<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:
    map<int,int>mpp;
    map<string,int>dp;
    set<string>s;
    bool isps(int x){
        int y  = sqrt(x);
        if(y*y==x)
        return true;
        return false;
    }
    int solve(vector<int>& nums,int n,vector<bool>& vis,string mask,int cnt,int last){
        if(cnt==n){
            if(s.find(mask)==s.end()){
                s.insert(mask);
                return 1;
            }
            return 0;
        }
        int ans = 0;
        if(dp.find(mask)!=dp.end())
        return 0;

        for(int i = 0;i<n;i++){
            if(vis[i])
            continue;
            vis[i]=true;
            if(last==-1||isps(last+nums[i]))
            ans+=solve(nums,n,vis,mask+" "+(to_string(mpp[i])),cnt+1,nums[i]);
            vis[i]=false;
        }
        return dp[mask]=ans;
    }
    int numSquarefulPerms(vector<int>& nums){
        map<int,vector<int>>mp;
        int n = nums.size();
        for(int i = 0;i<n;i++)
            mp[nums[i]].push_back(i);
        for(auto x:mp){
            int z = x.second[0];
            for(auto y:x.second)
                mpp[y]=z;
        }
        vector<bool>vis(nums.size(),false);
        return solve(nums,n,vis,"",0,-1);
    }
};
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