<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 checker(int a)
{
    for(int i=0;i<=a;i++)
    {
        int b=i*i;
        if(b==a)
        {
            return true;
        }
        if(b>a)
        {
            return false;
        }
    }
    return false;
}
int permute(int a)
{if(a==1){return 1;}
    return a*permute(a-1);
}
void helper(vector<int>& nums,vector<int>a,int &c,vector<bool>b)
{
    if(a.size()==nums.size())
    {
        c++;
        return;
    }
    for(int i=0;i<nums.size();i++)
    {
        if(b[i]==true|| (i > 0 && nums[i] == nums[i - 1] && !b[i - 1]))
        {
            continue;
        }
        if(a.size()==0||checker(nums[i]+a.back()))
        {
            
            a.push_back(nums[i]);
            b[i]=true;
            helper(nums,a,c,b);
            b[i]=false;
            a.pop_back();
        }
    }
}
    int numSquarefulPerms(vector<int>& nums) {
        sort(nums.begin(),nums.end());
        if(nums.size()==0)
        {
            return 0;
        }
        // map<int,int>d;
        // for(int i=0;i<nums.size();i++)
        // {
        //     d[nums[i]]++;
        // }
        // int m=0;
        // for(auto it:d)
        // {
        //     if((it.second)>1)
        //     {
        //         m=m+permute(it.second);
        //     }
        // }
        // unordered_map<vector<int>,int> s;
        vector<int>a;int c=0;
        vector<bool>b(nums.size(),false);
        helper(nums,a,c,b);
        // if(m!=0)return c/m;
        return c;
    }
};
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