<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>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int sum = 0;

    void check(vector<int> vec) {
        int ans = 0;
        for (int k: vec) {
            if (k % 2 == 1) {
                if (ans > 1) return;
                else ans++;
            }
        }
        if (ans > 1) return;
        sum++;
    }

    void helper(TreeNode *n, vector<int> vec) {
        if (n == nullptr) return;
        if (n->left == nullptr && n->right == nullptr) {
            vec[n->val-1]++;
            check(vec);
            return;
        }
        vec[n->val-1]++;
        helper(n->left, vec);
        helper(n->right, vec);
    }

    int pseudoPalindromicPaths (TreeNode* root) {
        vector<int> vec(9, 0);
        helper(root, vec);
        return sum;
    }
};
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