<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>

class Solution {
private:
    bool isPseudoPalindromic(const unordered_map<int, int>& freq) {
        int oddCount = 0;
        for (const auto& it : freq) {
            if (it.second % 2 == 1) {
                oddCount++;
                if (oddCount > 1) {
                    return false;
                }
            }
        }
        return true;
    }
    void dfs(TreeNode* node, unordered_map<int, int>& freq, int& fnl) {
        if (node == nullptr) {
            return;
        }
        freq[node->val]++;
        if (node->left == nullptr && node->right == nullptr) {
            if (isPseudoPalindromic(freq)) {
                fnl++;
            }
        }
        dfs(node->left, freq, fnl);
        dfs(node->right, freq, fnl);
        freq[node->val]--;  
        if (freq[node->val] == 0) {
            freq.erase(node->val);
        }
    }

public:
    int pseudoPalindromicPaths(TreeNode* root) {
        ios::sync_with_stdio(false); 
        cin.tie(0); cout.tie(0);
        int fnl = 0;
        unordered_map<int,int>freq;
        dfs(root,freq,fnl);
        return fnl;
    }
};
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