<p>Given a binary tree where node values are digits from 1 to 9. A path in the binary tree is said to be <strong>pseudo-palindromic</strong> if at least one permutation of the node values in the path is a palindrome.</p>

<p><em>Return the number of <strong>pseudo-palindromic</strong> paths going from the root node to leaf nodes.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2020/05/06/palindromic_paths_1.png" style="width: 300px; height: 201px;" /></p>

<pre>
<strong>Input:</strong> root = [2,3,1,3,1,null,1]
<strong>Output:</strong> 2 
<strong>Explanation:</strong> The figure above represents the given binary tree. There are three paths going from the root node to leaf nodes: the red path [2,3,3], the green path [2,1,1], and the path [2,3,1]. Among these paths only red path and green path are pseudo-palindromic paths since the red path [2,3,3] can be rearranged in [3,2,3] (palindrome) and the green path [2,1,1] can be rearranged in [1,2,1] (palindrome).
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/05/07/palindromic_paths_2.png" style="width: 300px; height: 314px;" /></strong></p>

<pre>
<strong>Input:</strong> root = [2,1,1,1,3,null,null,null,null,null,1]
<strong>Output:</strong> 1 
<strong>Explanation:</strong> The figure above represents the given binary tree. There are three paths going from the root node to leaf nodes: the green path [2,1,1], the path [2,1,3,1], and the path [2,1]. Among these paths only the green path is pseudo-palindromic since [2,1,1] can be rearranged in [1,2,1] (palindrome).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> root = [9]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 9</code></li>
</ul>

#pragma GCC target("avx, mmx, sse2, sse3, sse4")

auto disableSync = [](void) noexcept -> int
{
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    return 0;
}();

typedef struct TreeNode NodeBT_t;

class Solution final
{
private:
    int nbValidPaths = 0;

public:
    int pseudoPalindromicPaths(const NodeBT_t* const root) noexcept
    {
        std::array<size_t, 10> counter = {0};
        this->pseudoPalindromicPathsHelper(root, counter);
        return this->nbValidPaths;
    }

private:
    void pseudoPalindromicPathsHelper(const NodeBT_t* const root, std::array<size_t, 10> counter) noexcept
    {
        if (!root)
            return;
        ++counter[root->val];
        if (root->left == root->right && isPalindromic(counter))
            ++this->nbValidPaths;
        this->pseudoPalindromicPathsHelper(root->left, counter);
        this->pseudoPalindromicPathsHelper(root->right, counter);
    }

    static inline bool isPalindromic(const std::array<size_t, 10>& counter) noexcept
    {
        uint8_t nbOdds = 0;
        for (const size_t& count : counter)
            if ((count & 1) && ++nbOdds > 1)
                return false;
        return true;
    }
};
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