// s = '0==6=>iii22,28,65,7,102,157iii1==11=>iii22,28,65,7,4,244,78,212,244,7,61iii2==5=>iii22,28,65,7,98iii3==0=>iiiiii4==23=>iii22,28,65,7,126,253,124,215,243,24,247,249,62,199,171,221,191,66,201,138,6,249,118iii5==9=>iii22,28,65,7,61,156,95,228,82iii6==0=>iiiiii7==129=>iii22,28,65,7,214,14,236,62,164,125,64,172,153,235,0,77,7,168,151,85,87,81,89,196,177,96,103,166,83,163,234,138,29,180,222,24,224,51,233,230,112,2,39,196,85,30,114,114,224,76,153,146,230,115,107,25,34,87,190,254,60,88,163,75,88,83,187,15,133,247,22,149,80,209,197,104,12,167,109,100,210,35,193,174,81,83,135,140,190,44,209,117,217,218,87,184,235,215,36,82,215,103,75,76,155,134,217,174,155,148,97,33,182,33,30,77,28,78,57,175,76,223,166,1,145,199,227,151,192iii8==13=>iii22,28,65,7,101,202,160,32,241,232,156,85,166iii9==28=>iii22,28,65,7,122,74,129,24,234,55,100,241,58,37,96,21,239,191,165,255,194,149,136,44,148,54,245,230iii10==0=>iiiiii11==45=>iii22,28,65,7,49,112,7,114,214,182,87,143,49,204,38,65,145,90,152,90,34,149,46,101,82,32,249,196,170,145,210,145,174,129,254,237,220,88,243,40,105,145,24,33,69iii12==5=>iii22,28,65,7,13iii13==234=>iii22,28,65,7,123,220,143,88,154,91,137,20,173,90,76,23,101,91,199,206,80,58,186,211,155,251,132,187,127,246,57,66,118,230,103,174,252,29,1,224,189,192,248,242,66,165,243,117,69,160,99,132,53,76,137,199,46,208,27,141,152,74,120,183,29,234,233,46,139,89,85,173,143,139,127,188,46,136,153,144,220,218,117,124,138,209,186,175,78,171,193,125,92,198,74,71,226,74,116,104,80,89,164,112,165,5,62,46,149,209,75,93,153,14,4,95,71,139,150,104,252,209,232,196,162,113,184,41,48,69,47,172,27,222,81,129,119,50,24,23,3,30,44,35,197,34,238,166,35,133,18,125,152,17,136,207,66,239,121,100,145,137,37,208,220,86,145,238,211,36,31,14,94,169,176,218,55,20,102,12,63,158,18,87,87,63,36,8,74,92,141,184,227,57,231,148,204,129,99,248,8,214,139,28,186,65,171,56,145,49,8,224,83,23,51,114,150,219,9,185,107,13,222,123,65,28,115,82,17,83,80,117,134,50iii14==5=>iii22,28,65,7,236iii15==0=>iiiiii16==0=>iiiiii17==1061=>iii22,28,65,7,84,227,115,128,250,245,242,253,236,2,166,144,224,121,72,232,41,192,16,117,164,167,59,106,181,23,113,57,34,80,87,181,90,188,175,193,80,107,115,203,149,243,74,148,113,93,24,140,248,123,145,33,228,53,17,50,243,81,223,134,34,101,149,206,42,188,75,73,129,39,82,66,176,18,153,201,209,247,178,58,202,164,186,232,1,93,69,56,70,96,126,114,54,28,192,183,160,1,25,180,56,89,138,21,36,126,161,156,198,115,246,127,54,233,51,100,185,134,75,199,26,66,211,46,187,218,165,227,12,233,19,251,137,251,64,161,140,89,18,170,246,231,129,176,244,39,135,81,56,62,22,15,34,25,156,8,177,120,8,77,9,46,248,24,130,120,92,223,137,76,122,220,50,15,248,169,162,136,186,102,114,175,255,6,136,141,16,145,173,57,39,179,94,103,150,60,159,14,226,4,240,213,30,154,0,143,171,220,164,78,160,168,145,92,117,190,199,125,34,119,175,194,72,44,61,225,225,215,78,215,172,100,56,101,219,249,95,25,110,231,57,45,249,74,33,60,24,97,84,122,213,146,155,182,165,161,29,111,183,107,45,189,27,47,17,218,246,46,28,90,252,242,39,26,124,182,233,205,7,221,75,192,119,242,22,155,44,206,233,11,133,229,234,105,158,42,161,120,195,26,23,54,42,117,244,48,247,1,93,59,39,4,109,43,155,102,121,207,4,121,181,137,65,78,241,92,106,111,247,144,66,155,184,110,97,187,46,154,27,213,162,242,222,68,6,16,142,114,61,13,254,183,84,51,105,62,109,114,172,159,122,162,210,212,98,148,126,68,141,11,2,96,64,35,66,177,64,71,125,152,187,4,144,105,129,96,68,138,102,56,19,132,164,71,95,110