Problem:
Score : 500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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}.

Sample Input 1

0 0
1 1
2 0

Sample Output 1

0.292893218813

Sample Input 2

3 1
1 5
4 9

Sample Output 2

0.889055514217

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#include<math.h>
#include<iomanip>
#include<set>
#include<numeric>
#include<cstring>
#include<cstdio>
#include<functional>
#include<bitset>
#include<limits.h>
#include<cassert>
#include<iterator>
#include<complex>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<time.h>
#include<random>
#include<array>
using namespace std;
using ll = long long;
#define rep(i, a, b) for(int i = a; i < b; i++)
#define rrep(i, a, b) for(int i = b - 1; i >= a; i--)
#define ALL(a) a.begin(), a.end()
using pii = pair<int,int>;
using piii = pair<pii,int>;
using pll = pair<long long, long long>;
using plll = pair<pll, long long>;
// #pragma GCC optimize("Ofast")
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define pb push_back
#define mp make_pair
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define isSquare(x) (sqrt(x)*sqrt(x) == x)
template<class T>inline bool chmax(T &a, const T &b) {if(a<b){a = b; return 1;} return 0; };
template<class T>inline bool chmin(T &a, const T &b) {if(a>b){a = b; return 1;} return 0; };
inline void in(void){return;}
template <typename First, typename... Rest> void in(First& first, Rest&... rest){cin >> first;in(rest...);return;}
inline void out(void){cout << "\n";return;}
template <typename First, typename... Rest> void out(First first, Rest... rest){cout << first << " ";out(rest...);return;}
const double EPS = 1e-9;
const int mod = 1e9 + 7;
const int INF = 1e9;
const long long INFLL = 1e18;
void iosetup() {
    cin.tie(nullptr);ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
}
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
    os << p.first << " " << p.second;
    return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
    is >> p.first >> p.second;
    return is;
}
template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
    for(int i = 0; i < (int) v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
    for(T &in : v) is >> in;
    return is;
}
template<class T> vector<T> make_vec(size_t a) {return vector<T>(a); }
template<class T, class... Ts> auto make_vec(size_t a, Ts... ts){
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S, T>& t){return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S, T>& t){return pair<S,T>(s.first-t.first, s.second-t.second);}
template<class S, class T> pair<S,T> operator*(const pair<S,T> &s, const S& t){return pair<S,T>(s.first*t, s.second*t);}
template <typename T> void Exit(T first){cout << first << endl;exit(0); };
template< int mod > struct ModInt {
    unsigned x; ModInt() : x(0) {}
    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
    ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
    ModInt &operator*=(const ModInt &p) {x = (int) (1LL * x * p.x % mod);return *this;}
    ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); }return ModInt(u);}
    ModInt pow(int64_t n) const {ModInt ret(1), mul(x); while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}
    friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x;}
    friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); }
    static int get_mod() { return mod; }
}; using modint = ModInt< mod >;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
const pii dxy[4] = {pii(1,0), pii(0, 1), pii(-1, 0), pii(0, -1)};
const int calender[13] = {0, 31,28,31,30,31,30,31,31,30,31,30,31};
const int ucalender[13] = {0, 31,29,31,30,31,30,31,31,30,31,30,31};
bool range(int a, int b, int x){if(a <= x and x < b)return true;else return false;}
bool range(int a, int b, int c, int d, pii p){if(a <= p.first and p.first < b and c <= p.second and p.second < d) return true;else return false;}


int main(){
    iosetup();
    vector<complex<double>> P;
    rep(i, 0, 3){
        double x, y; cin >> x >> y;
        P.emplace_back(x, y);
    }
    vector<double> es;
    rep(i, 0, 3){
        complex<double> e = P[i] - P[(i+1)%3];
        es.emplace_back(abs(e));
    }
    sort(ALL(es));
    double s = accumulate(ALL(es), 0.0) / 2;
    double S = sqrt(s * (s - es[0]) * (s - es[1]) * (s - es[2]));
    double r = S / accumulate(ALL(es), 0.0) * 2;
    double M = *max_element(ALL(es));
    cout << M / (M / r + 2) << endl;

    return 0;
}