Problem: It's a beautiful April day and Wallace is playing football with his friends. But his friends do not know that Wallace actually stayed home with Gromit and sent them his robotic self instead. Robo-Wallace has several advantages over the other guys. For example, he can hit the ball directly to the specified point. And yet, the notion of a giveaway is foreign to him. The combination of these features makes the Robo-Wallace the perfect footballer — as soon as the ball gets to him, he can just aim and hit the goal. He followed this tactics in the first half of the match, but he hit the goal rarely. The opposing team has a very good goalkeeper who catches most of the balls that fly directly into the goal. But Robo-Wallace is a quick thinker, he realized that he can cheat the goalkeeper. After all, they are playing in a football box with solid walls. Robo-Wallace can kick the ball to the other side, then the goalkeeper will not try to catch the ball. Then, if the ball bounces off the wall and flies into the goal, the goal will at last be scored.

Your task is to help Robo-Wallace to detect a spot on the wall of the football box, to which the robot should kick the ball, so that the ball bounces once and only once off this wall and goes straight to the goal. In the first half of the match Robo-Wallace got a ball in the head and was severely hit. As a result, some of the schemes have been damaged. Because of the damage, Robo-Wallace can only aim to his right wall (Robo-Wallace is standing with his face to the opposing team's goal).

The football box is rectangular. Let's introduce a two-dimensional coordinate system so that point (0, 0) lies in the lower left corner of the field, if you look at the box above. Robo-Wallace is playing for the team, whose goal is to the right. It is an improvised football field, so the gate of Robo-Wallace's rivals may be not in the middle of the left wall.

<image>

In the given coordinate system you are given: 

  * y1, y2 — the y-coordinates of the side pillars of the goalposts of robo-Wallace's opponents; 
  * yw — the y-coordinate of the wall to which Robo-Wallace is aiming; 
  * xb, yb — the coordinates of the ball's position when it is hit; 
  * r — the radius of the ball. 



A goal is scored when the center of the ball crosses the OY axis in the given coordinate system between (0, y1) and (0, y2). The ball moves along a straight line. The ball's hit on the wall is perfectly elastic (the ball does not shrink from the hit), the angle of incidence equals the angle of reflection. If the ball bounces off the wall not to the goal, that is, if it hits the other wall or the goal post, then the opposing team catches the ball and Robo-Wallace starts looking for miscalculation and gets dysfunctional. Such an outcome, if possible, should be avoided. We assume that the ball touches an object, if the distance from the center of the ball to the object is no greater than the ball radius r.

Input

The first and the single line contains integers y1, y2, yw, xb, yb, r (1 ≤ y1, y2, yw, xb, yb ≤ 106; y1 < y2 < yw; yb + r < yw; 2·r < y2 - y1).

It is guaranteed that the ball is positioned correctly in the field, doesn't cross any wall, doesn't touch the wall that Robo-Wallace is aiming at. The goal posts can't be located in the field corners.

Output

If Robo-Wallace can't score a goal in the described manner, print "-1" (without the quotes). Otherwise, print a single number xw — the abscissa of his point of aiming. 

If there are multiple points of aiming, print the abscissa of any of them. When checking the correctness of the answer, all comparisons are made with the permissible absolute error, equal to 10 - 8. 

It is recommended to print as many characters after the decimal point as possible.

Examples

Input

4 10 13 10 3 1


Output

4.3750000000


Input

1 4 6 2 2 1


Output

-1


Input

3 10 15 17 9 2


Output

11.3333333333

Note

Note that in the first and third samples other correct values of abscissa xw are also possible.

Solution (in JAVA):

Solution:
import static java.lang.Math.PI;
import static java.lang.Math.abs;
import static java.lang.Math.acos;
import static java.lang.Math.cos;
import static java.lang.Math.min;
import static java.lang.Math.sin;
import static java.lang.Math.sqrt;
import static java.lang.System.in;
import static java.lang.System.out;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;
public class A249_usingLibrary {
	public static Scanner sc = new Scanner(in);
	StringBuilder sb = new StringBuilder();
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	double eps = 0.000001;

	public void run() throws IOException {
		String input;
		String[] inputArray;
		input = br.readLine();
		inputArray = input.split(" ");
		double y1 = Double.valueOf(inputArray[0]);
		double y2 = Double.valueOf(inputArray[1]);
		double yw = Double.valueOf(inputArray[2]);
		double bx = Double.valueOf(inputArray[3]);
		double by = Double.valueOf(inputArray[4]);
		double r = Double.valueOf(inputArray[5]);
		yw-=r; 
		y1+=r; 
		P ball = new P(bx,by), postUp = new P(0,y2), postDown = new P(0,y1);
		P cornerUp = new P(0,yw), origin = new P(0,0);
		L ceilingL = new L(cornerUp, new P(1,yw));

