Problem 67:
In [33]:
a = [[59],
[73,41],
[52,40,9],
[26,53,6,34],
[10,51,87,86,81],
[61,95,66,57,25,68],
[90,81,80,38,92,67,73],
[30,28,51,76,81,18,75,44],
[84,14,95,87,62,81,17,78,58],
[21,46,71,58,2,79,62,39,31,9],
[56,34,35,53,78,31,81,18,90,93,15],
[78,53,4,21,84,93,32,13,97,11,37,51],
[45,3,81,79,5,18,78,86,13,30,63,99,95],
[39,87,96,28,3,38,42,17,82,87,58,7,22,57],
[6,17,51,17,7,93,9,7,75,97,95,78,87,8,53],
[67,66,59,60,88,99,94,65,55,77,55,34,27,53,78,28],
[76,40,41,4,87,16,9,42,75,69,23,97,30,60,10,79,87],
[12,10,44,26,21,36,32,84,98,60,13,12,36,16,63,31,91,35],
[70,39,6,5,55,27,38,48,28,22,34,35,62,62,15,14,94,89,86],
[66,56,68,84,96,21,34,34,34,81,62,40,65,54,62,5,98,3,2,60],
[38,89,46,37,99,54,34,53,36,14,70,26,2,90,45,13,31,61,83,73,47],
[36,10,63,96,60,49,41,5,37,42,14,58,84,93,96,17,9,43,5,43,6,59],
[66,57,87,57,61,28,37,51,84,73,79,15,39,95,88,87,43,39,11,86,77,74,18],
[54,42,5,79,30,49,99,73,46,37,50,2,45,9,54,52,27,95,27,65,19,45,26,45],
[71,39,17,78,76,29,52,90,18,99,78,19,35,62,71,19,23,65,93,85,49,33,75,9,2],
[33,24,47,61,60,55,32,88,57,55,91,54,46,57,7,77,98,52,80,99,24,25,46,78,79,5],
[92,9,13,55,10,67,26,78,76,82,63,49,51,31,24,68,5,57,7,54,69,21,67,43,17,63,12],
[24,59,6,8,98,74,66,26,61,60,13,3,9,9,24,30,71,8,88,70,72,70,29,90,11,82,41,34],
[66,82,67,4,36,60,92,77,91,85,62,49,59,61,30,90,29,94,26,41,89,4,53,22,83,41,9,74,90],
[48,28,26,37,28,52,77,26,51,32,18,98,79,36,62,13,17,8,19,54,89,29,73,68,42,14,8,16,70,37],
[37,60,69,70,72,71,9,59,13,60,38,13,57,36,9,30,43,89,30,39,15,2,44,73,5,73,26,63,56,86,12],
[55,55,85,50,62,99,84,77,28,85,3,21,27,22,19,26,82,69,54,4,13,7,85,14,1,15,70,59,89,95,10,19],
[4,9,31,92,91,38,92,86,98,75,21,5,64,42,62,84,36,20,73,42,21,23,22,51,51,79,25,45,85,53,3,43,22],
[75,63,2,49,14,12,89,14,60,78,92,16,44,82,38,30,72,11,46,52,90,27,8,65,78,3,85,41,57,79,39,52,33,48],
[78,27,56,56,39,13,19,43,86,72,58,95,39,7,4,34,21,98,39,15,39,84,89,69,84,46,37,57,59,35,59,50,26,15,93],
[42,89,36,27,78,91,24,11,17,41,5,94,7,69,51,96,3,96,47,90,90,45,91,20,50,56,10,32,36,49,4,53,85,92,25,65],
[52,9,61,30,61,97,66,21,96,92,98,90,6,34,96,60,32,69,68,33,75,84,18,31,71,50,84,63,3,3,19,11,28,42,75,45,45],
[61,31,61,68,96,34,49,39,5,71,76,59,62,67,6,47,96,99,34,21,32,47,52,7,71,60,42,72,94,56,82,83,84,40,94,87,82,46],