,204,52,88,147,79,157,149,101,231,69,185,222,59,31,199,137,94,8,191,27,89,36,68,112,252,212,163,83,102,135,203,86,177,26,22,243,133,247,189,226,82,169,139,236,86,143,194,45,167,93,30,1,205,14,98,117,107,117,95,72,135,230,145,69,213,152,66,113,31,92,187,114,199,110,182,226,174,53,100,127,67,206,30,40,84,102,136,82,84,183,43,78,85,229,46,73,31,52,251,82,7,83,179,143,55,119,214,143,252,102,183,127,168,23,21,116,34,246,175,204,130,56,164,164,105,40,54,7,245,242,109,76,183,216,17,149,228,180,105,122,27,162,240,34,56,157,142,251,253,30,99,217,194,91,230,52,129,62,137,129,67,200,17,212,207,11,155,220,46,138,209,142,118,218,214,112,93,2,180,242,185,212,78,121,176,15,239,63,164,140,161,140,248,90,245,214,31,194,61,139,228,47,175,214,193,241,103,82,226,102,124,181,118,144,6,87,46,67,190,18,121,142,132,170,212,184,18,201,235,60,114,5,120,181,154,202,3,243,48,166,102,49,52,63,27,7,0,228,71,131,132,128,70,63,195,71,224,22,81,149,127,67,223,160,51,33,130,217,187,182,92,10,226,128,61,239,184,250,246,10,61,144,223,147,24,248,153,39,162,80,243,215,234,1,65,139,191,7,120,207,81,136,123,37,30,12,60,25,96,232,44,62,146,35,3,152,204,215,7,22,86,133,216,38,15,28,170,22,65,153,116,158,217,96,205,241,226,89,0,201,63,59,195,214,202,229,198,217,97,216,218,18,21,0,27,146,219,177,241,106,229,227,203,15,76,196,151,148,11,183,103,41,139,70,100,27,96,190,74,0,177,12,30,173,203,147,1,30,122,22,99,252,46,189,94,3,38,61,238,113,152,237,190,228,18,152,20,163,97,36,39,6,170,106,124,224,142,166,118,188,94,177,220,130,235,163,20,112,25,116,93,138,170,154,230,119,70,46,76,133,34,50,33,226,99,216,129,4,238,31,85,93,177,123,73,29,184,45,201,149,244,248,37,52,224,223,153,209,0,49,28,53,51,0,137,30,41,11,5,47,104,34,127,207,180,221,244,135,135,101,11,86,113,212,217,135,63,152,235,221,209,5,131,153,82,105,217,109,150,12,137,72,180,103,234,145,33,159,87,222,124,139,17,205,62,38,59,136,133,30,160,28,236,160,225,91,236,101,14,249,95,105,208,72,127,39,231,239,19,134,178,224,165,4,37,236,202,240,121,36,93,195,130,207,134,176,140,161,113,41,74,154,192,212,43,143,162,20,175,192,212,156,204,71,153,72,162,252,231,133,17,51,114,186,241,225,164,65,31,87,76,234,25,158,249,14,0,138,190,87,111,5,62,157,3,82,187,6,161,154,154,81,254,10,109,247,187,153,242,104,156,46,12,244,246,33,254,16,105,28,132,47,60,125,254,68,167,47,78,198,33,95,157,123,189,174,234,160,244,109,124iii18==5=>iii22,28,65,7,79iii19==13=>iii22,28,65,7,103,90,165,203,241,58,119,17,38iii20==6=>iii22,28,65,7,221,214iii21==25=>iii22,28,65,7,238,250,109,86,23,159,195,60,181,20,92,151,93,55,215,51,24,67,151,229,133iii22==47=>iii22,28,65,7,155,211,221,169,229,121,221,200,236,137,188,243,115,205,229,102,79,175,61,127,28,169,84,247,158,95,113,216,213,158,222,252,163,141,66,169,141,86,120,116,50,231,110iii23==6=>iii22,28,65,7,99,57iii24==30=>iii22,28,65,7,183,117,255,145,159,123,143,172,238,162,245,127,34,220,2,27,169,164,40,8,206,229,238,10,186,216iii25==6=>iii22,28,65,7,62,171iii26==9=>iii22,28,65,7,183,97,101,60,85iii27==15=>iii22,28,65,7,31,187,117,173,38,222,38,210,170,190,100iii28==5=>iii22,28,65,7,25iii29==6=>iii22,28,65,7,137,58iii30==0=>iiiiii31==0=>iiiiii32==12=>iii22,28,65,7,147,249,161,255,227,195,184,141iii33==94=>iii22,28,65,7,79,93,3,77,182,20,49,228,3,167,220,196,130,239,171,92,14,52,168,47,0,169,37,88,81,240,165,153,132,41,163,203,68,241,96,184,211,63,241,97,250,149,246,214,218,112,218,28,42,22,165,6,244,205,210,145,100,83,155,201,119,35,216,195,178,74