			
		P ballMirrored = L.LineSymmetricLP(new L(new P(0,yw), new P(1,yw)), ball);
			
		C goalC = new C(postUp, r);
			
		ArrayList<P> tangents = C.contact(goalC, ballMirrored);
		P xmin = tangents.get(0);
		if (tangents.get(0).y >= yw) xmin = tangents.get(1);
		else if (tangents.get(1).x > xmin.x) xmin = tangents.get(1);
		xmin = L.intersection(new L(ballMirrored, xmin),ceilingL);
		P xmax = L.intersection(new L(ballMirrored, postDown),ceilingL);
		if (xmax.x < xmin.x) ln("-1");
		else ln((xmin.x + xmax.x)/2);
		
		
	}

	public static void main(String[] args) throws IOException {
		new A249_usingLibrary().run();
	}
	public static void ln(Object obj) {
		out.println(obj);
	}

	static class P{
		
			static final double EPS=1e-10;
			static int signum(double x){
				return x<-EPS?-1:x>EPS?1:0;
			}
		static Comparator<P> comp=new Comparator<P>(){
			public int compare(P p1, P p2) {
				return signum(p1.x-p2.x)!=0?signum(p1.x-p2.x):signum(p1.y-p2.y);
			}
		};
		public static  final P O=new P(0,0);
		final double x,y;
		P(double _x,double _y){
			x=_x;y=_y;
		}
		
		P add(P a){
			return new P(x+a.x,y+a.y);
		}
		P sub(P a){
			return new P(x-a.x,y-a.y);
		}
		P mul(P a){
			return new P(x*a.x-y*a.y,x*a.y+y*a.x);
		}
		P div(P a){
			double d2=a.dist2(O);
			return new P(dot(a,this)/d2,cross(a,this)/d2);
		}
		
		P conj(){
			return new P(x,-y);
		}
		
		static double dot(P a,P b){
			return  a.x*b.x+a.y*b.y;
		}
		
		static double cross(P a,P b){
			return  a.x*b.y-a.y*b.x;
		}
		
		double dist2(P p){
			return (x-p.x)*(x-p.x)+(y-p.y)*(y-p.y);
		}
		
		double dist(P p){
			return sqrt(dist2(p));
		}
		public double norm(){
			return dist(O);
		}
		
		static int ccw(P a,P b,P c){
			b=b.sub(a);c=c.sub(a);
			if(cross(b,c)>EPS)return 1;
			if(cross(b,c)<-EPS)return -1;
			if(dot(b,c)<-EPS)return 2;
			if(b.norm()<c.norm()-EPS)return -2;
			return 0;
		}
		
		
		
		static double arg(P a,P o){
			P dir=a.sub(o);
			double s=acos(dir.x/dir.norm());
			return dir.y>=0?s:2*PI-s;
		}
		
		static double arg(P a,P b, P c){
			double angleA = P.arg(a,b);
			double angleB = P.arg(b,c);
			double angle =  Math.PI+angleA-angleB;
			if (angle-2*Math.PI>EPS) angle-=2*Math.PI;
			return angle;
		}
		
		P rotate(P o,double arg){
			return this.add(this.sub(o).mul(new P(cos(arg),sin(arg))));
		}
		
		static double S2(P a,P b,P o){
			return cross(a.sub(o),b.sub(o));
		}
		static double S(P a,P b,P o){
			return S2(a,b,o)/2;
		}
		
		static P polar(double abs,double arg){
			return new P(abs*cos(arg),abs*sin(arg));
		}
		
		static P proj(P p,P o){
			return o.mul(new P(dot(p,o)/o.norm(),0));
		}
		public boolean equals(Object obj) {
			if(obj instanceof P){
				P p=(P)obj;
				return signum(x-p.x)==0 && signum(y-p.y)==0;
			}
			return false;
		}
		public String toString(){
			return "("+x+","+y+")";
		}
	}
	
	
	
