How Many Trees?

A binary search tree is a binary tree with root k such that any node v reachable from its left has label (v) <label (k) and any node w reachable from its right has label (w) > label (k). It is a search structure which can find a node with label x in O(n log n) average time, where n is the size of the tree (number of vertices).

Given a number n, can you tell how many different binary search trees may be constructed with a set of numbers of size n such that each element of the set will be associated to the label of exactly one node in a binary search tree?

The input will contain a number 1 <= i <= 100 per line representing the number of elements of the set.

You have to print a line in the output for each entry with the answer to the previous question.

1
2
3

1
2
5

UVA