,143,141,180,91,202,96,168,114,170,39,36,80,145,103,237,202,209,208,186,112,232,185,63,81iii34==0=>iiiiii35==5=>iii22,28,65,7,127iii36==7=>iii22,28,65,7,6,171,198iii37==6=>iii22,28,65,7,163,169iii38==5=>iii22,28,65,7,247iii39==19=>iii22,28,65,7,150,92,195,237,131,90,86,113,29,127,155,167,240,88,237iii40==5=>iii22,28,65,7,176iii41==0=>iiiiii42==38=>iii22,28,65,7,123,231,72,48,179,59,132,119,104,255,156,158,149,93,138,32,221,162,187,240,69,62,31,100,106,202,163,248,176,219,209,169,29,119iii43==5=>iii22,28,65,7,15iii44==5=>iii22,28,65,7,99iii45==13=>iii22,28,65,7,249,225,143,186,127,182,199,53,34iii46==0=>iiiiii47==6=>iii22,28,65,7,85,59iii48==7=>iii22,28,65,7,28,249,132iii49==5=>iii22,28,65,7,221iii50==0=>iiiiii51==106=>iii22,28,65,7,49,14,159,159,15,151,79,34,220,240,139,18,212,185,38,119,126,156,125,249,221,7,194,235,242,22,104,161,147,56,140,146,228,205,89,137,25,167,175,101,204,59,24,209,178,167,127,87,143,242,152,92,184,33,63,38,179,46,248,199,66,194,205,163,17,208,249,107,27,88,193,204,217,159,213,188,75,68,226,84,232,125,182,190,88,165,69,123,81,69,217,140,240,206,146,13,46,13,254,114,168,176iii52==0=>iiiiii53==0=>iiiiii54==8=>iii22,28,65,7,8,216,96,71iii55==7=>iii22,28,65,7,17,75,111iii56==0=>iiiiii57==0=>iiiiii58==309=>iii22,28,65,7,121,147,153,138,86,36,246,234,208,156,43,51,183,85,172,21,94,180,243,198,91,155,26,122,187,191,83,168,5,94,11,114,202,198,73,40,116,10,83,201,64,32,103,134,252,105,94,138,81,11,123,94,44,103,124,25,58,218,91,26,215,33,171,131,83,86,231,204,242,219,136,210,185,86,236,172,62,14,174,5,149,95,130,43,12,187,157,59,125,87,80,128,160,194,231,73,129,97,81,162,191,14,8,74,236,38,4,151,139,127,52,229,104,193,117,30,200,237,209,206,39,145,76,51,142,134,3,28,108,242,41,145,78,205,207,215,220,139,197,22,155,155,54,83,217,36,47,212,125,82,15,165,187,111,168,100,207,110,193,205,212,194,151,92,146,170,247,108,129,207,72,78,13,27,63,91,236,189,80,119,196,221,232,66,201,209,160,18,102,104,208,37,164,187,169,29,17,31,84,141,239,145,168,136,239,156,32,99,95,48,193,120,21,34,205,215,112,185,69,153,247,224,149,86,140,30,247,42,57,167,179,139,24,9,237,31,101,28,243,156,109,155,142,102,230,101,5,237,126,50,242,137,16,248,239,158,40,170,113,12,32,42,28,1,161,145,109,57,119,13,224,201,112,237,130,164,182,161,128,226,38,229,103,44,244,75,46,66,215,51,191,43,135,247,193,20,199,41,38,72,111,116,73,112,51iii59==25=>iii22,28,65,7,210,92,229,181,138,138,238,180,141,188,217,244,1,50,110,37,31,19,182,240,74'
// s = '0==6=>iii22,28,65,7,102,157iii1==0=>iiiiii2==5=>iii22,28,65,7,98iii3==0=>iiiiii4==19=>iii22,28,65,7,126,253,124,215,179,110,222,195,54,199,27,95,26,64,181iii5==9=>iii22,28,65,7,61,156,95,228,82iii6==0=>iiiiii7==129=>iii22,28,65,7,214,14,236,62,164,125,64,172,153,235,0,77,7,168,151,85,87,81,89,196,177,96,103,166,83,163,234,138,29,180,222,24,224,51,233,230,112,2,39,196,85,30,114,114,224,76,153,146,230,115,107,25,34,87,190,254,60,88,163,75,88,83,187,15,133,247,22,149,80,209,197,104,12,167,109,100,210,35,193,174,81,83,135,140,190,44,209,117,217,218,87,184,235,215,36,82,215,103,75,76,155,134,217,174,155,148,97,33,182,33,30,77,28,78,57,175,76,223,166,1,145,199,227,151,192iii8==0=>iiiiii9==28=>iii22,28,65,7,122,74,129,24,234,55,100,241,58,37,96,21,239,191,165,255,194,149,136,44,148,54,245,230iii10==0=>iiiiii11==0=>iiiiii12==5=>iii22,28,65,7,13iii13==234=>iii22,28,65,7,123,220,143,88,154,91,137,20,173,90,76,23,101,91,199,206,80,58,186,211,155,251,132,187,127,246