	
	
	
	static class L extends AL{
		L(P _p1, P _p2) {super(_p1, _p2);}

		
		double dist(P p){
			return abs(P.S(p2,p,p1))/p1.sub(p2).norm();
		}
		boolean isIntersect(P p){
			return abs(P.S(p2,p,p1))<EPS;
		}
		boolean isIntersect(L l){
			if(isPoint() && l.isPoint())return p1.equals(l.p1);
			if(isPoint())return l.isIntersect(p1);
			if(l.isPoint())return isIntersect(l.p1);
			return !isParallel(l) || isIntersect(l.p1);
		}

		
		static P FootOfLP(L l,P p){
			return l.p1.add(P.proj(p.sub(l.p1),l.p2.sub(l.p1)));
		}

		
		static P LineSymmetricLP(L l,P p){
			return FootOfLP(l,p).mul(new P(2.0,0)).sub(p);
		}

		public boolean equals(Object obj) {
			if(obj instanceof L){
				L l=(L)obj;
				return isParallel(l) && isIntersect(l.p1);
			}
			return false;
		}
	}
	
	class S extends AL{
		S(P _p1, P _p2) {super(_p1, _p2);}
		boolean isIntersect(P p){
			return p1.sub(p).norm()+p2.sub(p).norm()<=p1.sub(p2).norm()+EPS;
		}
		boolean isIntersect(L l){
			return P.cross(l.p2.sub(l.p1),p1.sub(l.p1))*
				P.cross(l.p2.sub(l.p1),p2.sub(l.p1))<EPS;
		}
		boolean isIntersect(S l){
			return P.ccw(p1,p2,l.p1)*P.ccw(p1,p2,l.p2)<=0
			&& P.ccw(l.p1,l.p2,p1)*P.ccw(l.p1,l.p2,p2)<=0;
		}
		
		double dist(P p){
			if(P.dot(p2.sub(p1),p.sub(p1))<EPS)return p.sub(p1).norm();
			if(P.dot(p1.sub(p2),p.sub(p2))<EPS)return p.sub(p2).norm();
			return abs(P.S(p2,p,p1))/p1.sub(p2).norm();
		}
		
		double dist(L l){
			if(isIntersect(l))return 0;
			return min(l.dist(p1),l.dist(p2));
		}
		
		double dist(S l){
			if(isIntersect(l))return 0;
			return min(min(dist(l.p1),dist(l.p2)),min(l.dist(p1),l.dist(p2)));
		}
	}
	abstract static class AL{
		
			static final double EPS=1e-10;
			static int signum(double x){
				return x<-EPS?-1:x>EPS?1:0;
			}
		public P p1,p2;
		AL(P _p1,P _p2){
			p1=_p1;
			p2=_p2;
		}

		boolean isPoint(){
			return p1.equals(p2);
		}









		
		boolean isParallel(AL l){
			return abs(P.cross(p2.sub(p1),l.p2.sub(l.p1)))<EPS;
		}
		
		boolean isOrthogonal(AL l){
			return abs(P.dot(p2.sub(p1),l.p2.sub(l.p1)))<EPS;
		}

		
		static P intersection(AL l1,AL l2){
			P dl1=l1.p2.sub(l1.p1),dl2=l2.p2.sub(l2.p1);
			double a=P.cross(dl2,l2.p1.sub(l1.p1));
			double b=P.cross(dl2,dl1);
			if(abs(a)<EPS && abs(b) <EPS)return l1.p1;
			return l1.p1.add(dl1.mul(new P(a/b,0.0)));
		}


		public boolean equals(Object obj) {
			if(obj instanceof L){
				L l=(L)obj;
				return this.p1.equals(l.p1) && this.p2.equals(l.p2);
			}
			return false;
		}
		public String toString(){
			return p1+"-"+p2;
		}
	}
	static class C {
		
			static final double EPS=1e-10;
			static int signum(double x){
				return x<-EPS?-1:x>EPS?1:0;
			}
		P p;
		double r;
		C(P _p,double _r){
			p=_p;
			r=_r;
		}

		static  final C Unit=new C(P.O,1);

