Problem: The configuration of three circles packed inside a triangle such that each circle is tangent to the other two circles and to two of the edges of the triangle has been studied by many mathematicians for more than two centuries. Existence and uniqueness of such circles for an arbitrary triangle are easy to prove. Many methods of numerical calculation or geometric construction of such circles from an arbitrarily given triangle have been discovered. Today, such circles are called the Malfatti circles.

Figure 7 illustrates an example. The Malfatti circles of the triangle with the vertices (20, 80), (-40, -20) and (120, -20) are approximately

* the circle with the center (24.281677, 45.219486) and the radius 21.565935,
* the circle with the center (3.110950, 4.409005) and the radius 24.409005, and
* the circle with the center (54.556724, 7.107493) and the radius 27.107493.



Figure 8 illustrates another example. The Malfatti circles of the triangle with the vertices (20, -20), (120, -20) and (-40, 80) are approximately

* the circle with the center (25.629089, −10.057956) and the radius 9.942044,
* the circle with the center (53.225883, −0.849435) and the radius 19.150565, and
* the circle with the center (19.701191, 19.203466) and the radius 19.913790.



Your mission is to write a program to calculate the radii of the Malfatti circles of the given triangles.

<image>



Input

The input is a sequence of datasets. A dataset is a line containing six integers x1, y1 , x2 , y2, x3 and y3 in this order, separated by a space. The coordinates of the vertices of the given triangle are (x1 , y1 ), (x2 , y2 ) and (x3 , y3 ), respectively. You can assume that the vertices form a triangle counterclockwise. You can also assume that the following two conditions hold.

* All of the coordinate values are greater than −1000 and less than 1000.
* None of the Malfatti circles of the triangle has a radius less than 0.1.



The end of the input is indicated by a line containing six zeros separated by a space.

Output

For each input dataset, three decimal fractions r1 , r2 and r3 should be printed in a line in this order separated by a space. The radii of the Malfatti circles nearest to the vertices with the coordinates (x1 , y1 ), (x2 , y2 ) and (x3 , y3 ) should be r1 , r2 and r3 , respectively.

None of the output values may have an error greater than 0.0001. No extra character should appear in the output.

Example

Input

20 80 -40 -20 120 -20
20 -20 120 -20 -40 80
0 0 1 0 0 1
0 0 999 1 -999 1
897 -916 847 -972 890 -925
999 999 -999 -998 -998 -999
-999 -999 999 -999 0 731
-999 -999 999 -464 -464 999
979 -436 -955 -337 157 -439
0 0 0 0 0 0


Output

21.565935 24.409005 27.107493
9.942044 19.150565 19.913790
0.148847 0.207107 0.207107
0.125125 0.499750 0.499750
0.373458 0.383897 0.100456
0.706768 0.353509 0.353509
365.638023 365.638023 365.601038
378.524085 378.605339 378.605339
21.895803 22.052921 5.895714

Solution (in CPP):