,57,66,118,230,103,174,252,29,1,224,189,192,248,242,66,165,243,117,69,160,99,132,53,76,137,199,46,208,27,141,152,74,120,183,29,234,233,46,139,89,85,173,143,139,127,188,46,136,153,144,220,218,117,124,138,209,186,175,78,171,193,125,92,198,74,71,226,74,116,104,80,89,164,112,165,5,62,46,149,209,75,93,153,14,4,95,71,139,150,104,252,209,232,196,162,113,184,41,48,69,47,172,27,222,81,129,119,50,24,23,3,30,44,35,197,34,238,166,35,133,18,125,152,17,136,207,66,239,121,100,145,137,37,208,220,86,145,238,211,36,31,14,94,169,176,218,55,20,102,12,63,158,18,87,87,63,36,8,74,92,141,184,227,57,231,148,204,129,99,248,8,214,139,28,186,65,171,56,145,49,8,224,83,23,51,114,150,219,9,185,107,13,222,123,65,28,115,82,17,83,80,117,134,50iii14==0=>iiiiii15==0=>iiiiii16==0=>iiiiii17==1061=>iii22,28,65,7,84,227,115,128,250,245,242,253,236,2,166,144,224,121,72,232,41,192,16,117,164,167,59,106,181,23,113,57,34,80,87,181,90,188,175,193,80,107,115,203,149,243,74,148,113,93,24,140,248,123,145,33,228,53,17,50,243,81,223,134,34,101,149,206,42,188,75,73,129,39,82,66,176,18,153,201,209,247,178,58,202,164,186,232,1,93,69,56,70,96,126,114,54,28,192,183,160,1,25,180,56,89,138,21,36,126,161,156,198,115,246,127,54,233,51,100,185,134,75,199,26,66,211,46,187,218,165,227,12,233,19,251,137,251,64,161,140,89,18,170,246,231,129,176,244,39,135,81,56,62,22,15,34,25,156,8,177,120,8,77,9,46,248,24,130,120,92,223,137,76,122,220,50,15,248,169,162,136,186,102,114,175,255,6,136,141,16,145,173,57,39,179,94,103,150,60,159,14,226,4,240,213,30,154,0,143,171,220,164,78,160,168,145,92,117,190,199,125,34,119,175,194,72,44,61,225,225,215,78,215,172,100,56,101,219,249,95,25,110,231,57,45,249,74,33,60,24,97,84,122,213,146,155,182,165,161,29,111,183,107,45,189,27,47,17,218,246,46,28,90,252,242,39,26,124,182,233,205,7,221,75,192,119,242,22,155,44,206,233,11,133,229,234,105,158,42,161,120,195,26,23,54,42,117,244,48,247,1,93,59,39,4,109,43,155,102,121,207,4,121,181,137,65,78,241,92,106,111,247,144,66,155,184,110,97,187,46,154,27,213,162,242,222,68,6,16,142,114,61,13,254,183,84,51,105,62,109,114,172,159,122,162,210,212,98,148,126,68,141,11,2,96,64,35,66,177,64,71,125,152,187,4,144,105,129,96,68,138,102,56,19,132,164,71,95,110,204,52,88,147,79,157,149,101,231,69,185,222,59,31,199,137,94,8,191,27,89,36,68,112,252,212,163,83,102,135,203,86,177,26,22,243,133,247,189,226,82,169,139,236,86,143,194,45,167,93,30,1,205,14,98,117,107,117,95,72,135,230,145,69,213,152,66,113,31,92,187,114,199,110,182,226,174,53,100,127,67,206,30,40,84,102,136,82,84,183,43,78,85,229,46,73,31,52,251,82,7,83,179,143,55,119,214,143,252,102,183,127,168,23,21,116,34,246,175,204,130,56,164,164,105,40,54,7,245,242,109,76,183,216,17,149,228,180,105,122,27,162,240,34,56,157,142,251,253,30,99,217,194,91,230,52,129,62,137,129,67,200,17,212,207,11,155,220,46,138,209,142,118,218,214,112,93,2,180,242,185,212,78,121,176,15,239,63,164,140,161,140,248,90,245,214,31,194,61,139,228,47,175,214,193,241,103,82,226,102,124,181,118,144,6,87,46,67,190,18,121,142,132,170,212,184,18,201,235,60,114,5,120,181,154,202,3,243,48,166,102,49,52,63,27,7,0,228,71,131,132,128,70,63,195,71,224,22,81,149,127,67,223,160,51,33,130,217,187,182,92,10,226,128,61,239,184,250,246,10,61,144,223,147,24,248,153,39,162,80,243,215,234,1,65,139,191,7,120,207,81,136,123,37,30,12,60,25,96,232,44,62,146,35,3,152,204,215,7,22,86,133,216,38,15,28,170,22,65,153,116,158,217,96,205,241,226,89,0,201,63,59,195,214,202,229,198,217,97