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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

Được gửi lên bởi:Lê Đôn Khuê
Ngày:2008-06-28
Thời gian chạy:1s
Giới hạn mã nguồn:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Ngôn ngữ cho phép:ADA95 ASM32 BASH BF C CSHARP CPP C99 CLPS LISP sbcl LISP clisp D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PAS-GPC PAS-FPC PERL PHP PIKE PRLG-swi PYTHON RUBY SCM guile SCM qobi ST TEXT WHITESPACE
Nguồn bài:VNOI Marathon '08 - Round 3/DivB
Problem Setter: Lê Đôn Khuê

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