class Solution {
public:
int totalNQueens(int n) {
int res = 0;
vector<bool> cols(n), diag(2 * n), anti_diag(2 * n);
helper(n, 0, cols, diag, anti_diag, res);
return res;
}
void helper(int n, int row, vector<bool>& cols, vector<bool>& diag, vector<bool>& anti_diag, int& res) {
if (row == n) ++res;
for (int col = 0; col < n; ++col) {
int idx1 = col - row + n, idx2 = col + row;
if (cols[col] || diag[idx1] || anti_diag[idx2]) continue;
cols[col] = diag[idx1] = anti_diag[idx2] = true;
helper(n, row + 1, cols, diag, anti_diag, res);
cols[col] = diag[idx1] = anti_diag[idx2] = false;
}
}
};