		
		static double intersectS(C c1,C c2){
			double d=c1.p.sub(c2.p).norm();
			if(c1.r+c2.r<=d+EPS)return 0;
			if(d<=abs(c1.r-c2.r)+EPS){
				double r=min(c1.r,c2.r);
				return r*r*PI;
			}
			double rlcosA=(d*d+c1.r*c1.r-c2.r*c2.r)/(2*d);
			double A=acos(rlcosA/c1.r);
			double B=acos((d-rlcosA)/c2.r);
			return c1.r*c1.r*A+c2.r*c2.r*B-d*c1.r*sin(A);
		}


		
		static ArrayList<P> intersection(C c1,C c2){
			ArrayList<P> res=new ArrayList<P>();
	 		double d=c1.p.dist(c2.p);
			if(d<EPS && abs(c1.r-c2.r)<EPS){
			}else if(abs(c1.r+c2.r-d)<EPS){
				P diff=c2.p.sub(c1.p).div(new P(d,0));
				res.add(c1.p.add(diff.mul(new P(c1.r,0))));
			}else if(d<c1.r+c2.r){
				double rc=(d*d+c1.r*c2.r-c1.r*c1.r)/(2*d);
				double rs=Math.sqrt(c1.r*c1.r-rc*rc);
				P diff=c2.p.sub(c1.p).div(new P(d,0));
				res.add(c1.p.add(diff.mul(new P(rc,rs))));
				res.add(c1.p.add(diff.mul(new P(rc,-rs))));
			}else{
			}
			return res;
		}

		
		static ArrayList<P> intersection(L l,C c){
			ArrayList<P> res=new ArrayList<P>();
			double dist=l.dist(c.p);
			if(abs(dist-c.r)<EPS){
				res.add(L.FootOfLP(l,c.p));
			}else if(dist<c.r){
				P m=L.FootOfLP(l,c.p);
				P dir=l.p2.sub(l.p1);
				P u=dir.div(new P(dir.norm(),0));
				double t=sqrt(sqrt(c.r)-sqrt(dist));
				res.add(m.add(u.mul(new P(t,0))));
				res.add(m.sub(u.mul(new P(t,0))));
			}
			return res;
		}

		
		static ArrayList<P> contact(C c,P p){
			ArrayList<P> res=new ArrayList<P>();
	 		double d2=p.dist2(c.p);
	 		double r2=c.r*c.r;
			if(abs(r2-d2)<EPS){
				res.add(p);
				return res;
			}
			if(r2>d2)return res;
			P q1=p.sub(c.p).mul(new P(r2/d2,0));
			P q2=p.sub(c.p).mul(new P(0,c.r*sqrt(d2-r2)/d2));
			res.add(c.p.add(q1).add(q2));
			res.add(c.p.add(q1).sub(q2));
			return res;
		}

		
		static ArrayList<P> contact(C c1,C c2){
			ArrayList<P> res=new ArrayList<P>();
			double dist=c2.p.dist(c1.p);
			if(c1.r+c2.r>=dist-EPS)return res;
			double th=P.arg(c2.p,c1.p);
			double a1=acos((c1.r-c2.r)/dist);
			double a2=acos((c1.r+c2.r)/dist);

			res.add(c1.p.add(P.polar(c1.r, th+a1)));
			res.add(c2.p.add(P.polar(c2.r, th+a1)));

			res.add(c1.p.add(P.polar(c1.r, th-a1)));
			res.add(c2.p.add(P.polar(c1.r, th-a1)));

			res.add(c1.p.add(P.polar(c1.r, th+a2)));
			res.add(c2.p.add(P.polar(c1.r, th+a2+PI)));

			res.add(c1.p.add(P.polar(c1.r, th-a2)));
			res.add(c2.p.add(P.polar(c1.r, th-a2+PI)));
			return res;
		}
		










	



		C getFromTwoPointsAndRadious(P a,P b,double r){
			P v=b.sub(a);
			double dist=v.norm();
			if(dist>2*r+EPS)return null;

			P mid=a.add(b).div(new P(2,0));
			P nl=v.div(new P(0,dist));
			double x=sqrt(r*r-dist*dist/4);
			P c=mid.add(nl.mul(new P(x,0)));
			return new C(c,r);
		}
		C getFromThreePoints(P a,P b,P c){
			b=b.sub(a);c=c.sub(a);
			P x=new P(b.x,c.x);
			P y=new P(b.y,c.y);
			P p=new P(b.norm()/2,c.norm()/2);
			P center=new P(P.cross(p,y)/P.cross(x,y),P.cross(x, p)/P.cross(x,y)).add(a);
			return new C(center,a.dist(center));
		}
	}
}