Solution:
#include <vector>
#include <iostream>
#include <utility>
#include <algorithm>
#include <string>
#include <deque>
#include <queue>
#include <tuple>
#include <queue>
#include <stack>
#include <functional>
#include <cmath>
#include <iomanip>
#include <map>
#include <set>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <complex>
#include <iterator>
#include <array>
#include <memory>
#include <random>
//cin.sync_with_stdio(false);
//streambuf
using namespace std;
typedef long long ll;
typedef double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
using vi = vector<int>;
using vll = vector<ll>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using ti3 = tuple<int, int, int>;
using vti3 = vector<ti3>;
template<class T, int s>using va = vector<array<T, s>>;
template<class T, class T2> using umap = unordered_map<T, T2>;
template<class T> using uset = unordered_set<T>;
template<class T, class S> void cmin(T &a, const S &b) { if (a > b)a = b; }
template<class T, class S> void cmax(T &a, const S &b) { if (a < b)a = b; }
#define ALL(a) a.begin(),a.end()
#define rep(i,a) for(int i=0;i<a;i++)
#define rep1(i,a) for(int i=1;i<=a;i++)
#define rrep(i,a) for(int i=(a)-1;i>=0;i--)
#define rrep1(i,a) for(int i=a;i;i--)
#define repi(i,a,b) for(int i=a;i<b;i++);
const ll mod = 1000000007;
template<class T>using heap = priority_queue<T, vector<T>, greater<T>>;
template<class T>using pque = priority_queue<T, vector<T>, function<T(T, T)>>;
template <class T>
inline void hash_combine(size_t & seed, const T & v) {
	hash<T> hasher;
	seed ^= hasher(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}
namespace std {
	template<typename S, typename T> struct hash<pair<S, T>> {
		inline size_t operator()(const pair<S, T> & v) const {
			size_t seed = 0;
			hash_combine(seed, v.first);
			hash_combine(seed, v.second);
			return seed;
		}
	};
	// Recursive template code derived from Matthieu M.
	template <class Tuple, size_t Index = std::tuple_size<Tuple>::value - 1>
	struct HashValueImpl {
		static void apply(size_t& seed, Tuple const& tuple) {
			HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
			hash_combine(seed, std::get<Index>(tuple));
		}
	};
	template <class Tuple>
	struct HashValueImpl<Tuple, 0> {
		static void apply(size_t& seed, Tuple const& tuple) {
			hash_combine(seed, std::get<0>(tuple));
		}
	};
	template <typename ... TT>
	struct hash<std::tuple<TT...>> {
		size_t operator()(std::tuple<TT...> const& tt) const {
			size_t seed = 0;
			HashValueImpl<std::tuple<TT...> >::apply(seed, tt);
			return seed;
		}
	};
}
template<class T>int id(vector<T> &a, T b) {
	return lower_bound(ALL(a), b) - a.begin();
}
ll pow(ll base, ll i, ll mod) {
	ll a = 1;
	while (i) {
		if (i & 1) {
			a *= base;
			a %= mod;
		}
		base *= base;
		base %= mod;
		i /= 2;
	}
	return a;
}
ll gcd(ll a, ll b) {
	while (b) {
		ll c = a%b;
		a = b;
		b = c;
	}
	return a;
}
ll lcm(ll a, ll b) {
	return a / gcd(a, b)*b;
}
int popcnt(unsigned long long a) {
	a = (a & 0x5555555555555555) + (a >> 1 & 0x5555555555555555);
	a = (a & 0x3333333333333333) + (a >> 2 & 0x3333333333333333);
	a = (a & 0x0f0f0f0f0f0f0f0f) + (a >> 4 & 0x0f0f0f0f0f0f0f0f);
	a = (a & 0x00ff00ff00ff00ff) + (a >> 8 & 0x00ff00ff00ff00ff);
	a = (a & 0x0000ffff0000ffff) + (a >> 16 & 0x0000ffff0000ffff);
	return (a & 0xffffffff) + (a >> 32);
}
class unionfind {
	vector<int> par, rank, size_;//????????§??????????????¢???????????????????????????rank???????????????size?????????
public:
	unionfind(int n) :par(n), rank(n), size_(n, 1) {
		iota(ALL(par), 0);
	}
	int find(int x) {
		if (par[x] == x)return x;
		return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y)return;
		if (rank[x] < rank[y])swap(x, y);
		par[y] = x;
		size_[x] += size_[y];
		if (rank[x] == rank[y])rank[x]++;
	}
	bool same(int x, int y) {
		return find(x) == find(y);
	}
	int size(int x) {
		return size_[find(x)];
	}
};
typedef complex<ld> P;
typedef vector<P> VP;
const ld eps = 1e-11, pi = acos(-1.0);

ld dot(P a, P b) { return real(conj(a) * b); }
ld cross(P a, P b) { return imag(conj(a) * b); }

namespace std {
	bool operator<(const P &a, const P &b) {
		return abs(a.real() - b.real()) < eps ? a.imag() < b.imag() : a.real() < b.real();
	}
}

struct L { P a, b; };//line->l,segment->s
struct C { P p; ld r; };

int ccw(P a, P b, P c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // counter clockwise
	if (cross(b, c) < -eps) return -1; // clockwise
	if (dot(b, c) < 0) return 2;       // c--a--b on line
	if (norm(b) < norm(c)) return -2;  // a--b--c on line
	return 0;                          // a--c--b on line
}

bool isis_ll(L l, L m) {//is intersect
	return abs(cross(l.b - l.a, m.b - m.a)) > eps;
}

bool isis_ls(L l, L s) {
	ld a = cross(l.b - l.a, s.a - l.a);
	ld b = cross(l.b - l.a, s.b - l.a);
	return (a * b < eps);
}

bool isis_lp(L l, P p) {
	return abs(cross(l.b - p, l.a - p)) < eps;
}

bool isis_ss(L s, L t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

P is_ll(L s, L t) { //intersect
	P sv = s.b - s.a, tv = t.b - t.a;
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

bool isis_sp(L s, P p) {
	return abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps;
}

