{
  import numpy as np

grd_old = [ [0, 0, 0, 0],
            [0, 0, 0, 0],
            [0, 0, 0, 0],
            [0, 0, 0, 0] ]


chkl  = [ [1, 0],[2, 0] ]
chkr  = [ [1, 3],[2, 3] ]
chku  = [ [0, 1],[0, 2] ]
chkd  = [ [3, 1],[3, 2] ]
term  = [ [0, 0],[3, 3] ]   # terminal states

r = -1
grd = [[0] * 4] * 4
iter = 3

for k in range(iter):
    for i in range(4):
        for j in range(4):
            if [i, j] in chkl :
                grd[i][j] = ( grd_old[i][j] + grd_old[i-1][j] + grd_old[i+1]    [j] + grd_old[i][j+1] + (4*r)) / 4
            elif [i, j] in chkr :
                grd[i][j] = ( grd_old[i][j] + grd_old[i-1][j] + grd_old[i+1]    [j] + grd_old[i][j-1] + (4*r)) / 4
            elif [i, j] in chku :
                grd[i][j] = ( grd_old[i][j] + grd_old[i+1][j] + grd_old[i][j-1] + grd_old[i][j+1] + (4*r)) / 4
            elif [i, j] in chkd :
                grd[i][j] = ( grd_old[i][j] + grd_old[i-1][j] + grd_old[i][j-1] + grd_old[i][j+1] + (4*r)) / 4
            elif [i, j] in term :
                grd[i][j] = 0
            elif [i, j] == [3, 0] :
                grd[i][j] = ( (2*grd_old[i][j]) + grd_old[i-1][j] +     grd_old[i][j+1] + (4*r)) / 4
            elif [i, j] == [0, 3] :
                grd[i][j] = ( (2*grd_old[i][j]) + grd_old[i][j-1] + grd_old[i+1][j] + (4*r)) / 4
            else:
                grd[i][j] = ( grd_old[i-1][j] + grd_old[i+1][j] + grd_old[i][j-1] + grd_old[i][j+1] + (4*r)) / 4
    print(grd)
    print('----------------------------------------------------')
    grd_old = grd.copy()

}