Problem:
 Score : 500 points    Problem Statement We have a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i -th row from the top and the j -th column from the left.  The square (i, j) has two numbers A_{ij} and B_{ij} written on it.  First, for each square, Takahashi paints one of the written numbers red and the other blue.  Then, he travels from the square (1, 1) to the square (H, W) . In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1) . He must not leave the grid.  Let the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1, 1) and (H, W) .  Takahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.  Find the minimum unbalancedness possible.      Constraints  2 \leq H \leq 80  2 \leq W \leq 80  0 \leq A_{ij} \leq 80  0 \leq B_{ij} \leq 80  All values in input are integers.         Input Input is given from Standard Input in the following format:  H  W  A_{11}  A_{12}  \ldots  A_{1W}  :  A_{H1}  A_{H2}  \ldots  A_{HW}  B_{11}  B_{12}  \ldots  B_{1W}  :  B_{H1}  B_{H2}  \ldots  B_{HW}       Output Print the minimum unbalancedness possible.        Sample Input 1 2 2
1 2
3 4
3 4
2 1      Sample Output 1 0  By painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7 , respectively, for the unbalancedness of 0 .        Sample Input 2 2 3
1 10 80
80 10 1
1 2 3
4 5 6      Sample Output 2 2

Solution (Python):
import numpy as np
i8 = np.int64
i4 = np.int32


def calc(dp1, dp2, k):
    dp2[k:] += dp1[:dp1.shape[0]-k]
    dp2[:dp2.shape[0]-k] += dp1[k:]


def solve(z, dp):
    zero = dp.shape[2] // 2
    dp[0, 0, zero + z[0, 0]] = 1
    dp[0, 0, zero - z[0, 0]] = 1
    for x in range(1, z.shape[1]):
        calc(dp[0, x - 1], dp[0, x], z[0, x])
    for y in range(1, z.shape[0]):
        calc(dp[y - 1, 0], dp[y, 0], z[y, 0])
        for x in range(1, z.shape[1]):
            calc(dp[y, x - 1], dp[y, x], z[y, x])
            calc(dp[y - 1, x], dp[y, x], z[y, x])
            if (x + y) % 50 == 0:
                dp[y, x] = dp[y, x] > 0
    for i in range(zero, dp.shape[2]):
        if dp[dp.shape[0] - 1, dp.shape[1] - 1, i] > 0:
            return i - zero
    return -1


def main():
    stdin = open('/dev/stdin', 'rb')
    pin = np.fromstring(stdin.read(), i8, sep=' ')
    H, W = pin[:2]
    a = pin[2: 2 + H * W].reshape(H, W)
    b = pin[2 + H * W:].reshape(H, W)
    z = np.abs(a - b)
    dp = np.zeros((H, W, 80 * 80 *2 + 1), i8)
    ans = solve(z, dp)
    print(ans)


if __name__ == '__main__':
    main()