Leetcode N-Queens II

Follow up for N-Queens problem.

Now, instead outputting board configurations, return the total number of distinct solutions.

class Solution {
public:
    int totalNQueens(int n) {
       vector<int> queen(n,0);
       for(int i = 0 ; i < n; ++ i) queen[i] = i;
       int cnt = 0;
       do{
           bool flag = false;
           for(int i = 1; i < n && !flag; ++ i){
               for(int j = 0 ; j < i && !flag ; ++ j){
                   if(abs(i-j) == abs(queen[i]-queen[j])) flag=true;
               }
           }
           if(!flag) cnt++;
       }while(next_permutation(queen.begin(),queen.end()));
       return cnt;
    }
};