,216,218,18,21,0,27,146,219,177,241,106,229,227,203,15,76,196,151,148,11,183,103,41,139,70,100,27,96,190,74,0,177,12,30,173,203,147,1,30,122,22,99,252,46,189,94,3,38,61,238,113,152,237,190,228,18,152,20,163,97,36,39,6,170,106,124,224,142,166,118,188,94,177,220,130,235,163,20,112,25,116,93,138,170,154,230,119,70,46,76,133,34,50,33,226,99,216,129,4,238,31,85,93,177,123,73,29,184,45,201,149,244,248,37,52,224,223,153,209,0,49,28,53,51,0,137,30,41,11,5,47,104,34,127,207,180,221,244,135,135,101,11,86,113,212,217,135,63,152,235,221,209,5,131,153,82,105,217,109,150,12,137,72,180,103,234,145,33,159,87,222,124,139,17,205,62,38,59,136,133,30,160,28,236,160,225,91,236,101,14,249,95,105,208,72,127,39,231,239,19,134,178,224,165,4,37,236,202,240,121,36,93,195,130,207,134,176,140,161,113,41,74,154,192,212,43,143,162,20,175,192,212,156,204,71,153,72,162,252,231,133,17,51,114,186,241,225,164,65,31,87,76,234,25,158,249,14,0,138,190,87,111,5,62,157,3,82,187,6,161,154,154,81,254,10,109,247,187,153,242,104,156,46,12,244,246,33,254,16,105,28,132,47,60,125,254,68,167,47,78,198,33,95,157,123,189,174,234,160,244,109,124iii18==5=>iii22,28,65,7,79iii19==13=>iii22,28,65,7,103,90,165,203,241,58,119,17,38iii20==6=>iii22,28,65,7,221,214iii21==26=>iii22,28,65,7,238,250,109,86,23,159,195,60,181,20,92,151,93,55,212,56,2,92,150,225,180,47iii22==47=>iii22,28,65,7,155,211,221,169,229,121,221,200,236,137,188,243,115,205,229,102,79,175,61,127,28,169,84,247,158,95,113,216,213,158,222,252,163,141,66,169,141,86,120,116,50,231,110iii23==6=>iii22,28,65,7,99,57iii24==30=>iii22,28,65,7,169,117,255,158,159,123,143,172,238,162,245,127,34,220,2,27,169,164,40,8,206,229,238,30,187,216iii25==6=>iii22,28,65,7,62,171iii26==9=>iii22,28,65,7,183,97,101,60,85iii27==15=>iii22,28,65,7,31,187,117,173,38,222,38,210,170,190,100iii28==5=>iii22,28,65,7,25iii29==6=>iii22,28,65,7,137,58iii30==0=>iiiiii31==0=>iiiiii32==12=>iii22,28,65,7,147,249,161,255,227,195,184,141iii33==94=>iii22,28,65,7,79,93,3,77,182,20,49,228,3,167,220,196,130,239,171,92,14,52,168,47,0,169,37,88,81,240,165,153,132,41,163,203,68,241,96,184,211,63,241,97,250,149,246,214,218,112,218,28,42,22,165,6,244,205,210,145,100,83,155,201,119,35,216,195,178,74,143,141,180,91,202,96,168,114,170,39,36,80,145,103,237,202,209,208,186,112,232,185,63,81iii34==0=>iiiiii35==5=>iii22,28,65,7,127iii36==7=>iii22,28,65,7,6,171,198iii37==6=>iii22,28,65,7,163,169iii38==5=>iii22,28,65,7,247iii39==22=>iii22,28,65,7,150,92,195,237,131,90,86,113,29,127,250,50,234,176,138,98,126,58iii40==0=>iiiiii41==0=>iiiiii42==0=>iiiiii43==0=>iiiiii44==5=>iii22,28,65,7,99iii45==13=>iii22,28,65,7,249,225,143,186,127,182,199,53,34iii46==0=>iiiiii47==6=>iii22,28,65,7,85,59iii48==0=>iiiiii49==5=>iii22,28,65,7,221iii50==0=>iiiiii51==106=>iii22,28,65,7,49,14,159,159,15,151,79,34,220,240,139,18,212,185,38,119,126,156,125,249,221,7,194,235,242,22,104,161,147,56,140,146,228,205,89,137,25,167,175,101,204,59,24,209,178,167,127,87,143,242,152,92,184,33,63,38,179,46,248,199,66,194,205,163,17,208,249,107,27,88,193,204,217,159,213,188,75,68,226,84,232,125,182,190,88,165,69,123,81,69,217,140,240,206,146,13,46,13,254,114,168,176iii52==0=>iiiiii53==0=>iiiiii54==0=>iiiiii55==7=>iii22,28,65,7,17,75,111iii56==0=>iiiiii57==0=>iiiiii58==309=>iii22,28,65,7,121,147,153,138,86,36,246,234,208,156,43,51,183,85,172,21,94,180,243,198,91,155,26,122,187,191,83,168,5,94,11,114,202,198,73,40,116,10,83,201,64,32,103,134,252,105,94,138,81,11,