Algorithms and Data Structures

Is the binary tree symmetric?

A binary tree is symmetric if the right subtree of the root node is the mirror reflection of its left subtree.
Given a binary tree, you are asked to check if it’s symmetric.
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Input

The input contains space-separated integers representing the values in the nodes of the binary tree. The order of the values is given by traversing from the left to the right subtree every time. A value of 0 means that the node does not exist. It’s guaranteed that the input binary tree is valid.

Output

The program should print Yes if the given binary tree is symmetric, and No otherwise.

Examples

Input
Output
1 2 3 8 5 0 0 0 0 5 8 0 0 0 0
Yes
1 2 3 4 5 0 0 7 8 0 0 0 0 0 6 0 0
No

Explanation

Example 1:
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Example 2:
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Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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