<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) {
        int n = nums.size();
        vector<vector<int>> dp(n, vector<int>(1 << n));
        for(int i = 0; i < n; i++) {
            dp[i][1 << i] = 1;
        }
        auto is_sqr = [&](int v) {
            int sv = int(sqrt(v));
            return sv * sv == v;
        };
        for(int i = 1; i < (1 << n); i++) {
            for(int j = 0; j < n; j++) {
                if(dp[j][i] == 0) continue;
                for(int k = 0; k < n; k++) {
                    if(i & (1 << k)) continue;
                    if(is_sqr(nums[j] + nums[k])) {
                        dp[k][i | (1 << k)] += dp[j][i];
                    }
                }
            }
        }
        int ret = 0;
        for(int i = 0; i < n; i++) {
            ret += dp[i][(1 << n) - 1];
        }
        map<int, int> cmp;
        for(int i: nums) {
            cmp[i]++;
        }
        vector<int> fac(n + 1);
        fac[0] = 1;
        for(int i = 1; i <= n; i++) {
            fac[i] = fac[i - 1] * i;
        }
        for(auto& [i, j]: cmp) {
            assert(ret % fac[j] == 0);
            ret /= fac[j];
        }
        return ret;
    }
};
13600