123,94,44,103,124,25,58,218,91,26,215,33,171,131,83,86,231,204,242,219,136,210,185,86,236,172,62,14,174,5,149,95,130,43,12,187,157,59,125,87,80,128,160,194,231,73,129,97,81,162,191,14,8,74,236,38,4,151,139,127,52,229,104,193,117,30,200,237,209,206,39,145,76,51,142,134,3,28,108,242,41,145,78,205,207,215,220,139,197,22,155,155,54,83,217,36,47,212,125,82,15,165,187,111,168,100,207,110,193,205,212,194,151,92,146,170,247,108,129,207,72,78,13,27,63,91,236,189,80,119,196,221,232,66,201,209,160,18,102,104,208,37,164,187,169,29,17,31,84,141,239,145,168,136,239,156,32,99,95,48,193,120,21,34,205,215,112,185,69,153,247,224,149,86,140,30,247,42,57,167,179,139,24,9,237,31,101,28,243,156,109,155,142,102,230,101,5,237,126,50,242,137,16,248,239,158,40,170,113,12,32,42,28,1,161,145,109,57,119,13,224,201,112,237,130,164,182,161,128,226,38,229,103,44,244,75,46,66,215,51,191,43,135,247,193,20,199,41,38,72,111,116,73,112,51iii59==25=>iii22,28,65,7,210,92,229,181,138,138,238,180,141,188,217,244,1,50,110,37,31,19,182,240,74'
// s = '0==6=>iii22,28,65,7,102,157iii1==11=>iii22,28,65,7,4,244,78,212,244,7,61iii2==5=>iii22,28,65,7,98iii3==0=>iiiiii4==15=>iii22,28,65,7,126,71,204,2,208,84,31,35,33,31,51iii5==9=>iii22,28,65,7,61,156,95,228,82iii6==0=>iiiiii7==129=>iii22,28,65,7,214,14,236,62,164,125,64,172,153,235,0,77,7,168,151,85,87,81,89,196,177,96,103,166,83,163,234,138,29,180,222,24,224,51,233,230,112,2,39,196,85,30,114,114,224,76,153,146,230,115,107,25,34,87,190,254,60,88,163,75,88,83,187,15,133,247,22,149,80,209,197,104,12,167,109,100,210,35,193,174,81,83,135,140,190,44,209,117,217,218,87,184,235,215,36,82,215,103,75,76,155,134,217,174,155,148,97,33,182,33,30,77,28,78,57,175,76,223,166,1,145,199,227,151,192iii8==13=>iii22,28,65,7,101,202,160,32,241,232,156,85,166iii9==28=>iii22,28,65,7,122,74,129,24,234,55,100,241,58,37,96,21,239,191,165,255,194,149,136,44,148,54,245,230iii10==0=>iiiiii11==45=>iii22,28,65,7,49,112,7,114,214,182,87,143,49,204,38,65,145,90,152,90,34,149,46,101,82,32,249,196,170,145,210,145,174,129,254,237,220,88,243,40,105,145,24,33,69iii12==5=>iii22,28,65,7,13iii13==234=>iii22,28,65,7,123,220,143,88,154,91,137,20,173,90,76,23,101,91,199,206,80,58,186,211,155,251,132,187,127,246,57,66,118,230,103,174,252,29,1,224,189,192,248,242,66,165,243,117,69,160,99,132,53,76,137,199,46,208,27,141,152,74,120,183,29,234,233,46,139,89,85,173,143,139,127,188,46,136,153,144,220,218,117,124,138,209,186,175,78,171,193,125,92,198,74,71,226,74,116,104,80,89,164,112,165,5,62,46,149,209,75,93,153,14,4,95,71,139,150,104,252,209,232,196,162,113,184,41,48,69,47,172,27,222,81,129,119,50,24,23,3,30,44,35,197,34,238,166,35,133,18,125,152,17,136,207,66,239,121,100,145,137,37,208,220,86,145,238,211,36,31,14,94,169,176,218,55,20,102,12,63,158,18,87,87,63,36,8,74,92,141,184,227,57,231,148,204,129,99,248,8,214,139,28,186,65,171,56,145,49,8,224,83,23,51,114,150,219,9,185,107,13,222,123,65,28,115,82,17,83,80,117,134,50iii14==5=>iii22,28,65,7,236iii15==0=>iiiiii16==0=>iiiiii17==1061=>iii22,28,65,7,84,227,115,128,250,245,242,253,236,2,166,144,224,121,72,232,41,192,16,117,164,167,59,106,181,23,113,57,34,80,87,181,90,188,175,193,80,107,115,203,149,243,74,148,113,93,24,140,248,123,145,33,228,53,17,50,243,81,223,134,34,101,149,206,42,188,75,73,129,39,82,66,176,18,153,201,209,247,178,58,202,164,186,232,1,93,69,56,70,96,126,114,54,28,192,183,160,1,25,180,56,89,138,21,36,126,161,156,198,115,246,127,54,233,51,100,185,134,