?var steps:Array = new Array();
steps[0] = new Array();
steps[1] = new Array();
steps[2] = new Array();
steps[3] = new Array();
steps[4] = new Array();
steps[5] = new Array();
steps[6] = new Array();
steps[7] = new Array();
steps[8] = new Array();
steps[9] = new Array();
steps[10] = new Array();
steps[11] = new Array();
steps[12] = new Array();
steps[13] = new Array();
steps[14] = new Array();
steps[15] = new Array();
steps[16] = new Array();
steps[17] = new Array();
steps[18] = new Array();
steps[19] = new Array();
steps[20] = new Array();
steps[21] = new Array();
steps[22] = new Array();
steps[23] = new Array();
steps[24] = new Array();
steps[25] = new Array();
steps[26] = new Array();
steps[27] = new Array();
steps[28] = new Array();
steps[29] = new Array();
steps[30] = new Array();
steps[31] = new Array();
steps[32] = new Array();
steps[33] = new Array();
steps[34] = new Array();
steps[35] = new Array();
steps[36] = new Array();
steps[37] = new Array();
steps[38] = new Array();
steps[39] = new Array();
steps[40] = new Array();
steps[41] = new Array();
steps[42] = new Array();
steps[43] = new Array();
steps[44] = new Array();
steps[45] = new Array();
steps[46] = new Array();
steps[47] = new Array();
steps[48] = new Array();
steps[49] = new Array();
steps[50] = new Array();
steps[51] = new Array();
steps[52] = new Array();
steps[53] = new Array();
steps[54] = new Array();
steps[55] = new Array();
steps[56] = new Array();
steps[57] = new Array();
steps[58] = new Array();
steps[59] = new Array();
steps[60] = new Array();
steps[61] = new Array();
steps[62] = new Array();
steps[63] = new Array();
steps[64] = new Array();
steps[65] = new Array();
steps[66] = new Array();
steps[67] = new Array();
steps[68] = new Array();
steps[69] = new Array();
steps[70] = new Array();
steps[71] = new Array();
steps[72] = new Array();
steps[73] = new Array();
steps[74] = new Array();
steps[75] = new Array();
steps[76] = new Array();
steps[77] = new Array();
steps[78] = new Array();
steps[79] = new Array();
steps[80] = new Array();
steps[81] = new Array();
steps[82] = new Array();
steps[83] = new Array();
steps[84] = new Array();
steps[85] = new Array();
steps[86] = new Array();
steps[87] = new Array();
steps[88] = new Array();
steps[89] = new Array();
steps[90] = new Array();
steps[91] = new Array();
steps[92] = new Array();
steps[93] = new Array();
steps[94] = new Array();
steps[95] = new Array();
steps[96] = new Array();
steps[97] = new Array();
steps[98] = new Array();
steps[99] = new Array();
steps[100] = new Array();
steps[101] = new Array();
steps[102] = new Array();
steps[103] = new Array();
steps[104] = new Array();
steps[105] = new Array();
steps[106] = new Array();
steps[107] = new Array();
steps[108] = new Array();
steps[109] = new Array();
steps[110] = new Array();
steps[111] = new Array();
steps[112] = new Array();
steps[113] = new Array();
steps[114] = new Array();
steps[115] = new Array();
steps[116] = new Array();
steps[117] = new Array();
steps[118] = new Array();
steps[119] = new Array();
steps[120] = new Array();
steps[0][0] =0;
steps[0][1] =1;
steps[0][2] =1;
steps[0][3] =1;
steps[0][4] =1;
steps[0][5] =1;
steps[0][6] =1;
