B. The Monster and the Squirrel

B. The Monster and the Squirrel

Ari the monster always wakes up very early with the first ray of the

sun and the first thing she does is feeding her squirrel.

Ari draws a regular convex polygon on the floor and numbers it’s

vertices 1, 2, …, n in clockwise order. Then starting from the

vertex 1 she draws a ray in the direction of each other vertex. The

ray stops when it reaches a vertex or intersects with another ray

drawn before. Ari repeats this process for vertex 2, 3, …, n (in

this particular order). And then she puts a walnut in each region

inside the polygon.



Ada the squirrel wants to collect all the walnuts, but she is not

allowed to step on the lines drawn by Ari. That means Ada have to

perform a small jump if she wants to go from one region to another.

Ada can jump from one region P to another region Q if and only if P

and Q share a side or a corner.

Assuming that Ada starts from outside of the picture, what is the

minimum number of jumps she has to perform in order to collect all the

walnuts?

Input The first and only line of the input contains a single integer n

(3 ≤ n ≤ 54321) - the number of vertices of the regular polygon drawn

by Ari.

Output Print the minimum number of jumps Ada should make to collect

all the walnuts. Note, that she doesn’t need to leave the polygon

after.

Examples
Input
5
Output
9
Input
3
Output
1

Note One of the possible solutions for the first sample is shown on

the picture above.

题解如下

解题说明：题目的意思是每个点依次和其他点连线，如果这条直线连接的过程中，和另外一条直线相交的话，就会被截断。然后问你，正n边形，被截成了多少块。此题可以考虑用找规律的方法，先从边数少的n边型开始，计算数目，最后发现规律，值为(n-2)*(n-2)。网上有详细证明过程：

After drawing the rays from the first vertex (n - 2) triangles are formed. The subsequent rays will generate independently sub-regions in these triangles. Let’s analyse the triangle determined by vertices 1, i, i + 1, after drawing the rays from vertex i and (i + 1) the triangle will be divided into (n - i) + (i - 2) = n - 2 regions. Therefore the total number of convex regions is (n - 2)2



If the squirrel starts from the region that have 1 as a vertex, then she can go through each region of triangle (1, i, i + 1) once. That implies that the squirrel can collect all the walnuts in (n - 2)2 jumps.

思路如下

#include<iostream>
#include<algorithm>
using namespace std;

int main()
{
	long long n;
	cin>>n;
	cout<<(n-2)*(n-2)<<endl;
	return 0;
}