<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:
    bool isPerfectSquare(int num) {
        int root = static_cast<int>(sqrt(num));
        return root * root == num;
    }

    void numSquarefulPermsRec(vector<int>& nums, vector<int> curr, map<vector<int>, bool>& map, int& perms) {
        if (map[curr])
            return;
        map[curr] = true;

        if (nums.empty()){
            ++perms;
            return;
        }

        for(int i=0; i<nums.size(); ++i){
            if (isPerfectSquare(curr[curr.size()-1]+nums[i])){
                curr.push_back(nums[i]);

                vector<int> tempNums = nums;
                tempNums.erase(tempNums.begin() + i);

                numSquarefulPermsRec(tempNums, curr, map, perms);

                curr.pop_back();
            }
        }
    }

    int numSquarefulPerms(vector<int>& nums) {
        map<vector<int>, bool> map;

        int perms = 0;
        for(int i=0; i<nums.size(); ++i){
            vector<int> curr = {nums[i]};
            vector<int> tempNums = nums;
            tempNums.erase(tempNums.begin() + i);
            numSquarefulPermsRec(tempNums, curr, map, perms);
        }
        return perms;
    }
};
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