Find the number of solutions to a n queen problem

n-queens.py

from sys import argv
from itertools import combinations


class Board:
    def __init__(self, n):
        self.board = [[0]*n for _ in range(n)]


    def __repr__(self):
        repr = ''
        n = len(self)
        for i in range(n):
            for j in range(n):
                repr += str(self[i][j])
                if j < n - 1:
                    repr += '  '
            if i < n - 1:
                repr += '\n'

        return repr


    def __len__(self):
        return len(self.board)


    def __getitem__(self, key):
        if key not in range(len(self)):
            raise IndexError
        return self.board[key]


def success(board):
    n = len(board)
    for i in range(n):
        for j in range(n):
            if board[i][j]:
                for k in range(n):
                    if board[k][j] and k != i or board[i][k] and k != j:
                        return False
                for a, b in zip(range(i+1, n), range(j+1, n)):
                    if board[a][b]: return False
                for a, b in zip(range(i+1, n), range(j-1, -1, -1)):
                    if board[a][b]: return False
                for a, b in zip(range(i-1, -1, -1), range(j+1, n)):
                    if board[a][b]: return False
                for a, b in zip(range(i-1, -1, -1), range(j-1, -1, -1)):
                    if board[a][b]: return False

    return True


n = int(argv[1])
count = 0
iter = combinations(range(n**2), n)
for e in iter:
    b = Board(n)
    for i in range(n):
        b[e[i]//n][e[i]%n] = 1
    if success(b):
        count += 1

print(count)