<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:
    bool issquare(int n){
        int a=sqrt(n);
        return ((a*a)==n);
    }
    void func(vector<int>&nums,int idx,set<vector<int>>&ans){
        if((idx>1)&&issquare(nums[idx-1]+nums[idx-2])==false){
            return;
        }
 
        int n=nums.size();
        if(idx==n-1){
            bool flag=true;
          for(int i=0;i<(n-1);i++){
            if(issquare(nums[i]+nums[i+1])==false){
               flag=false;
               break;
            }
          }
          if(flag){
            ans.insert(nums);
          }
          return;
        }
        
        func(nums,idx+1,ans);
        

        for(int i=idx+1;i<n;i++){
            if(nums[idx]==nums[i]) continue;
            swap(nums[idx],nums[i]);
        
        func(nums,idx+1,ans);
        
            swap(nums[idx],nums[i]);
        }

    }
    int numSquarefulPerms(vector<int>& nums) {
        set<vector<int>>ans;
        func(nums,0,ans);
        return ans.size();
    }
};
10800