<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(), m = 2 * *max_element(nums.begin(), nums.end());
        unordered_set<int> squares;
        for (int i = 0; i * i <= m; i++) squares.insert(i * i);
        
        vector<vector<int>> graph(n);
        for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) {
            if (squares.find(nums[i] + nums[j]) != squares.end()) {
                graph[i].emplace_back(j);
                graph[j].emplace_back(i);
            }
        }

        unordered_set<int> perm;
        vector<int> ids(n);
        for (int i = 0; i < n; i++) ids[i] = i;
        return dfs(graph, nums, ids, perm, n);
    }

    int dfs(vector<vector<int>>& graph, vector<int>& nums, vector<int>& next, unordered_set<int>& perm, int n) {
        if (perm.size() == n) return 1;

        unordered_set<int> visited;
        int ans = 0;

        for (auto i : next) if (perm.find(i) == perm.end() && visited.find(nums[i]) == visited.end()) {
            perm.insert(i);
            visited.insert(nums[i]);
            ans += dfs(graph, nums, graph[i], perm, n);
            perm.erase(i);
        }

        return ans;
    }
};
46900