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CWAY - Counting paths in a complete graph

A complete graph of N verticles is a graph in which there is an edge between every pair of nodes.

Your task is to count the number of paths between any pair of nodes in the graph. Note that a path cannot visit a vertex more than once.

Input

A single integer N that is the number of verticles in the graph (2 ≤ N ≤ 1000).

Output

A single integer that is the number of paths between any two nodes in the graph.

Example

Input
4

Output
5

Description
For example, there are 5 paths between 1 and 2:
1-2
1-3-2
1-3-4-2
1-4-2
1-4-3-2

Added by:Lê Đôn Khuê
Date:2008-06-28
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 SCM qobi VB.NET
Resource:VNOI Marathon '08 - Round 3/DivB
Problem Setter: Lê Đôn Khuê

hide comments
2012-08-08 13:24:30 Albert
Not more than 10000
2010-07-23 22:02:42 cegprakash
i understood the problem
but confusing how to think of an algorithm for this
can anyone help??

Last edit: 2010-07-23 22:12:40
2010-07-12 15:11:10 Anoop Narang
i submitted solution .... My result is 0 , but it got accepted . What does it means??
2009-06-26 08:13:21 Dunno
Hey
How many digits when n equal to 1000
HELP ????
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