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.

#### 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

Example 1:
Example 2:

#### Constraints

Time limit: 0.2 seconds

Memory limit: 512 MB

Output limit: 1 MB