ACM: CodeForces 140A New Year Table-数学几何

CodeForces 140A New Year Table

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u 

Description

Gerald is setting the New Year table. The table has the form of a circle; its radius equals R. Gerald invited many guests and is concerned whether the table has enough space for plates for all those guests. Consider all plates to be round and have the same radii that equal r. Each plate must be completely inside the table and must touch the edge of the table. Of course, the plates must not intersect, but they can touch each other. Help Gerald determine whether the table is large enough for n plates.

Input

The first line contains three integers n, R and r (1 ≤ n ≤ 100, 1 ≤ r, R ≤ 1000) — the number of plates, the radius of the table and the plates' radius.

Output

Print "YES" (without the quotes) if it is possible to place n plates on the table by the rules given above. If it is impossible, print "NO".

Remember, that each plate must touch the edge of the table.

Sample Input

Input

4 10 4

Output

YES

Input

5 10 4

Output

NO

Input

1 10 10

Output

YES

Hint

The possible arrangement of the plates for the first sample is:

/*/
很有趣的几何题。

题意：

给出要切的小圆板个数，给出大圆板的半径，给出小圆板的半径。

小圆板沿着大圆板的边去切。问是否能切出要求个数的小圆板。





AC代码：

/*/ 

#include"map"
#include"cmath"
#include"string"
#include"cstdio"
#include"vector"
#include"cstring"
#include"iostream"
#include"algorithm"
using namespace std;
typedef long long LL;
#define memset(x,y) memset(x,y,sizeof(x))

double pi=acos(-1);

int main() {
	int n;
	double r,R;
	while(~scanf("%d%lf%lf",&n,&R,&r)) {
		double a=asin(r/(R-r));
		if(R<2*r&&n!=1)puts("NO");
		else if(R<r)puts("NO");
		else if(pi-a*n<-1e-12)puts("NO");
		else puts("YES");
	}
	return 0;
}