<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>

void printArr(const vector<int> & a){
    for(int i = 0 ; i < a.size() ; i ++) cout<<a[i]<<" ";
    cout<<endl;
}
bool isSquare(int val){
    int x = sqrt(val);
    return (x * x) == val;
}
string Convert(int a){
    string s = "";
    while(a > 0){
        s.push_back('0' + a % 10);
        a /= 10;
    }
    return s;
}
string Convert(const vector<int> & a){
    int i; string s = "";
    for(i = 0 ; i < a.size() ; i ++){
        s.append(Convert(a[i]));
        s.push_back(',');
    }
    return s;
}
class Solution {
public:
    unordered_set<string> s;
    void DFS(vector<int> & nums, int idx, int & ans){
        if(idx == nums.size()){
            string nums_s = Convert(nums);
            if(s.find(nums_s) == s.end()){
                //printArr(nums);
                ans ++;          
                s.insert(nums_s);
            }
            return;
        }
        int i;
        if(idx == 0){
            DFS(nums, idx + 1, ans);
            for(i = 1 ; i < nums.size() ; i ++){
                if(nums[idx] == nums[i]) continue;
                swap(nums[idx], nums[i]);
                DFS(nums, idx + 1, ans);
                swap(nums[idx], nums[i]);
            }
        }else{
            if(isSquare(nums[idx - 1] + nums[idx])) DFS(nums, idx + 1, ans);
            for(i = idx + 1; i < nums.size() ; i ++){
                if(nums[idx] == nums[i]) continue;
                if(isSquare(nums[idx - 1] + nums[i])){
                    swap(nums[idx], nums[i]);
                    DFS(nums, idx + 1, ans);
                    swap(nums[idx], nums[i]);
                }
            }
        }
    }
    int numSquarefulPerms(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int ans = 0;
        DFS(nums, 0, ans);
        return ans;
    }
};
13200