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>
#include<unordered_set>
#include<unordered_map>
using namespace std;
#define int long long
#define REP(i,m,n) for(int i=(m);i<(n);i++)
#define rep(i,n) REP(i,0,n)
#define pb push_back
#define all(a) a.begin(),a.end()
#define rall(c) (c).rbegin(),(c).rend()
#define mp make_pair
#define endl '\n'
typedef long long ll;
typedef pair<ll,ll> pll;
typedef long double ld;
const ll inf=1e9+7;
const ll mod=998244353;
double length(double a,double b,double c,double d){
    return sqrt((a-c)*(a-c)+(b-d)*(b-d));
}
double hero(double a,double b,double c){
    double s=(a+b+c)/2.0;
    return sqrt(s*(s-a)*(s-b)*(s-c));
}
double center_of_incircle(double a,double b,double c){
    double s=(a+b+c)/2.0;
    return hero(a,b,c)/s;
}
signed main(){
    double x1,y1,x2,y2,x3,y3;
    cin>>x1>>y1>>x2>>y2>>x3>>y3;
    double r1,r2,r3;
    double l1=length(x1,y1,x2,y2);
    double l2=length(x2,y2,x3,y3);
    double l3=length(x3,y3,x1,y1);
    double r=center_of_incircle(l1,l2,l3);
    r1=l1*r/(2.0*r+l1);
    r2=l2*r/(2.0*r+l2);
    r3=l3*r/(2.0*r+l3);
    cout<<fixed<<setprecision(10)<<max(r1,max(r2,r3))<<endl;
}