<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 fun(int prev, int mask, vector<int>& nums, vector<vector<int>>& dp) {
        if (mask == (1 << nums.size()) - 1) {
            return 1; 
        }
        if(prev==nums.size())return 0;
        if (dp[mask][prev+1] != -1) return dp[mask][prev+1];

        int ans = 0;
        for (int j = 0; j < nums.size(); j++) {
            if ((mask & (1 << j)) || (j > 0 && nums[j] == nums[j - 1] && !(mask & (1 << (j - 1))))) {
                continue;
            }
            if (prev == -1 || sqrt(nums[j] + nums[prev]) == (int)sqrt(nums[j] + nums[prev])) {
                ans += fun(j, mask | (1 << j), nums, dp);
            }
        }
        return dp[mask][prev+1] = ans;
    }

    int numSquarefulPerms(vector<int>& nums) {
        sort(nums.begin(), nums.end()); // Handle duplicates by sorting
        // vector<int> dp(1 << nums.size(), -1);
        // vector<vector<int>>dp(1<<nums.size(),vector<int>(nums.size()+2),-1);
        vector<vector<int>> dp(1 << nums.size(), vector<int>(nums.size() + 2, -1));

        return fun(-1, 0, nums, dp);
    }
};

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