<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 numSquarefulPerms(vector<int>& nums) {
        sort(nums.begin(),nums.end());
        int n = nums.size(),x;
        vector<vector<int>> dp(1<<n, vector<int>(n,0));
        //initialize dp
        x = -1;
        for (int i=0; i<n; ++i) 
            if (nums[i]!=x){
                x = nums[i];
                dp[1<<i][i] = 1;
            }
        
        //percolate
        for (int mask=1; mask<((1<<n)-1); mask++){
            for (int i=0; i<n; ++i)
                if (mask&(1<<i) && dp[mask][i]>0){
                    x = -1;
                    for (int j=0; j<n; ++j){
                        if (nums[j]==x) continue;
                        if ((mask&(1<<j))==0 && ((x=nums[j])|1) && isSqr(nums[i]+nums[j]))
                            dp[mask^(1<<j)][j] += dp[mask][i];
                    }
                }
        }
        int ans = 0;
        for (int i=0; i<n; ++i)
            ans += dp[(1<<n)-1][i];
        return ans;
    }

private:
    bool isSqr(int x){
        return ceil(sqrt(x))==floor(sqrt(x));
    }
};
16000