All Possible Full Binary Trees

easy
Given an integer n, return a list of all possible full binary trees with n nodes. Each node of each tree in the answer must have Node.val == 0.

Each element of the answer is the root node of one possible tree. You may return the final list of trees in any order.

A full binary tree is a binary tree where each node has exactly 0 or 2 children.

Input Format

Integer n

Output Format

List of treenode type

Constraints

1 <= n <= 20

Notice

NA

Example

Input

        
Output

        
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