Problem: Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).

He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.

Constraints

* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.

Input

The input is given from Standard Input in the following format:


x_1 y_1
x_2 y_2
x_3 y_3


Output

Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.

Examples

Input

0 0
1 1
2 0


Output

0.292893218813


Input

3 1
1 5
4 9


Output

0.889055514217

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
using namespace std;
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL;
typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll;
template<typename T, typename U> static void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> static void amax(T &x, U y) { if(x < y) x = y; }

int main() {
	int x1; int y1;
	while(~scanf("%d%d", &x1, &y1)) {
		int x2; int y2;
		scanf("%d%d", &x2, &y2);
		int x3; int y3;
		scanf("%d%d", &x3, &y3);
		double a = hypot(x1 - x2, y1 - y2);
		double b = hypot(x2 - x3, y2 - y3);
		double c = hypot(x3 - x1, y3 - y1);
		double s = (a + b + c) / 2;
		double r = sqrt((s - a) * (s - b) * (s - c) / s);
		double lo = 0, up = r;
		rep(k, 64) {
			double x = (lo + up) / 2;
			if((1 - x / r) * max({ a, b, c }) >= 2 * x)
				lo = x;
			else
				up = x;
		}
		printf("%.10f\n", (lo + up) / 2);
	}
	return 0;
}