Problem Description

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? 

 

Input

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

 

Output

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

 

Sample Input

 

Sample Output

 

Source

UVA

import java.math.BigInteger;

import java.util.Scanner;

public class Main {

	static BigInteger []F =  new BigInteger[105];

	public static void ini()

	{

		F[1] = BigInteger.valueOf(1);

		for(int i = 2;i < 105;i++)

		{

			F[i] = F[i-1].multiply(BigInteger.valueOf(i*4-2)).divide(BigInteger.valueOf(i+1));

		}

	}

	public static void main(String[] args) {

		// TODO 自动生成的方法存根

		ini();

		Scanner Reader = new Scanner(System.in);

		int x;

		while(Reader.hasNext())

		{

			x = Reader.nextInt();

			System.out.println(F[x]);

		}

	}

}