<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 {
private:
    int dp[(1<<12)][12][12] = {};
    int vui(int x) {
        int ans = 1;
        for (int i = 2; i <= x; i++) ans *= i;
        return ans;
    }
public:
    int magic(vector<int>& nums, int mask, int prev, int i) {
        if (i == nums.size()) return 1;
        if (dp[mask][prev][i] != -1) return dp[mask][prev][i];
        int ans = 0;
        for (int j = 0; j < nums.size(); j++) {
            if ((!(mask & (1<<j)) && pow((int)sqrt(nums[j]+nums[prev]),2) == nums[j]+nums[prev])) ans += magic(nums, mask | (1<<j), j, i+1);
        }
        return dp[mask][prev][i] = ans;
    }
    int numSquarefulPerms(vector<int>& nums) {
        memset(dp,-1,sizeof(dp));
        int ans = 0;
        for (int i = 0; i < nums.size(); i++) {
            ans += magic(nums, (1<<i), i, 1);
        }
        sort(nums.begin(), nums.end());
        int c = 1;
        for (int i = 1; i < nums.size(); i++) {
            if (nums[i] != nums[i-1]) {
                ans /= vui(c);
                c = 0;
            }
            c++;
        }
        return ans/vui(c);
    }
};
12000