codeforces 140 A. New Year Table

A. New Year Table

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Examples

input

4 10 4

output

YES

input

5 10 4

output

NO

input

1 10 10

output

YES

Note

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

思路：小圆的半径一定<=大圆的半径，当n==1时，是R/2<r<=R的情况；当n==2时，是r=R/2的情况；当n>=3时，求每个圆可能占有的角度，符合条件即可

code

#include <iostream>#include<cstdio>#include<cmath>#define PI acos(-1.0)#define esp 1e-10using namespace std;int main(){    double n,R,r;    while(~scanf("%lf%lf%lf",&n,&R,&r))    {        if(r<=R)        {            if(n==1)                printf("YES\n");            else{                if(r>R/2)                    printf("NO\n");                else if(r==R/2&&n==2)                    printf("YES\n");                else if(asin(r/(R-r))*n-PI<esp)                     //浮点型数在计算过程中会有一定的误差                    printf("YES\n");                else                    printf("NO\n");            }        }        else        {            printf("NO\n");        }    }    return 0;}