P proj(L l, P p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

ld dist_lp(L l, P p) {
	return abs(p - proj(l, p));
}

ld dist_ll(L l, L m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(L l, L s) {
	if (isis_ls(l, s)) return 0;
	return min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(L s, P p) {
	P r = proj(s, p);
	if (isis_sp(s, r)) return abs(r - p);
	return min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(L s, L t) {
	if (isis_ss(s, t)) return 0;
	ld a = min(dist_sp(s, t.a), dist_sp(t, s.a));
	ld b = min(dist_sp(s, t.b), dist_sp(t, s.b));
	return min(a, b);
}

VP is_cc(C c1, C c2) {
	VP res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	P diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * P(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * P(rc, -rs));
	return res;
}

bool isis_vc(vector<C> vc) {
	VP crs;
	int n = vc.size();
	rep(i, n)rep(j, i)
		for (P p : is_cc(vc[i], vc[j]))
			crs.push_back(p);
	rep(i, n)
		crs.push_back(vc[i].p);
	for (P p : crs) {
		bool valid = true;
		rep(i, n)
			if (abs(p - vc[i].p)>vc[i].r + eps)
				valid = false;
		if (valid) return true;
	}
	return false;
}

VP is_lc(C c, L l) {
	VP res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		P nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

VP is_sc(C c, L l) {
	VP v = is_lc(c, l), res;
	for (P p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

vector<L> tangent_cp(C c, P p) {//????????\????
	vector<L> ret;
	P v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (std::isnan(l)) { return ret; }
	P v1 = v * P(l / d, c.r / d);
	P v2 = v * P(l / d, -c.r / d);
	ret.push_back(L{ p, p + v1 });
	if (l < eps) return ret;
	ret.push_back(L{ p, p + v2 });
	return ret;
}

vector<L> tangent_cc(C c1, C c2) {
	vector<L> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		P center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		P out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<L> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		P v = c2.p - c1.p;
		v /= abs(v);
		P q1 = c1.p + v * P(0, 1) * c1.r;
		P q2 = c1.p + v * P(0, -1) * c1.r;
		ret.push_back(L{ q1, q1 + v });
		ret.push_back(L{ q2, q2 + v });
	}
	return ret;
}

ld area(const VP &p) {//??¢?????
	ld res = 0;
	int n = p.size();
	rep(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

bool is_polygon(L l, VP &g) {
	int n = g.size();
	for (int i = 0; i < n; i++) {
		P a = g[i];
		P b = g[(i + 1) % n];
		if (isis_ss(l, L{ a, b })) return true;
	}
	return false;
}

int is_in_Polygon(const VP &g, P p) {
	bool in = false;
	int n = g.size();
	for (int i = 0; i < n; i++) {
		P a = g[i] - p, b = g[(i + 1) % n] - p;
		if (imag(a) > imag(b)) swap(a, b);
		if (imag(a) <= 0 && 0 < imag(b))
			if (cross(a, b) < 0) in = !in;
		if (abs(cross(a, b)) < eps && dot(a, b) < eps) return 0; // on
	}
	if (in) return 1; // in
	return -1; // out
}

VP ConvexHull(VP ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	VP ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

