Chessboard and Queens

#include <bits/stdc++.h>
using namespace std;
 
const int DIM = 8;
 
int main() {
	vector<vector<bool>> blocked(DIM, vector<bool>(DIM));
	for (int r = 0; r < DIM; r++) {
		string row;
		cin >> row;
		for (int c = 0; c < DIM; c++) { blocked[r][c] = row[c] == '*'; }
	}
 
    // here, queens[i] denotes the row number of queen placed in the i_th column
	vector<int> queens(DIM);  
	// Set the initial values to 0, 1...7
	iota(queens.begin(), queens.end(), 0);
 
	int valid_num = 0;
	do {
		bool works = true;
		// Check if any cells have been blocked off by the input
		for (int c = 0; c < DIM; c++) {
			if (blocked[queens[c]][c]) {
				works = false;
				break;
			}
		}
 
		// Check the diagonals from the top-left to the bottom-right
		vector<bool> taken(DIM * 2 - 1);
		for (int c = 0; c < DIM; c++) {
			// Check if the diagonal with sum has been taken
			if (taken[c + queens[c]]) {
				works = false;
				break;
			}
			taken[c + queens[c]] = true;
		}
 
		// Check the diagonals from the top-right to the bottom-left
		taken = vector<bool>(DIM * 2 - 1);
		for (int c = 0; c < DIM; c++) {
			// queens[c] - c can be negative; the DIM - 1 offsets that
			if (taken[queens[c] - c + DIM - 1]) {
				works = false;
				break;
			}
			taken[queens[c] - c + DIM - 1] = true;
		}
 
		if (works) { valid_num++; }
	} while (next_permutation(queens.begin(), queens.end()));
 
	cout << valid_num << endl;
}