Algorithms and Data Structures

Find the height of the binary tree

Given a binary tree, you are asked to find its height. The height of a binary tree is the height of its root - which is the maximum number of levels of nodes beneath the root node.
In the case on the right:
  • Nodes with values 4, 6, 7, and 8 have a height of 1
  • Nodes with values 3, and 5 have a height of 2
  • Node with value 2 has a height of 3
  • The root node with value 1 has a height of 4.
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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 the height of the binary tree.

Examples

Input
Output
1 2 3 8 5 0 0 0 0 5 8 0 0 0 0
3
1 2 3 4 5 0 0 7 8 0 0 0 0 0 6 0 0
4

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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