[1,20,60,14,17,38,26,78,66,81,45,95,18,51,98,81,48,16,53,88,37,52,69,95,72,93,22,34,98,20,54,27,73,61,56,63,60,34,63],
[93,42,94,83,47,61,27,51,79,79,45,1,44,73,31,70,83,42,88,25,53,51,30,15,65,94,80,44,61,84,12,77,2,62,2,65,94,42,14,94],
[32,73,9,67,68,29,74,98,10,19,85,48,38,31,85,67,53,93,93,77,47,67,39,72,94,53,18,43,77,40,78,32,29,59,24,6,2,83,50,60,66],
[32,1,44,30,16,51,15,81,98,15,10,62,86,79,50,62,45,60,70,38,31,85,65,61,64,6,69,84,14,22,56,43,9,48,66,69,83,91,60,40,36,61],
[92,48,22,99,15,95,64,43,1,16,94,2,99,19,17,69,11,58,97,56,89,31,77,45,67,96,12,73,8,20,36,47,81,44,50,64,68,85,40,81,85,52,9],
[91,35,92,45,32,84,62,15,19,64,21,66,6,1,52,80,62,59,12,25,88,28,91,50,40,16,22,99,92,79,87,51,21,77,74,77,7,42,38,42,74,83,2,5],
[46,19,77,66,24,18,5,32,2,84,31,99,92,58,96,72,91,36,62,99,55,29,53,42,12,37,26,58,89,50,66,19,82,75,12,48,24,87,91,85,2,7,3,76,86],
[99,98,84,93,7,17,33,61,92,20,66,60,24,66,40,30,67,5,37,29,24,96,3,27,70,62,13,4,45,47,59,88,43,20,66,15,46,92,30,4,71,66,78,70,53,99],
[67,60,38,6,88,4,17,72,10,99,71,7,42,25,54,5,26,64,91,50,45,71,6,30,67,48,69,82,8,56,80,67,18,46,66,63,1,20,8,80,47,7,91,16,3,79,87],
[18,54,78,49,80,48,77,40,68,23,60,88,58,80,33,57,11,69,55,53,64,2,94,49,60,92,16,35,81,21,82,96,25,24,96,18,2,5,49,3,50,77,6,32,84,27,18,38],
[68,1,50,4,3,21,42,94,53,24,89,5,92,26,52,36,68,11,85,1,4,42,2,45,15,6,50,4,53,73,25,74,81,88,98,21,67,84,79,97,99,20,95,4,40,46,2,58,87],
[94,10,2,78,88,52,21,3,88,60,6,53,49,71,20,91,12,65,7,49,21,22,11,41,58,99,36,16,9,48,17,24,52,36,23,15,72,16,84,56,2,99,43,76,81,71,29,39,49,17],
[64,39,59,84,86,16,17,66,3,9,43,6,64,18,63,29,68,6,23,7,87,14,26,35,17,12,98,41,53,64,78,18,98,27,28,84,80,67,75,62,10,11,76,90,54,10,5,54,41,39,66],
[43,83,18,37,32,31,52,29,95,47,8,76,35,11,4,53,35,43,34,10,52,57,12,36,20,39,40,55,78,44,7,31,38,26,8,15,56,88,86,1,52,62,10,24,32,5,60,65,53,28,57,99],
[3,50,3,52,7,73,49,92,66,80,1,46,8,67,25,36,73,93,7,42,25,53,13,96,76,83,87,90,54,89,78,22,78,91,73,51,69,9,79,94,83,53,9,40,69,62,10,79,49,47,3,81,30],
[71,54,73,33,51,76,59,54,79,37,56,45,84,17,62,21,98,69,41,95,65,24,39,37,62,3,24,48,54,64,46,82,71,78,33,67,9,16,96,68,52,74,79,68,32,21,13,78,96,60,9,69,20,36],
