# Height of the Tree

Implement the binary search tree for integers. The program reads a sequence of integers and builds a tree from them. Elements are inserted to the tree according to the search results of their place. If the item already exists in the tree, do not add it. The balance operations on the tree are not performed.

Find the height of the built tree.

## Input

The program receives a sequence of integers. The sequence ends with the number 0, which means the end of input, do not add it to the tree. It is guaranteed that the input sequence contains no more than 10^5 numbers, each of them does not exceed 2·10^9 in absolute value.

## Output

Print one number - the height of the resulting tree.

Example corresponds to the following tree:

Note that the height of the tree is measured in vertices.