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<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll MOD = (1e+9)+7;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-11;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
typedef pair<ld, ld> LDP;
ld a, b, c;
ld rad() {
	ld res = 2;
	ld t1 = sqrt(((ld)2 * a*b + a * a + b * b - c * c) / ((ld)2 * a*b - a * a - b * b + c * c));
	swap(b, c);
	ld t2 = sqrt(((ld)2 * a*b + a * a + b * b - c * c) / ((ld)2 * a*b - a * a - b * b + c * c));
	res += t1 + t2;
	return a / res;
}
int main() {
	ld x[3], y[3];
	rep(i, 3) {
		cin >> x[i] >> y[i];
	}
	a = sqrt(pow(x[1] - x[0], 2) + pow(y[1] - y[0], 2));
	b = sqrt(pow(x[2] - x[1], 2) + pow(y[2] - y[1], 2));
	c = sqrt(pow(x[0] - x[2], 2) + pow(y[0] - y[2], 2));
	ld out = -1;
	out = max(out, rad());
	swap(a, b);
	out = max(out, rad());
	swap(a, b);
	out = max(out, rad());
	cout << fixed << setprecision(10) << out << endl;
	return 0;
}