<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) {
        const int N = nums.size();
        unordered_map<int, int> val_count_map;
        unordered_map<int, unordered_set<int>> val_partners_map;
        for(int i = 0; i < N; i++) val_count_map[nums[i]]++;
        
        for(auto& pair1 : val_count_map) {
            for(auto& pair2 : val_count_map) {
                int x = pair1.first, y = pair2.first;
                int root = sqrt(x + y);
                if(root * root == x + y) {
                    val_partners_map[x].insert(y);
                }
            }
        }
        
        int ans = 0;
        int progs = 0;
        for(auto& pair : val_partners_map) {
            int start_val = pair.first;
            dfs(N, val_count_map, val_partners_map, progs, start_val, ans);
        }
        return ans;
    }
private:
    void dfs(int N, unordered_map<int, int>& val_count_map, unordered_map<int, unordered_set<int>>& val_partners_map, int progs, int insert_val, int& ans) {
        if(progs >= N - 1) {
            ans++;
            return;
        }
        val_count_map[insert_val]--;
        for(auto& partner : val_partners_map[insert_val]) {
            if(val_count_map[partner] > 0) {
                dfs(N, val_count_map, val_partners_map, progs + 1, partner, ans);
            }
        }
        val_count_map[insert_val]++;
    }
};
9900