<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 isValid(const int a, const int b) {
        int root = std::sqrt(a + b);
        return (root * root) == (a + b);
    }
    int solve(std::vector<int> &nums, int index, int n, int mask, std::vector<std::vector<int>> &dpTable) {
        if (mask == (1 << n) - 1) return 1;

        if (dpTable[index + 1][mask] != -1) return dpTable[index + 1][mask];

        int result = 0;
        for (int next = 0; next < n; ++next) {
            if ((mask & (1 << next))) continue;
            if (next > 0 && (nums[next] == nums[next - 1]) && (mask & (1 << (next - 1)))) continue;
            
            if (index == -1 || isValid(nums[index], nums[next])) {
                result += solve(nums, next, n, mask | (1 << next), dpTable);
            }
        }

        return dpTable[index + 1][mask] = result;
    }
    int numSquarefulPerms(vector<int>& nums) {
        std::sort(nums.begin(), nums.end());
        int n = static_cast<int>(nums.size());
        std::vector<std::vector<int>> dpTable(n + 1, std::vector<int>(1 << n, -1));
        return solve(nums, -1, n, 0, dpTable);
    }
};
13700