<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:

    static bool has_perfect_square(int num)
    {
        static std::unordered_set<int> perfect_squares;
        if (perfect_squares.empty())
        {
            for (int i = 0; i < 31623; ++i)
            {
                perfect_squares.insert(i * i);
            }
        }
        return perfect_squares.count(num) != 0;
    }

    int dfs(int mask, int prev, std::vector<int> &nums)
    {
        auto n = nums.size();
        if (1 + mask == (1 << n))
        {
            return 1;
        }

        if (m_memo[mask][prev] != -1)
        {
            return m_memo[mask][prev];
        }
        int count = 0;
        std::unordered_map<int, bool> visited;
        for (int i = 0; i < n; ++i)
        {
            auto bit = (1 << i);
            auto sum = nums[prev] + nums[i];
            if (  (mask & bit) != bit
               && has_perfect_square(sum)
               && !visited[nums[i]])
            {
                visited[nums[i]] = true;
                count += dfs(mask | bit, i, nums);
            }
        }
        return m_memo[mask][prev] = count;
    }

    int numSquarefulPerms(std::vector<int> &nums)
    {
        std::sort(std::begin(nums), std::end(nums));
        int count = 0;
        int n = nums.size();
        m_memo.resize(1 << n, std::vector<int>(n, -1));
        std::unordered_map<int, bool> visited;
        for (int i = 0; i < n; ++i)
        {
            int mask = (1 << i);
            if (!visited[nums[i]])
            {
                count += dfs(mask, i, nums);
            }
            visited[nums[i]] = true;
        }
        return count;
    }
    std::vector<std::vector<int>> m_memo;
};
19700