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.