<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>

vector<vector<int>> dp;
class Solution {
public:
    int rec(int level,int mask, vector<int>& nums){
        if(mask==(1<<nums.size())-1) return 1;
        if(dp[level][mask]!=-1) return dp[level][mask];
        int ans=0;
        for(int i=0;i<nums.size();i++){
            if(!(mask&(1<<i))){
                int val=nums[i]+nums[level];
                if(floor(sqrt(val))==ceil(sqrt(val))){
                    ans+=rec(i,mask|(1<<i),nums);
                }

            }
        }
        return dp[level][mask]=ans;
    }
    int numSquarefulPerms(vector<int>& nums) {
        dp.assign(nums.size(),vector<int>((1<<nums.size()),-1));
        int ans=0;
        for(int i=0;i<nums.size();i++){
            ans+=rec(i,1<<i,nums);
        }
        for(int i=0;i<nums.size();i++){
            int k=1;
            for(int j=i+1;j<nums.size();j++){
                if(nums[i]==nums[j]) k++;
            }
            ans/=k;
        }
        return ans;
    }
};
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