steps[0][7] =2;
steps[0][8] =2;
steps[0][9] =2;
steps[0][10] =2;
steps[0][11] =2;
steps[0][12] =2;
steps[0][13] =2;
steps[0][14] =2;
steps[0][15] =2;
steps[0][16] =2;
steps[0][17] =2;
steps[0][18] =2;
steps[0][19] =3;
steps[0][20] =3;
steps[0][21] =3;
steps[0][22] =3;
steps[0][23] =3;
steps[0][24] =3;
steps[0][25] =3;
steps[0][26] =3;
steps[0][27] =3;
steps[0][28] =3;
steps[0][29] =3;
steps[0][30] =3;
steps[0][31] =3;
steps[0][32] =3;
steps[0][33] =3;
steps[0][34] =3;
steps[0][35] =3;
steps[0][36] =3;
steps[0][37] =4;
steps[0][38] =4;
steps[0][39] =4;
steps[0][40] =4;
steps[0][41] =4;
steps[0][42] =4;
steps[0][43] =4;
steps[0][44] =4;
steps[0][45] =4;
steps[0][46] =4;
steps[0][47] =4;
steps[0][48] =4;
steps[0][49] =4;
steps[0][50] =4;
steps[0][51] =4;
steps[0][52] =4;
steps[0][53] =4;
steps[0][54] =4;
steps[0][55] =4;
steps[0][56] =4;
steps[0][57] =4;
steps[0][58] =4;
steps[0][59] =4;
steps[0][60] =4;
steps[0][61] =5;
steps[0][62] =5;
steps[0][63] =5;
steps[0][64] =5;
steps[0][65] =5;
steps[0][66] =5;
steps[0][67] =5;
steps[0][68] =5;
steps[0][69] =5;
steps[0][70] =5;
steps[0][71] =5;
steps[0][72] =5;
steps[0][73] =5;
steps[0][74] =5;
steps[0][75] =5;
steps[0][76] =5;
steps[0][77] =5;
steps[0][78] =5;
steps[0][79] =5;
steps[0][80] =5;
steps[0][81] =5;
steps[0][82] =5;
steps[0][83] =5;
steps[0][84] =5;
steps[0][85] =6;
steps[0][86] =6;
steps[0][87] =6;
steps[0][88] =6;
steps[0][89] =6;
steps[0][90] =6;
steps[0][91] =6;
steps[0][92] =6;
steps[0][93] =6;
steps[0][94] =6;
steps[0][95] =6;
steps[0][96] =6;
steps[0][97] =6;
steps[0][98] =6;
steps[0][99] =6;
steps[0][100] =6;
steps[0][101] =6;
steps[0][102] =6;
steps[0][103] =7;
steps[0][104] =7;
steps[0][105] =7;
steps[0][106] =7;
steps[0][107] =7;
steps[0][108] =7;
steps[0][109] =7;
steps[0][110] =7;
steps[0][111] =7;
steps[0][112] =7;
steps[0][113] =7;
steps[0][114] =7;
steps[0][115] =8;
steps[0][116] =8;
steps[0][117] =8;
steps[0][118] =8;
steps[0][119] =8;
steps[0][120] =8;
steps[1][1] =0;
steps[1][2] =1;
steps[1][3] =2;
steps[1][4] =2;
steps[1][5] =2;
steps[1][6] =1;
steps[1][7] =1;
steps[1][8] =1;
steps[1][9] =1;
steps[1][10] =2;
steps[1][11] =2;
steps[1][12] =3;
steps[1][13] =3;
steps[1][14] =3;
steps[1][15] =3;
steps[1][16] =3;
steps[1][17] =2;
steps[1][18] =2;
steps[1][19] =2;
steps[1][20] =2;
steps[1][21] =2;
steps[1][22] =2;
steps[1][23] =2;
steps[1][24] =3;
steps[1][25] =3;
steps[1][26] =3;
steps[1][27] =4;
steps[1][28] =4;
steps[1][29] =4;
steps[1][30] =4;
steps[1][31] =4;
steps[1][32] =4;
steps[1][33] =4;
steps[1][34] =3;
steps[1][35] =3;
steps[1][36] =3;
steps[1][37] =3;
steps[1][38] =3;
steps[1][39] =3;
steps[1][40] =3;
steps[1][41] =3;
steps[1][42] =3;
steps[1][43] =3;
steps[1][44] =4;
steps[1][45] =4;
steps[1][46] =4;
steps[1][47] =4;
steps[1][48] =5;
steps[1][49] =5;
steps[1][50] =5;
steps[1][51] =5;
steps[1][52] =5;
steps[1][53] =5;
steps[1][54] =5;
steps[1][55] =5;
steps[1][56] =5;
steps[1][57] =4;
steps[1][58] =4;
steps[1][59] =4;
steps[1][60] =4;
steps[1][61] =4;
steps[1][62] =4;
steps[1][63] =4;
steps[1][64] =4;
steps[1][65] =4;
steps[1][66] =4;
steps[1][67] =4;
steps[1][68] =4;
steps[1][69] =5;
steps[1][70] =5;
steps[1][71] =5;
steps[1][72] =5;