75,199,26,66,211,46,187,218,165,227,12,233,19,251,137,251,64,161,140,89,18,170,246,231,129,176,244,39,135,81,56,62,22,15,34,25,156,8,177,120,8,77,9,46,248,24,130,120,92,223,137,76,122,220,50,15,248,169,162,136,186,102,114,175,255,6,136,141,16,145,173,57,39,179,94,103,150,60,159,14,226,4,240,213,30,154,0,143,171,220,164,78,160,168,145,92,117,190,199,125,34,119,175,194,72,44,61,225,225,215,78,215,172,100,56,101,219,249,95,25,110,231,57,45,249,74,33,60,24,97,84,122,213,146,155,182,165,161,29,111,183,107,45,189,27,47,17,218,246,46,28,90,252,242,39,26,124,182,233,205,7,221,75,192,119,242,22,155,44,206,233,11,133,229,234,105,158,42,161,120,195,26,23,54,42,117,244,48,247,1,93,59,39,4,109,43,155,102,121,207,4,121,181,137,65,78,241,92,106,111,247,144,66,155,184,110,97,187,46,154,27,213,162,242,222,68,6,16,142,114,61,13,254,183,84,51,105,62,109,114,172,159,122,162,210,212,98,148,126,68,141,11,2,96,64,35,66,177,64,71,125,152,187,4,144,105,129,96,68,138,102,56,19,132,164,71,95,110,204,52,88,147,79,157,149,101,231,69,185,222,59,31,199,137,94,8,191,27,89,36,68,112,252,212,163,83,102,135,203,86,177,26,22,243,133,247,189,226,82,169,139,236,86,143,194,45,167,93,30,1,205,14,98,117,107,117,95,72,135,230,145,69,213,152,66,113,31,92,187,114,199,110,182,226,174,53,100,127,67,206,30,40,84,102,136,82,84,183,43,78,85,229,46,73,31,52,251,82,7,83,179,143,55,119,214,143,252,102,183,127,168,23,21,116,34,246,175,204,130,56,164,164,105,40,54,7,245,242,109,76,183,216,17,149,228,180,105,122,27,162,240,34,56,157,142,251,253,30,99,217,194,91,230,52,129,62,137,129,67,200,17,212,207,11,155,220,46,138,209,142,118,218,214,112,93,2,180,242,185,212,78,121,176,15,239,63,164,140,161,140,248,90,245,214,31,194,61,139,228,47,175,214,193,241,103,82,226,102,124,181,118,144,6,87,46,67,190,18,121,142,132,170,212,184,18,201,235,60,114,5,120,181,154,202,3,243,48,166,102,49,52,63,27,7,0,228,71,131,132,128,70,63,195,71,224,22,81,149,127,67,223,160,51,33,130,217,187,182,92,10,226,128,61,239,184,250,246,10,61,144,223,147,24,248,153,39,162,80,243,215,234,1,65,139,191,7,120,207,81,136,123,37,30,12,60,25,96,232,44,62,146,35,3,152,204,215,7,22,86,133,216,38,15,28,170,22,65,153,116,158,217,96,205,241,226,89,0,201,63,59,195,214,202,229,198,217,97,216,218,18,21,0,27,146,219,177,241,106,229,227,203,15,76,196,151,148,11,183,103,41,139,70,100,27,96,190,74,0,177,12,30,173,203,147,1,30,122,22,99,252,46,189,94,3,38,61,238,113,152,237,190,228,18,152,20,163,97,36,39,6,170,106,124,224,142,166,118,188,94,177,220,130,235,163,20,112,25,116,93,138,170,154,230,119,70,46,76,133,34,50,33,226,99,216,129,4,238,31,85,93,177,123,73,29,184,45,201,149,244,248,37,52,224,223,153,209,0,49,28,53,51,0,137,30,41,11,5,47,104,34,127,207,180,221,244,135,135,101,11,86,113,212,217,135,63,152,235,221,209,5,131,153,82,105,217,109,150,12,137,72,180,103,234,145,33,159,87,222,124,139,17,205,62,38,59,136,133,30,160,28,236,160,225,91,236,101,14,249,95,105,208,72,127,39,231,239,19,134,178,224,165,4,37,236,202,240,121,36,93,195,130,207,134,176,140,161,113,41,74,154,192,212,43,143,162,20,175,192,212,156,204,71,153,72,162,252,231,133,17,51,114,186,241,225,164,65,31,87,76,234,25,158,249,14,0,138,190,87,111,5,62,157,3,82,187,6,161,154,154,81,254,10,109,247,187,153,242,104,156,46,12,244,246,33,254,16,105,28,132,47,60,125,254,68,167,47,78,198,33,95,157,123,189,174,234,160,244,109,124iii18==5=>iii22,28,65,7,79iii19==13=>iii22,28,65,7,103,90,165,203,241,58,119,17,38iii20==6=>iii22