n-queen problem

# Eight queens problem
# we implement a backtracking algorithm to solve the problem
# we use a two-dimensional array to represent the chessboard
# 0 stands for an empty cell, 1 stands for a queen

sz = 8 # size of the board

def main():
    a = [[0 for i in range(sz)] for j in range(sz)] # 1 stands for a queen
    search(a, 0)

def isLegal(a, k, i): # can put a queen at a[k][i]?
    # check row
    for j in range(0, sz):
        if a[k][j] == 1:
            return False
    # check column
    for j in range(0, sz):
        if a[j][i] == 1:
            return False
    # check diagonal
    for x in range(0, sz):
        for y in range(0, sz):
            if x + y == k + i and a[x][y] == 1:
                return False
            if x - y == k - i and a[x][y] == 1:
                return False

    return True

def search(a, k): # search for a solution starting from row k in a existing chessboard a
    if k == sz: # we have found a solution
        printFormated(a)
        return
    for i in range(0, sz):
        if isLegal(a, k, i):
            a[k][i] = 1 # put a queen at a[k][i]
            search(a, k + 1) # search for a solution starting from row k + 1
            a[k][i] = 0 # remove the queen at a[k][i]

kase = 0
def printFormated(a):
    global kase
    kase += 1
    print("Case", kase, ":")
    for i in range(0, sz):
        for j in range(0, sz):
            if a[i][j] == 1:
                print("Q", end = " ")
            else:
                print("*", end = " ")
        print('')
    print('')

main()
print("Total:", kase)