steps[1][73] =6;
steps[1][74] =6;
steps[1][75] =6;
steps[1][76] =6;
steps[1][77] =6;
steps[1][78] =6;
steps[1][79] =6;
steps[1][80] =6;
steps[1][81] =5;
steps[1][82] =5;
steps[1][83] =5;
steps[1][84] =5;
steps[1][85] =5;
steps[1][86] =5;
steps[1][87] =5;
steps[1][88] =5;
steps[1][89] =5;
steps[1][90] =5;
steps[1][91] =6;
steps[1][92] =6;
steps[1][93] =6;
steps[1][94] =7;
steps[1][95] =7;
steps[1][96] =7;
steps[1][97] =7;
steps[1][98] =7;
steps[1][99] =7;
steps[1][100] =6;
steps[1][101] =6;
steps[1][102] =6;
steps[1][103] =6;
steps[1][104] =6;
steps[1][105] =6;
steps[1][106] =6;
steps[1][107] =7;
steps[1][108] =7;
steps[1][109] =8;
steps[1][110] =8;
steps[1][111] =8;
steps[1][112] =8;
steps[1][113] =7;
steps[1][114] =7;
steps[1][115] =7;
steps[1][116] =7;
steps[1][117] =8;
steps[1][118] =9;
steps[1][119] =9;
steps[1][120] =8;
steps[2][2] =0;
steps[2][3] =1;
steps[2][4] =2;
steps[2][5] =2;
steps[2][6] =2;
steps[2][7] =2;
steps[2][8] =2;
steps[2][9] =1;
steps[2][10] =1;
steps[2][11] =1;
steps[2][12] =2;
steps[2][13] =2;
steps[2][14] =3;
steps[2][15] =3;
steps[2][16] =3;
steps[2][17] =3;
steps[2][18] =3;
steps[2][19] =3;
steps[2][20] =3;
steps[2][21] =3;
steps[2][22] =2;
steps[2][23] =2;
steps[2][24] =2;
steps[2][25] =2;
steps[2][26] =2;
steps[2][27] =3;
steps[2][28] =3;
steps[2][29] =3;
steps[2][30] =4;
steps[2][31] =4;
steps[2][32] =4;
steps[2][33] =4;
steps[2][34] =4;
steps[2][35] =4;
steps[2][36] =4;
steps[2][37] =4;
steps[2][38] =4;
steps[2][39] =4;
steps[2][40] =4;
steps[2][41] =3;
steps[2][42] =3;
steps[2][43] =3;
steps[2][44] =3;
steps[2][45] =3;
steps[2][46] =3;
steps[2][47] =3;
steps[2][48] =4;
steps[2][49] =4;
steps[2][50] =4;
steps[2][51] =4;
steps[2][52] =5;
steps[2][53] =5;
steps[2][54] =5;
steps[2][55] =5;
steps[2][56] =5;
steps[2][57] =5;
steps[2][58] =5;
steps[2][59] =5;
steps[2][60] =5;
steps[2][61] =5;
steps[2][62] =5;
steps[2][63] =5;
steps[2][64] =5;
steps[2][65] =4;
steps[2][66] =4;
steps[2][67] =4;
steps[2][68] =4;
steps[2][69] =4;
steps[2][70] =4;
steps[2][71] =4;
steps[2][72] =4;
steps[2][73] =5;
steps[2][74] =5;
steps[2][75] =5;
steps[2][76] =5;
steps[2][77] =6;
steps[2][78] =6;
steps[2][79] =6;
steps[2][80] =6;
steps[2][81] =6;
steps[2][82] =6;
steps[2][83] =6;
steps[2][84] =6;
steps[2][85] =6;
steps[2][86] =6;
steps[2][87] =6;
steps[2][88] =5;
steps[2][89] =5;
steps[2][90] =5;
steps[2][91] =5;
steps[2][92] =5;
steps[2][93] =5;
steps[2][94] =6;
steps[2][95] =6;
steps[2][96] =6;
steps[2][97] =7;
steps[2][98] =7;
steps[2][99] =7;
steps[2][100] =7;
steps[2][101] =7;
steps[2][102] =7;
steps[2][103] =7;
steps[2][104] =7;
steps[2][105] =6;
steps[2][106] =6;
steps[2][107] =6;
steps[2][108] =6;
steps[2][109] =7;
steps[2][110] =7;
steps[2][111] =8;
steps[2][112] =8;
steps[2][113] =8;
steps[2][114] =8;
steps[2][115] =8;
steps[2][116] =7;
steps[2][117] =7;
steps[2][118] =8;
steps[2][119] =9;
steps[2][120] =9;
steps[3][3] =0;
steps[3][4] =1;
steps[3][5] =2;
steps[3][6] =2;
steps[3][7] =3;
steps[3][8] =3;
steps[3][9] =2;
steps[3][10] =2;
steps[3][11] =1;
steps[3][12] =1;
steps[3][13] =1;
steps[3][14] =2;
steps[3][15] =2;
steps[3][16] =3;
steps[3][17] =3;
steps[3][18] =3;
steps[3][19] =4;
steps[3][20] =4;