[73,26,21,44,46,38,17,83,65,98,7,23,52,46,61,97,33,13,60,31,70,15,36,77,31,58,56,93,75,68,21,36,69,53,90,75,25,82,39,50,65,94,29,30,11,33,11,13,96,2,56,47,7,49,2],
[76,46,73,30,10,20,60,70,14,56,34,26,37,39,48,24,55,76,84,91,39,86,95,61,50,14,53,93,64,67,37,31,10,84,42,70,48,20,10,72,60,61,84,79,69,65,99,73,89,25,85,48,92,56,97,16],
[3,14,80,27,22,30,44,27,67,75,79,32,51,54,81,29,65,14,19,4,13,82,4,91,43,40,12,52,29,99,7,76,60,25,1,7,61,71,37,92,40,47,99,66,57,1,43,44,22,40,53,53,9,69,26,81,7],
[49,80,56,90,93,87,47,13,75,28,87,23,72,79,32,18,27,20,28,10,37,59,21,18,70,4,79,96,3,31,45,71,81,6,14,18,17,5,31,50,92,79,23,47,9,39,47,91,43,54,69,47,42,95,62,46,32,85],
[37,18,62,85,87,28,64,5,77,51,47,26,30,65,5,70,65,75,59,80,42,52,25,20,44,10,92,17,71,95,52,14,77,13,24,55,11,65,26,91,1,30,63,15,49,48,41,17,67,47,3,68,20,90,98,32,4,40,68],
[90,51,58,60,6,55,23,68,5,19,76,94,82,36,96,43,38,90,87,28,33,83,5,17,70,83,96,93,6,4,78,47,80,6,23,84,75,23,87,72,99,14,50,98,92,38,90,64,61,58,76,94,36,66,87,80,51,35,61,38],
[57,95,64,6,53,36,82,51,40,33,47,14,7,98,78,65,39,58,53,6,50,53,4,69,40,68,36,69,75,78,75,60,3,32,39,24,74,47,26,90,13,40,44,71,90,76,51,24,36,50,25,45,70,80,61,80,61,43,90,64,11],
[18,29,86,56,68,42,79,10,42,44,30,12,96,18,23,18,52,59,2,99,67,46,60,86,43,38,55,17,44,93,42,21,55,14,47,34,55,16,49,24,23,29,96,51,55,10,46,53,27,92,27,46,63,57,30,65,43,27,21,20,24,83],
[81,72,93,19,69,52,48,1,13,83,92,69,20,48,69,59,20,62,5,42,28,89,90,99,32,72,84,17,8,87,36,3,60,31,36,36,81,26,97,36,48,54,56,56,27,16,91,8,23,11,87,99,33,47,2,14,44,73,70,99,43,35,33],
[90,56,61,86,56,12,70,59,63,32,1,15,81,47,71,76,95,32,65,80,54,70,34,51,40,45,33,4,64,55,78,68,88,47,31,47,68,87,3,84,23,44,89,72,35,8,31,76,63,26,90,85,96,67,65,91,19,14,17,86,4,71,32,95],
[37,13,4,22,64,37,37,28,56,62,86,33,7,37,10,44,52,82,52,6,19,52,57,75,90,26,91,24,6,21,14,67,76,30,46,14,35,89,89,41,3,64,56,97,87,63,22,34,3,79,17,45,11,53,25,56,96,61,23,18,63,31,37,37,47],
[77,23,26,70,72,76,77,4,28,64,71,69,14,85,96,54,95,48,6,62,99,83,86,77,97,75,71,66,30,19,57,90,33,1,60,61,14,12,90,99,32,77,56,41,18,14,87,49,10,14,90,64,18,50,21,74,14,16,88,5,45,73,82,47,74,44],
[22,97,41,13,34,31,54,61,56,94,3,24,59,27,98,77,4,9,37,40,12,26,87,9,71,70,7,18,64,57,80,21,12,71,83,94,60,39,73,79,73,19,97,32,64,29,41,7,48,84,85,67,12,74,95,20,24,52,41,67,56,61,29,93,35,72,69],
