Problem: For given two circles $c1$ and $c2$, print the coordinates of the cross points of them.

Constraints

* The given circle have at least one cross point and have different center coordinates.
* $-10,000 \leq c1x, c1y, c2x, c2y \leq 10,000$
* $1 \leq c1r, c2r \leq 10,000$

Input

The input is given in the following format.

$c1x\; c1y\; c1r$
$c2x\; c2y\; c2r$


$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle. $c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle. All input values are given in integers.

Output

Print the coordinates ($x1$, $y1$) and ($x2$, $y2$) of the cross points $p1$ and $p2$ respectively in the following rules.

* If there is one cross point, print two coordinates with the same values.
* Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.



The output values should be in a decimal fraction with an error less than 0.000001.

Examples

Input

0 0 2
2 0 2


Output

1.00000000 -1.73205080 1.00000000 1.73205080


Input

0 0 2
0 3 1


Output

0.00000000 2.00000000 0.00000000 2.00000000

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60

typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-9, pi = acos(-1.0);
namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}
Point input_point() { ld x, y; cin >> x >> y; return Point(x, y); } // ????????\???
bool eq(ld a, ld b) { return (abs(a - b) < eps); } // ????????????????????????
ld dot(Point a, Point b) { return real(conj(a) * b); } // ??????
ld cross(Point a, Point b) { return imag(conj(a) * b); } // ??????

														 // ??´????????????
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
	Point operator[](const int _num) {
		if (_num == 0)return a;
		else if (_num == 1)return b;
		else assert(false);
	}
};

// ????????????
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// ??????????¶?
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,c??????????¨???¨?????????????????¶
	if (cross(b, c) < -eps) return -1; // a,b,c???????¨???¨?????????????????¶
	if (dot(b, c) < 0) return 2;       // c,a,b???????????´???????????¶
	if (norm(b) < norm(c)) return -2;  // a,b,c???????????´???????????¶
	return 0;                          // a,c,b???????????´???????????¶
}

/* ???????????? */
// ??´?????¨??´??????????????????
bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); }
// ??´?????¨?????????????????????
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}
// ????????¨?????????????????????
bool isis_ss(Line s, Line 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;
}
// ????????´????????????
bool isis_lp(Line l, Point p) { return (abs(cross(l.b - p, l.a - p)) < eps); }
// ?????????????????????
bool isis_sp(Line s, Point p) { return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps); }

/* ?????¢ */
// ??´?????¨??´????????????
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// ??´?????¨???????????¢
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// ??´?????¨??´???????????¢
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// ??´?????¨??????????????¢
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// ????????¨???????????¢
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// ????????¨??????????????¢
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


// ?????¨????????????
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> 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);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

int main(void) {
	cin.tie(0); ios::sync_with_stdio(false);
	Circle c1,c2;
	c1.p = input_point(); cin >> c1.r;
	c2.p = input_point(); cin >> c2.r;

	auto ps = is_cc(c1, c2);
	sort(ps.begin(), ps.end());
	cout << fixed << setprecision(10);
	for (int i = 0; i < (int)ps.size();i++) {
		cout << ps[i].real() << " " << ps[i].imag();
		if (i == 0 && (int)ps.size() == 1) {
			cout << " " << ps[i].real() << " " << ps[i].imag() << endl;
			break;
		}
		if (i == 0) cout << " ";
		else cout << endl;
	}
	return 0;
}