Shared code

/* 777 */
#include "bits/stdc++.h"
using namespace std;

#define int long long 
#define endl '\n'
using vi = vector <int>;
using vii = vector <vi>;
using pii = pair<int,int>;
using vpii = vector<pii>;
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
#define sortf(x) sort(all(x))
#define sortr(x) sort(all(x),greater<int>())

// const int MOD=1e9+7;
// const int inf=1e9;
vi vec;
// vpii vecp;
// const int N=1e6;
int n;
int cols[8], diags[15], anti_diags[15];
int available[8][8];
int res = 0;

void pre(){

}

bool is_valid(int row, int col) {
	return cols[col] || diags[row + col] || anti_diags[row - col + 7];
}

void rec(int row) {
	if (row == n) {
		++res;
		return;
	}
	
	for(int col = 0 ; col < n ; ++col) {
		if (!available[row][col] || is_valid(row, col)) continue;
		// cout << row << col << endl;
		cols[col] = 1;
		diags[row + col] = 1; // row + col -> ranges from 0 to 14
		anti_diags[row - col + 7] = 1; // ranges from row - col -> ranges from -7 to 7
		rec(row + 1);
		cols[col] = diags[row + col] = anti_diags[row - col + 7] = 0; // backtrack
	}
}

void solve(){
	// cin>>n;
	n = 8;
	char c;
	for (int i = 0 ; i < n ; ++i) {
		for (int j = 0 ; j < n ; ++j) {
			cin >> c;
			available[i][j] = (c == '.');
		}
	}

	rec(0);

	cout << res << endl;
}

signed main(){
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	pre();
	solve();
}