An undirected graph is a set V of vertices and a set of edges.An undirected graph is connected if and only if for every pair (u,v) of vertices,u is reachable from v. You are to write a program that tries to calculate the number of different connected undirected graph with n vertices.
For example,there are 4 different connected undirected graphs with 3 vertices.
输入描述:
The input contains several test cases. Each test case contains an integer n, denoting the number of vertices. You may assume that . The last test case is followed by one zero.
输出描述:
For each test case output the answer on a single line.