[72,23,63,66,1,11,7,30,52,56,95,16,65,26,83,90,50,74,60,18,16,48,43,77,37,11,99,98,30,94,91,26,62,73,45,12,87,73,47,27,1,88,66,99,21,41,95,80,2,53,23,32,61,48,32,43,43,83,14,66,95,91,19,81,80,67,25,88],
[8,62,32,18,92,14,83,71,37,96,11,83,39,99,5,16,23,27,10,67,2,25,44,11,55,31,46,64,41,56,44,74,26,81,51,31,45,85,87,9,81,95,22,28,76,69,46,48,64,87,67,76,27,89,31,11,74,16,62,3,60,94,42,47,9,34,94,93,72],
[56,18,90,18,42,17,42,32,14,86,6,53,33,95,99,35,29,15,44,20,49,59,25,54,34,59,84,21,23,54,35,90,78,16,93,13,37,88,54,19,86,67,68,55,66,84,65,42,98,37,87,56,33,28,58,38,28,38,66,27,52,21,81,15,8,22,97,32,85,27],
[91,53,40,28,13,34,91,25,1,63,50,37,22,49,71,58,32,28,30,18,68,94,23,83,63,62,94,76,80,41,90,22,82,52,29,12,18,56,10,8,35,14,37,57,23,65,67,40,72,39,93,39,70,89,40,34,7,46,94,22,20,5,53,64,56,30,5,56,61,88,27],
[23,95,11,12,37,69,68,24,66,10,87,70,43,50,75,7,62,41,83,58,95,93,89,79,45,39,2,22,5,22,95,43,62,11,68,29,17,40,26,44,25,71,87,16,70,85,19,25,59,94,90,41,41,80,61,70,55,60,84,33,95,76,42,63,15,9,3,40,38,12,3,32],
[9,84,56,80,61,55,85,97,16,94,82,94,98,57,84,30,84,48,93,90,71,5,95,90,73,17,30,98,40,64,65,89,7,79,9,19,56,36,42,30,23,69,73,72,7,5,27,61,24,31,43,48,71,84,21,28,26,65,65,59,65,74,77,20,10,81,61,84,95,8,52,23,70],
[47,81,28,9,98,51,67,64,35,51,59,36,92,82,77,65,80,24,72,53,22,7,27,10,21,28,30,22,48,82,80,48,56,20,14,43,18,25,50,95,90,31,77,8,9,48,44,80,90,22,93,45,82,17,13,96,25,26,8,73,34,99,6,49,24,6,83,51,40,14,15,10,25,1],
[54,25,10,81,30,64,24,74,75,80,36,75,82,60,22,69,72,91,45,67,3,62,79,54,89,74,44,83,64,96,66,73,44,30,74,50,37,5,9,97,70,1,60,46,37,91,39,75,75,18,58,52,72,78,51,81,86,52,8,97,1,46,43,66,98,62,81,18,70,93,73,8,32,46,34],
[96,80,82,7,59,71,92,53,19,20,88,66,3,26,26,10,24,27,50,82,94,73,63,8,51,33,22,45,19,13,58,33,90,15,22,50,36,13,55,6,35,47,82,52,33,61,36,27,28,46,98,14,73,20,73,32,16,26,80,53,47,66,76,38,94,45,2,1,22,52,47,96,64,58,52,39],
[88,46,23,39,74,63,81,64,20,90,33,33,76,55,58,26,10,46,42,26,74,74,12,83,32,43,9,2,73,55,86,54,85,34,28,23,29,79,91,62,47,41,82,87,99,22,48,90,20,5,96,75,95,4,43,28,81,39,81,1,28,42,78,25,39,77,90,57,58,98,17,36,73,22,63,74,51],
