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

*Return the number of pseudo-palindromic paths going from the root node to leaf nodes.*

**Example 1:**

Input:root = [2,3,1,3,1,null,1]Output:2Explanation: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).

**Example 2:**

Input:root = [2,1,1,1,3,null,null,null,null,null,1]Output:1Explanation: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).

**Example 3:**

Input:root = [9]Output:1

**Constraints:**

- The number of nodes in the tree is in the range
`[1, 10`

.^{5}] `1 <= Node.val <= 9`