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 nplates.
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:
题意：给你一个大圆（半径为R）问可不可以在大圆内放置n个小圆（半径为r），要求小圆与大圆相切
解题思路：用R和r求出图中角的角度（arcsin），比较n个角与PI的大小即可。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
int main()
{
int n;
double R, r;
double eps=1e-10;
double PI=acos(-1);
while(cin>>n>>R>>r)
{
if(n==1)
{
if(R>=r)
puts("YES");
else
puts("NO");
continue;
}
double tmp=asin(r/(R-r));
if(PI/tmp-n>-eps)
puts("YES");
else
puts("NO");
}
return 0;
}