<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:
    vector<int>movex = {0,0,1,-1,1,-1,1,-1};
    vector<int>movey = {1,-1,0,0,1,1,-1,-1};

    bool check(int x, int y, int n){
        if(x>=0 && x<n && y>=0 && y<n) return true;
        return false;
    }

    vector<string> color(int n, int x, int y, vector<string>v){
        v[x][y] = 'Q';
        for(int i=1;i<=n;i++){
            for(int j=0;j<8;j++){
                int newx = x+i*movex[j];
                int newy = y+i*movey[j];
                if(check(newx, newy, n)){
                    v[newx][newy] = '.';
                }
            }
        }
        return v;
    }

    void rec(int n, int d, int &ans, vector<string>v){
        for(int i=0;i<n;i++){
            if(v[d][i]=='X' && d<n-1){
                vector<string>temp = color(n, d, i, v);
                rec(n, d+1, ans, temp);
            }
            if(v[d][i]=='X' && d==n-1){
                vector<string>temp = color(n, d, i, v);
                ans++;
            }
        }
    }
    int totalNQueens(int n) {
        vector<string>v;
        for(int i=0;i<n;i++){
            string s = "";
            for(int j=0;j<n;j++){
                s+='X';
            }
            v.push_back(s);
        }
        int ans;
        rec(n, 0, ans, v);
        return ans;
    }
};
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