M', 'u'): -3.14e+100,
 ('M', 'ud'): -3.14e+100,
 ('M', 'ug'): -3.14e+100,
 ('M', 'uj'): -3.14e+100,
 ('M', 'ul'): -3.14e+100,
 ('M', 'uv'): -3.14e+100,
 ('M', 'uz'): -3.14e+100,
 ('M', 'v'): -3.14e+100,
 ('M', 'vd'): -3.14e+100,
 ('M', 'vg'): -3.14e+100,
 ('M', 'vi'): -3.14e+100,
 ('M', 'vn'): -3.14e+100,
 ('M', 'vq'): -3.14e+100,
 ('M', 'w'): -3.14e+100,
 ('M', 'x'): -3.14e+100,
 ('M', 'y'): -3.14e+100,
 ('M', 'yg'): -3.14e+100,
 ('M', 'z'): -3.14e+100,
 ('M', 'zg'): -3.14e+100,
 ('S', 'a'): -3.9025396831295227,
 ('S', 'ad'): -11.048458480182255,
 ('S', 'ag'): -6.954113917960154,
 ('S', 'an'): -12.84021794941031,
 ('S', 'b'): -6.472888763970454,
 ('S', 'bg'): -3.14e+100,
 ('S', 'c'): -4.786966795861212,
 ('S', 'd'): -3.903919764181873,
 ('S', 'df'): -3.14e+100,
 ('S', 'dg'): -8.948397651299683,
 ('S', 'e'): -5.942513006281674,
 ('S', 'en'): -3.14e+100,
 ('S', 'f'): -5.194820249981676,
 ('S', 'g'): -6.507826815331734,
 ('S', 'h'): -8.650563207383884,
 ('S', 'i'): -3.14e+100,
 ('S', 'in'): -3.14e+100,
 ('S', 'j'): -4.911992119644354,
 ('S', 'jn'): -3.14e+100,
 ('S', 'k'): -6.940320595827818,
 ('S', 'l'): -3.14e+100,
 ('S', 'ln'): -3.14e+100,
 ('S', 'm'): -3.269200652116097,
 ('S', 'mg'): -10.825314928868044,
 ('S', 'mq'): -3.14e+100,
 ('S', 'n'): -3.8551483897645107,
 ('S', 'ng'): -4.913434861102905,
 ('S', 'nr'): -4.483663103956885,
 ('S', 'nrfg'): -3.14e+100,
 ('S', 'nrt'): -3.14e+100,
 ('S', 'ns'): -3.14e+100,
 ('S', 'nt'): -12.147070768850364,
 ('S', 'nz'): -3.14e+100,
 ('S', 'o'): -8.464460927750023,
 ('S', 'p'): -2.9868401813596317,
 ('S', 'q'): -4.888658618255058,
 ('S', 'qe'): -3.14e+100,
 ('S', 'qg'): -3.14e+100,
 ('S', 'r'): -2.7635336784127853,
 ('S', 'rg'): -10.275268591948773,
 ('S', 'rr'): -3.14e+100,
 ('S', 'rz'): -3.14e+100,
 ('S', 's'): -3.14e+100,
 ('S', 't'): -3.14e+100,
 ('S', 'tg'): -6.272842531880403,
 ('S', 'u'): -6.940320595827818,
 ('S', 'ud'): -7.728230161053767,
 ('S', 'ug'): -7.5394037026636855,
 ('S', 'uj'): -6.85251045118004,
 ('S', 'ul'): -8.4153713175535,
 ('S', 'uv'): -8.15808672228609,
 ('S', 'uz'): -9.299258625372996,
 ('S', 'v'): -3.053292303412302,
 ('S', 'vd'): -3.14e+100,
 ('S', 'vg'): -5.9430181843676895,
 ('S', 'vi'): -3.14e+100,
 ('S', 'vn'): -11.453923588290419,
 ('S', 'vq'): -3.14e+100,
 ('S', 'w'): -3.14e+100,
 ('S', 'x'): -8.427419656069674,
 ('S', 'y'): -6.1970794699489575,
 ('S', 'yg'): -13.533365129970255,
 ('S', 'z'): -3.14e+100,
 ('S', 'zg'): -3.14e+100}