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 itโ€™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. Itโ€™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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ย 
ย 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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