<p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
public:
    bool isValidPos(int i,int j, vector<vector<char>> board){
        int rr = i-1 , cc = j-1;
        // up left diagonal ....
        while(rr >=0 && cc >=0){
            if(board[rr][cc] == 'Q') return false;
            rr-- , cc-- ;
        }
        // up right diagonal ....
        rr = i-1 , cc = j + 1;
        while(rr>=0 && cc<board.size()){
            if(board[rr][cc] == 'Q') return false;
            rr-- , cc++;
        }

        return true;
    }
    void nQueen(int idx , vector< bool > &column , vector<vector< char >>&board , int &res ){
        if(idx >= board.size()) res += 1;
        else{
            for(int i=0 ; i<board.size() ; i++){
                if( board[idx][i] == '.' && column[i] == false && isValidPos(idx , i , board)){
                    board[idx][i] = 'Q';
                    column[i] = true;
                    nQueen( idx+1 , column , board , res );
                    column[i] = false;
                    board[idx][i] = '.';
                }
            }
        }
    }
    int totalNQueens(int n) {
        ios_base :: sync_with_stdio( false );
        int res = 0;
        vector< vector<char>> vec( n , vector<char>(n , '.'));
        vector< bool >column( n , false);
        nQueen( 0 , column , vec , res);
        return res;
    }
};
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