[29,39,74,94,95,78,64,24,38,86,63,87,93,6,70,92,22,16,80,64,29,52,20,27,23,50,14,13,87,15,72,96,81,22,8,49,72,30,70,24,79,31,16,64,59,21,89,34,96,91,48,76,43,53,88,1,57,80,23,81,90,79,58,1,80,87,17,99,86,90,72,63,32,69,14,28,88,69],
[37,17,71,95,56,93,71,35,43,45,4,98,92,94,84,96,11,30,31,27,31,60,92,3,48,5,98,91,86,94,35,90,90,8,48,19,33,28,68,37,59,26,65,96,50,68,22,7,9,49,34,31,77,49,43,6,75,17,81,87,61,79,52,26,27,72,29,50,7,98,86,1,17,10,46,64,24,18,56],
[51,30,25,94,88,85,79,91,40,33,63,84,49,67,98,92,15,26,75,19,82,5,18,78,65,93,61,48,91,43,59,41,70,51,22,15,92,81,67,91,46,98,11,11,65,31,66,10,98,65,83,21,5,56,5,98,73,67,46,74,69,34,8,30,5,52,7,98,32,95,30,94,65,50,24,63,28,81,99,57],
[19,23,61,36,9,89,71,98,65,17,30,29,89,26,79,74,94,11,44,48,97,54,81,55,39,66,69,45,28,47,13,86,15,76,74,70,84,32,36,33,79,20,78,14,41,47,89,28,81,5,99,66,81,86,38,26,6,25,13,60,54,55,23,53,27,5,89,25,23,11,13,54,59,54,56,34,16,24,53,44,6],
[13,40,57,72,21,15,60,8,4,19,11,98,34,45,9,97,86,71,3,15,56,19,15,44,97,31,90,4,87,87,76,8,12,30,24,62,84,28,12,85,82,53,99,52,13,94,6,65,97,86,9,50,94,68,69,74,30,67,87,94,63,7,78,27,80,36,69,41,6,92,32,78,37,82,30,5,18,87,99,72,19,99],
[44,20,55,77,69,91,27,31,28,81,80,27,2,7,97,23,95,98,12,25,75,29,47,71,7,47,78,39,41,59,27,76,13,15,66,61,68,35,69,86,16,53,67,63,99,85,41,56,8,28,33,40,94,76,90,85,31,70,24,65,84,65,99,82,19,25,54,37,21,46,33,2,52,99,51,33,26,4,87,2,8,18,96],
[54,42,61,45,91,6,64,79,80,82,32,16,83,63,42,49,19,78,65,97,40,42,14,61,49,34,4,18,25,98,59,30,82,72,26,88,54,36,21,75,3,88,99,53,46,51,55,78,22,94,34,40,68,87,84,25,30,76,25,8,92,84,42,61,40,38,9,99,40,23,29,39,46,55,10,90,35,84,56,70,63,23,91,39],
[52,92,3,71,89,7,9,37,68,66,58,20,44,92,51,56,13,71,79,99,26,37,2,6,16,67,36,52,58,16,79,73,56,60,59,27,44,77,94,82,20,50,98,33,9,87,94,37,40,83,64,83,58,85,17,76,53,2,83,52,22,27,39,20,48,92,45,21,9,42,24,23,12,37,52,28,50,78,79,20,86,62,73,20,59],
[54,96,80,15,91,90,99,70,10,9,58,90,93,50,81,99,54,38,36,10,30,11,35,84,16,45,82,18,11,97,36,43,96,79,97,65,40,48,23,19,17,31,64,52,65,65,37,32,65,76,99,79,34,65,79,27,55,33,3,1,33,27,61,28,66,8,4,70,49,46,48,83,1,45,19,96,13,81,14,21,31,79,93,85,50,5],