VP ConvexCut(const VP &ps, L l) {
	VP Q;
	for (int i = 0; i < (int)ps.size(); i++) {
		P A = ps[i], B = ps[(i + 1) % ps.size()];
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0)
			Q.push_back(is_ll(L{ A, B }, l));
	}
	return Q;
}
//end of lib
//template<class S=void,int ptr_num, class T = char>class trie {
//	umap<T, trie<S, ptr_num, T> next;
//public:
//	S key;
//	trie<S, ptr_num, T>* ptr[ptr_num] = {};
//	trie(S &&data) :key(data) {}
//	trie(const S &data) :key(data) {}
//	void add(T x,S data) {
//		if (!next.find(x))next.insert(x, data);
//	}
//	trie& operator[](T x) {
//		return next[x];
//	}
//	bool find(T x) {
//		retun next.find(x);
//	}
//};
//template<class T=char>class AhoCorasick {
//	trie<pair<bool,int>, 2, T> tree;
//	AhoCorasick(vector<string> p) {
//		int num = 0;
//		vector<decltype(&tree)> que(p.size(),&tree);
//		for (int i = 0;; i++) {
//			bool end = 1;
//			int i = 0;
//			for (auto a : p) {
//				if (i >= a.size())break;
//				end = ;0
//				que[i] = (*que[i])[a[i]];
//				i++;
//			}
//			if (end)break;
//		}
//	}
//};
#include <fstream>
#include <sstream>
class svg {
	ofstream f;
	stringstream s;
	double x1 = 1e9, y1 = 1e9, x2 = -1e9, y2 = -1e9;
public:
	svg(string path) :f(path, ios::trunc) {
	}
	~svg(){
		f << "<?xml version=\"1.0\" standalone=\"no\"?><svg viewBox='"<<x1*1.1-x2*0.1<<" "<<y1*1.1-y2*0.1<<" "<<(x2-x1)*1.2<<" "<<(y2-y1)*1.2<<"' xmlns = \"http://www.w3.org/2000/svg\" xmlns:xlink = \"http://www.w3.org/1999/xlink\" >\n";
		f << s.str();
		f << "</svg>";
	}
	void circle(C c) {
		s << fixed << "<circle cx = \"" << c.p.real() << "\" cy = \"" << c.p.imag() << "\" r = \"" << c.r << "\" stroke=\"black\" stroke-width=\"0.01\" fill = \"none\"/>\n";
		cmin(x1, c.p.real() - c.r);
		cmin(y1, c.p.imag() - c.r);
		cmax(x2, c.p.real() + c.r);
		cmax(y2, c.p.imag() + c.r);
	}
	void line(L l) {
		s << fixed << "<line x1=\"" << l.a.real() << "\" y1=\"" << l.a.imag() << "\" x2=\"" << l.b.real() << "\" y2=\"" << l.b.imag() << "\" stroke=\"black\" stroke-width=\"0.01\"/>\n";
		cmin(x1, l.a.real());
		cmin(y1, l.a.imag());
		cmax(x2, l.a.real());
		cmax(y2, l.a.imag());
		cmin(x1, l.b.real());
		cmin(y1, l.b.imag());
		cmax(x2, l.b.real());
		cmax(y2, l.b.imag());
	}
};
int main() {
	VP p(3);
	for (;;) {
		rep(i, 3) {
			int x, y;
			cin >> x >> y;
			p[i] = { (double)x,(double)y };
		}
		if (p[0] == p[1])break;
		P up1 = (p[1] * abs(p[2] - p[0]) + p[2] * abs(p[1] - p[0])) / (abs(p[2] - p[0]) + abs(p[1] - p[0]));
		P dn1 = p[0];
		P up2, up3;
		double r1, r2, r3;
		rep(i, 50) {
			P m1 = (up1 + dn1) * 0.5;
			r1 = dist_lp({ p[0],p[1] }, m1);
			up2 = (p[0] * abs(p[2] - p[1]) + p[2] * abs(p[0] - p[1])) / (abs(p[2] - p[1]) + abs(p[0] - p[1]));
			up3 = (p[0] * abs(p[2] - p[1]) + p[1] * abs(p[0] - p[2])) / (abs(p[2] - p[1]) + abs(p[0] - p[2]));
			P dn2 = p[1], dn3 = p[2];
			rep(j, 50) {
				P m2 = (up2 + dn2)*0.5, m3 = (up3 + dn3)*0.5;
				r2 = dist_lp({ p[0],p[1] }, m2);
				r3 = dist_lp({ p[0],p[2] }, m3);
				if (!isis_ls({ p[0],up1 }, { p[1],m2 }) && dist_lp({ p[0],p[2] }, m2) > r2 && abs(m1 - m2) > r1 + r2)dn2 = m2;
				else up2 = m2;
				if (!isis_ls({ p[0],up1 }, { p[2],m3 }) && dist_lp({ p[0],p[1] }, m3) > r3 && abs(m3 - m1) > r1 + r3)dn3 = m3;
				else up3 = m3;
			}
			if (dist_lp({ p[1],p[2] }, m1) > r1&&abs(up2 - up3) < r2 + r3)dn1 = m1;
			else up1 = m1;
		}
		cout << fixed << setprecision(10) << r1 << " " << r2 << " " << r3 << endl;
		svg s("out.svg");
		rep(i, 3)s.line({ p[i],p[(i + 1) % 3] });
		s.circle({ up1,r1 });
		s.circle({ up2,r2 });
		s.circle({ up3,r3 });
	}
}