,28,65,7,221,214iii21==24=>iii22,28,65,7,238,250,109,86,23,159,195,60,181,20,92,151,93,55,214,60,24,70,146,210iii22==47=>iii22,28,65,7,155,211,221,169,229,121,221,200,236,137,188,243,115,205,229,102,79,175,61,127,28,169,84,247,158,95,113,216,213,158,222,252,163,141,66,169,141,86,120,116,50,231,110iii23==6=>iii22,28,65,7,99,57iii24==30=>iii22,28,65,7,169,117,255,158,159,123,143,172,238,162,245,127,34,220,2,27,169,164,40,8,206,229,238,30,187,216iii25==6=>iii22,28,65,7,62,171iii26==9=>iii22,28,65,7,183,97,101,60,85iii27==15=>iii22,28,65,7,31,187,117,173,38,222,38,210,170,190,100iii28==5=>iii22,28,65,7,25iii29==6=>iii22,28,65,7,137,58iii30==0=>iiiiii31==0=>iiiiii32==12=>iii22,28,65,7,147,249,161,255,227,195,184,141iii33==94=>iii22,28,65,7,79,93,3,77,182,20,49,228,3,167,220,196,130,239,171,92,14,52,168,47,0,169,37,88,81,240,165,153,132,41,163,203,68,241,96,184,211,63,241,97,250,149,246,214,218,112,218,28,42,22,165,6,244,205,210,145,100,83,155,201,119,35,216,195,178,74,143,141,180,91,202,96,168,114,170,39,36,80,145,103,237,202,209,208,186,112,232,185,63,81iii34==0=>iiiiii35==5=>iii22,28,65,7,127iii36==7=>iii22,28,65,7,6,171,198iii37==6=>iii22,28,65,7,163,169iii38==5=>iii22,28,65,7,247iii39==19=>iii22,28,65,7,150,92,195,237,131,90,86,113,29,127,155,167,240,88,237iii40==5=>iii22,28,65,7,176iii41==0=>iiiiii42==38=>iii22,28,65,7,123,231,72,48,179,59,132,119,104,255,156,158,149,93,138,32,221,162,187,240,69,62,31,100,106,202,163,248,176,219,209,169,29,119iii43==5=>iii22,28,65,7,15iii44==5=>iii22,28,65,7,99iii45==13=>iii22,28,65,7,249,225,143,186,127,182,199,53,34iii46==0=>iiiiii47==6=>iii22,28,65,7,85,59iii48==7=>iii22,28,65,7,28,249,132iii49==5=>iii22,28,65,7,221iii50==0=>iiiiii51==106=>iii22,28,65,7,49,14,159,159,15,151,79,34,220,240,139,18,212,185,38,119,126,156,125,249,221,7,194,235,242,22,104,161,147,56,140,146,228,205,89,137,25,167,175,101,204,59,24,209,178,167,127,87,143,242,152,92,184,33,63,38,179,46,248,199,66,194,205,163,17,208,249,107,27,88,193,204,217,159,213,188,75,68,226,84,232,125,182,190,88,165,69,123,81,69,217,140,240,206,146,13,46,13,254,114,168,176iii52==0=>iiiiii53==0=>iiiiii54==8=>iii22,28,65,7,8,216,96,71iii55==7=>iii22,28,65,7,17,75,111iii56==0=>iiiiii57==0=>iiiiii58==309=>iii22,28,65,7,121,147,153,138,86,36,246,234,208,156,43,51,183,85,172,21,94,180,243,198,91,155,26,122,187,191,83,168,5,94,11,114,202,198,73,40,116,10,83,201,64,32,103,134,252,105,94,138,81,11,123,94,44,103,124,25,58,218,91,26,215,33,171,131,83,86,231,204,242,219,136,210,185,86,236,172,62,14,174,5,149,95,130,43,12,187,157,59,125,87,80,128,160,194,231,73,129,97,81,162,191,14,8,74,236,38,4,151,139,127,52,229,104,193,117,30,200,237,209,206,39,145,76,51,142,134,3,28,108,242,41,145,78,205,207,215,220,139,197,22,155,155,54,83,217,36,47,212,125,82,15,165,187,111,168,100,207,110,193,205,212,194,151,92,146,170,247,108,129,207,72,78,13,27,63,91,236,189,80,119,196,221,232,66,201,209,160,18,102,104,208,37,164,187,169,29,17,31,84,141,239,145,168,136,239,156,32,99,95,48,193,120,21,34,205,215,112,185,69,153,247,224,149,86,140,30,247,42,57,167,179,139,24,9,237,31,101,28,243,156,109,155,142,102,230,101,5,237,126,50,242,137,16,248,239,158,40,170,113,12,32,42,28,1,161,145,109,57,119,13,224,201,112,237,130,164,182,161,128,226,38,229,103,44,244,75,46,66,215,51,191,43,135,247,193,20,199,41,38,72,111,116,73,112,51iii59==25=>iii22,28,65,7,210,92,229,181,138,138,238,180,141,188,217,244,1,50,110,37,31,19,182,240,74'