[92,92,48,84,59,98,31,53,23,27,15,22,79,95,24,76,5,79,16,93,97,89,38,89,42,83,2,88,94,95,82,21,1,97,48,39,31,78,9,65,50,56,97,61,1,7,65,27,21,23,14,15,80,97,44,78,49,35,33,45,81,74,34,5,31,57,9,38,94,7,69,54,69,32,65,68,46,68,78,90,24,28,49,51,45,86,35],
[41,63,89,76,87,31,86,9,46,14,87,82,22,29,47,16,13,10,70,72,82,95,48,64,58,43,13,75,42,69,21,12,67,13,64,85,58,23,98,9,37,76,5,22,31,12,66,50,29,99,86,72,45,25,10,28,19,6,90,43,29,31,67,79,46,25,74,14,97,35,76,37,65,46,23,82,6,22,30,76,93,66,94,17,96,13,20,72],
[63,40,78,8,52,9,90,41,70,28,36,14,46,44,85,96,24,52,58,15,87,37,5,98,99,39,13,61,76,38,44,99,83,74,90,22,53,80,56,98,30,51,63,39,44,30,91,91,4,22,27,73,17,35,53,18,35,45,54,56,27,78,48,13,69,36,44,38,71,25,30,56,15,22,73,43,32,69,59,25,93,83,45,11,34,94,44,39,92],
[12,36,56,88,13,96,16,12,55,54,11,47,19,78,17,17,68,81,77,51,42,55,99,85,66,27,81,79,93,42,65,61,69,74,14,1,18,56,12,1,58,37,91,22,42,66,83,25,19,4,96,41,25,45,18,69,96,88,36,93,10,12,98,32,44,83,83,4,72,91,4,27,73,7,34,37,71,60,59,31,1,54,54,44,96,93,83,36,4,45],
[30,18,22,20,42,96,65,79,17,41,55,69,94,81,29,80,91,31,85,25,47,26,43,49,2,99,34,67,99,76,16,14,15,93,8,32,99,44,61,77,67,50,43,55,87,55,53,72,17,46,62,25,50,99,73,5,93,48,17,31,70,80,59,9,44,59,45,13,74,66,58,94,87,73,16,14,85,38,74,99,64,23,79,28,71,42,20,37,82,31,23],
[51,96,39,65,46,71,56,13,29,68,53,86,45,33,51,49,12,91,21,21,76,85,2,17,98,15,46,12,60,21,88,30,92,83,44,59,42,50,27,88,46,86,94,73,45,54,23,24,14,10,94,21,20,34,23,51,4,83,99,75,90,63,60,16,22,33,83,70,11,32,10,50,29,30,83,46,11,5,31,17,86,42,49,1,44,63,28,60,7,78,95,40],
[44,61,89,59,4,49,51,27,69,71,46,76,44,4,9,34,56,39,15,6,94,91,75,90,65,27,56,23,74,6,23,33,36,69,14,39,5,34,35,57,33,22,76,46,56,10,61,65,98,9,16,69,4,62,65,18,99,76,49,18,72,66,73,83,82,40,76,31,89,91,27,88,17,35,41,35,32,51,32,67,52,68,74,85,80,57,7,11,62,66,47,22,67],
[65,37,19,97,26,17,16,24,24,17,50,37,64,82,24,36,32,11,68,34,69,31,32,89,79,93,96,68,49,90,14,23,4,4,67,99,81,74,70,74,36,96,68,9,64,39,88,35,54,89,96,58,66,27,88,97,32,14,6,35,78,20,71,6,85,66,57,2,58,91,72,5,29,56,73,48,86,52,9,93,22,57,79,42,12,1,31,68,17,59,63,76,7,77],
[73,81,14,13,17,20,11,9,1,83,8,85,91,70,84,63,62,77,37,7,47,1,59,95,39,69,39,21,99,9,87,2,97,16,92,36,74,71,90,66,33,73,73,75,52,91,11,12,26,53,5,26,26,48,61,50,90,65,1,87,42,47,74,35,22,73,24,26,56,70,52,5,48,41,31,18,83,27,21,39,80,85,26,8,44,2,71,7,63,22,5,52,19,8,20],
