<p>An array is <strong>squareful</strong> if the sum of every pair of adjacent elements is a <strong>perfect square</strong>.</p>

<p>Given an integer array nums, return <em>the number of permutations of </em><code>nums</code><em> that are <strong>squareful</strong></em>.</p>

<p>Two permutations <code>perm1</code> and <code>perm2</code> are different if there is some index <code>i</code> such that <code>perm1[i] != perm2[i]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,17,8]
<strong>Output:</strong> 2
<strong>Explanation:</strong> [1,8,17] and [17,8,1] are the valid permutations.
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,2,2]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 12</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    int sol;
    bool check(vector<bool> vis){
        for(auto it:vis) if(it==false) return false;
        return true;
    }
    bool check_sqr(int n){
        int p=sqrt(n);
        if(p*p==n) return true;
        return false;
    }
    void dfs(int ind,vector<vector<int>> v,vector<bool> vis,vector<int> nums){
      if(check(vis)) sol++;
      int prev=-1;
      for(auto it:v[ind]){
        if(!vis[it]&&nums[it]!=prev){
                vis[it]=true;
                dfs(it,v,vis,nums);
                vis[it]=false;
            prev=nums[it];
        }
      }
      return;
    }
    int numSquarefulPerms(vector<int>& nums) {
        int n=nums.size();
        sol=0;
        sort(nums.begin(),nums.end());
        vector<vector<int>> v(n);
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(i!=j&&check_sqr(nums[i]+nums[j])) v[i].push_back(j);
            }
        }
        vector<bool> vis(n,0);
        vis[0]=true;
        dfs(0,v,vis,nums);
        vis[0]=false;
        for(int i=1;i<n;i++){
          if(nums[i]!=nums[i-1]){
            vis[i]=true;
            dfs(i,v,vis,nums);
            vis[i]=false;
          }
        }
        return sol;
    }
};
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