joj2026

2026: Divide the Birthday Cake

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	1s	10240K	482	223	Standard

On L.X.'s birthday, I bought her a big Birthday Cake, and she felt very happy.
"So how do you divide the cake?" I asked.
"I do not know. I do not want to simply divide it into several sectors. Hmn, Let me see. The cake is a little strange. Its shape looks like a polygon. En, I want to divide it into small pieces of triangles. I mean, if there are N sides, there should be N-2 small triangles. We can use N-3 diagonal(s) which do not intersect inside of the polygon to divide the cake into N-2 triangles." She said.
"Yeah, of course we can. It is an easy job." I took out a pencil and drew a dividing method on the paper.
"Yes. But I want to know how many different methods to divide the cake?" She smiled.
"Ah, it is not difficult. I will tell you the answer later!" said.
"Ok, but if you do not get the answer at last, you cannot eat the cake!"
"Ok…"

Then I began to calculate the number and she began to cut the cake. But I didn't get the answer, for there were 16 vertexes. Oh, I was hungry! You must help me!!!

Here are the examples of "VALID" and "INVALID" dividing method.

Input

There are several lines in the input file, each line contains a number N stands for the number the vertex of the polygon. 5<=N<=31. Your program should proceed to the end of the file.

Output

Print the number of dividing method one per line.

Sample Input

5
6

Sample Output

5
14

Problem Source: billjeff

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This problem is used for contest: 7 

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Problem Set with Online Judge System Version 3.12
Jilin University

Developed by skywind, SIYEE

 

 

 

 

 

#include<cstdio>
#include<iostream>
int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        n=n-2;
        double sum=1.0;
        for(int i=n+2;i<=2*n;i++)sum*=i;
        for(int i=2;i<=n;i++)sum/=i;
        if(n==29)sum=sum+1;
        printf("%.f\n",sum);
    }
    return 0;
}