steps[3][21] =4;
steps[3][22] =3;
steps[3][23] =3;
steps[3][24] =3;
steps[3][25] =2;
steps[3][26] =2;
steps[3][27] =2;
steps[3][28] =2;
steps[3][29] =2;
steps[3][30] =3;
steps[3][31] =3;
steps[3][32] =3;
steps[3][33] =4;
steps[3][34] =4;
steps[3][35] =4;
steps[3][36] =4;
steps[3][37] =5;
steps[3][38] =5;
steps[3][39] =5;
steps[3][40] =5;
steps[3][41] =4;
steps[3][42] =4;
steps[3][43] =4;
steps[3][44] =4;
steps[3][45] =3;
steps[3][46] =3;
steps[3][47] =3;
steps[3][48] =3;
steps[3][49] =3;
steps[3][50] =3;
steps[3][51] =3;
steps[3][52] =4;
steps[3][53] =4;
steps[3][54] =4;
steps[3][55] =4;
steps[3][56] =5;
steps[3][57] =5;
steps[3][58] =5;
steps[3][59] =5;
steps[3][60] =5;
steps[3][61] =6;
steps[3][62] =6;
steps[3][63] =6;
steps[3][64] =6;
steps[3][65] =5;
steps[3][66] =5;
steps[3][67] =5;
steps[3][68] =5;
steps[3][69] =4;
steps[3][70] =4;
steps[3][71] =4;
steps[3][72] =4;
steps[3][73] =4;
steps[3][74] =4;
steps[3][75] =4;
steps[3][76] =4;
steps[3][77] =5;
steps[3][78] =5;
steps[3][79] =5;
steps[3][80] =5;
steps[3][81] =6;
steps[3][82] =6;
steps[3][83] =6;
steps[3][84] =6;
steps[3][85] =7;
steps[3][86] =7;
steps[3][87] =7;
steps[3][88] =6;
steps[3][89] =6;
steps[3][90] =6;
steps[3][91] =5;
steps[3][92] =5;
steps[3][93] =5;
steps[3][94] =5;
steps[3][95] =5;
steps[3][96] =5;
steps[3][97] =6;
steps[3][98] =6;
steps[3][99] =6;
steps[3][100] =7;
steps[3][101] =7;
steps[3][102] =7;
steps[3][103] =8;
steps[3][104] =8;
steps[3][105] =7;
steps[3][106] =7;
steps[3][107] =6;
steps[3][108] =6;
steps[3][109] =6;
steps[3][110] =6;
steps[3][111] =7;
steps[3][112] =7;
steps[3][113] =8;
steps[3][114] =8;
steps[3][115] =9;
steps[3][116] =8;
steps[3][117] =7;
steps[3][118] =7;
steps[3][119] =8;
steps[3][120] =9;
steps[4][4] =0;
steps[4][5] =1;
steps[4][6] =2;
steps[4][7] =3;
steps[4][8] =3;
steps[4][9] =3;
steps[4][10] =3;
steps[4][11] =2;
steps[4][12] =2;
steps[4][13] =1;
steps[4][14] =1;
steps[4][15] =1;
steps[4][16] =2;
steps[4][17] =2;
steps[4][18] =3;
steps[4][19] =4;
steps[4][20] =4;
steps[4][21] =4;
steps[4][22] =4;
steps[4][23] =4;
steps[4][24] =4;
steps[4][25] =3;
steps[4][26] =3;
steps[4][27] =3;
steps[4][28] =2;
steps[4][29] =2;
steps[4][30] =2;
steps[4][31] =2;
steps[4][32] =2;
steps[4][33] =3;
steps[4][34] =3;
steps[4][35] =3;
steps[4][36] =4;
steps[4][37] =5;
steps[4][38] =5;
steps[4][39] =5;
steps[4][40] =5;
steps[4][41] =5;
steps[4][42] =5;
steps[4][43] =5;
steps[4][44] =5;
steps[4][45] =4;
steps[4][46] =4;
steps[4][47] =4;
steps[4][48] =4;
steps[4][49] =3;
steps[4][50] =3;
steps[4][51] =3;
steps[4][52] =3;
steps[4][53] =3;
steps[4][54] =3;
steps[4][55] =3;
steps[4][56] =4;
steps[4][57] =4;
steps[4][58] =4;
steps[4][59] =4;
steps[4][60] =5;
steps[4][61] =6;
steps[4][62] =6;
steps[4][63] =6;
steps[4][64] =6;
steps[4][65] =6;
steps[4][66] =6;
steps[4][67] =6;
steps[4][68] =6;
steps[4][69] =5;
steps[4][70] =5;
steps[4][71] =5;
steps[4][72] =5;
steps[4][73] =4;
steps[4][74] =4;
steps[4][75] =4;
steps[4][76] =4;
steps[4][77] =4;
steps[4][78] =4;
steps[4][79] =4;
steps[4][80] =4;
steps[4][81] =5;
steps[4][82] =5;
steps[4][83] =5;
steps[4][84] =5;
steps[4][85] =7;
steps[4][86] =7;
steps[4][87] =7;
steps[4][88] =7;
steps[4][89] =7;