[17,25,21,11,72,93,33,49,64,23,53,82,3,13,91,65,85,2,40,5,42,31,77,42,5,36,6,54,4,58,7,76,87,83,25,57,66,12,74,33,85,37,74,32,20,69,3,97,91,68,82,44,19,14,89,28,85,85,80,53,34,87,58,98,88,78,48,65,98,40,11,57,10,67,70,81,60,79,74,72,97,59,79,47,30,20,54,80,89,91,14,5,33,36,79,39],
[60,85,59,39,60,7,57,76,77,92,6,35,15,72,23,41,45,52,95,18,64,79,86,53,56,31,69,11,91,31,84,50,44,82,22,81,41,40,30,42,30,91,48,94,74,76,64,58,74,25,96,57,14,19,3,99,28,83,15,75,99,1,89,85,79,50,3,95,32,67,44,8,7,41,62,64,29,20,14,76,26,55,48,71,69,66,19,72,44,25,14,1,48,74,12,98,7],
[64,66,84,24,18,16,27,48,20,14,47,69,30,86,48,40,23,16,61,21,51,50,26,47,35,33,91,28,78,64,43,68,4,79,51,8,19,60,52,95,6,68,46,86,35,97,27,58,4,65,30,58,99,12,12,75,91,39,50,31,42,64,70,4,46,7,98,73,98,93,37,89,77,91,64,71,64,65,66,21,78,62,81,74,42,20,83,70,73,95,78,45,92,27,34,53,71,15],
[30,11,85,31,34,71,13,48,5,14,44,3,19,67,23,73,19,57,6,90,94,72,57,69,81,62,59,68,88,57,55,69,49,13,7,87,97,80,89,5,71,5,5,26,38,40,16,62,45,99,18,38,98,24,21,26,62,74,69,4,85,57,77,35,58,67,91,79,79,57,86,28,66,34,72,51,76,78,36,95,63,90,8,78,47,63,45,31,22,70,52,48,79,94,15,77,61,67,68],
[23,33,44,81,80,92,93,75,94,88,23,61,39,76,22,3,28,94,32,6,49,65,41,34,18,23,8,47,62,60,3,63,33,13,80,52,31,54,73,43,70,26,16,69,57,87,83,31,3,93,70,81,47,95,77,44,29,68,39,51,56,59,63,7,25,70,7,77,43,53,64,3,94,42,95,39,18,1,66,21,16,97,20,50,90,16,70,10,95,69,29,6,25,61,41,26,15,59,63,35]]
Short example:
In [24]:
a=[[3],
[7, 4],
[2, 4, 6],
[8, 5, 9, 3]]
Problem 18:
In [35]:
a = [[75],
[95,64],
[17,47,82],
[18,35,87,10],
[20,4,82,47,65],
[19,1,23,75,3,34],
[88,2,77,73,7,63,67],
[99,65,4,28,6,16,70,92],
[41,41,26,56,83,40,80,70,33],
[41,48,72,33,47,32,37,16,94,29],
[53,71,44,65,25,43,91,52,97,51,14],
[70,11,33,28,77,73,17,78,39,68,17,57],
[91,71,52,38,17,14,91,43,58,50,27,29,48],
[63,66,4,68,89,53,67,30,73,16,69,87,40,31],
[4,62,98,27,23,9,70,98,73,93,38,53,60,4,23]]
Algorithm, dynamic programming:
In [36]:
l=max(len(i) for i in a)
sums = [ 0 for i in range(1,l+1)]
for row in a:
prev_sums=list(sums)
for i, s in enumerate(row):
l = 0 if i == 0 else prev_sums[i-1]
r = 0 if i == len(row) else prev_sums[i]
sums[i] = max(row[i] + l, row[i] + r)
print(max(sums))