Problem: You have got a new job, and it's very interesting, you are a ship captain. Your first task is to move your ship from one point to another point, and for sure you want to move it at the minimum cost.

And it's well known that the shortest distance between any 2 points is the length of the line segment between these 2 points. But unfortunately there is an island in the sea, so sometimes you won't be able to move your ship in the line segment between the 2 points.

You can only move to safe points. A point is called safe if it's on the line segment between the start and end points, or if it's on the island's edge.

But you are too lucky, you have got some clever and strong workers and they can help you in your trip, they can help you move the ship in the sea and they will take 1 Egyptian pound for each moving unit in the sea, and they can carry the ship (yes, they are very strong) and walk on the island and they will take 2 Egyptian pounds for each moving unit in the island. The money which you will give to them will be divided between all workers, so the number of workers does not matter here.

You can move your ship on the island edge, and it will be considered moving in the sea.

Now you have a sea map, and you have to decide what is the minimum cost for your trip.

Your starting point is (xStart, yStart), and the end point is (xEnd, yEnd), both points will be different.

The island will be a convex polygon and there will be no more than 2 polygon points on the same line, also the starting and the end points won't be inside or on the boundary of the island. The points for the polygon will be given in the anti-clockwise order.

Input

The first line contains 4 integers, xStart, yStart, xEnd and yEnd ( - 100 ≤ xStart, yStart, xEnd, yEnd ≤ 100). The second line contains an integer n, which is the number of points in the polygon (3 ≤ n ≤ 30), followed by a line containing n pairs of integers x and y, which are the coordinates of the points ( - 100 ≤ x, y ≤ 100), the polygon points will be distinct.

Output

Print one line which contains the minimum possible cost. The absolute or relative error in the answer should not exceed 10 - 6.

Examples

Input

1 7 6 7
4
4 2 4 12 3 12 3 2


Output

6.000000000


Input

-1 0 2 0
4
0 0 1 0 1 1 0 1


Output

3.000000000

Solution (in JAVA):

Solution:
import java.util.*;
import static java.lang.Math.*;

public class E {
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		st = new Point(in.nextInt(), in.nextInt());
		en = new Point(in.nextInt(), in.nextInt());
		int N = in.nextInt();
		Point[] P = new Point[N];
		for(int i = 0; i < N;i++)
			P[i] = new Point(in.nextInt(), in.nextInt());
		ArrayList<ArrayList<Edge>> G = new ArrayList<ArrayList<Edge>>();
		for(int i = 0; i < N;i++){
			G.add(new ArrayList<Edge>());
			int prev = (i-1+N)%N;
			int next = (i+1)%N;
			G.get(i).add(new Edge(prev, P[i].dist(P[prev])));
			G.get(i).add(new Edge(next, P[i].dist(P[next])));
		}
		ArrayList<Point> inter = new ArrayList<Point>();
		inter.add(st);
		inter.add(en);
		for(int i = 0; i < N;i++){
			Line s1 = new Line(st, en);
			Line s2 = new Line(P[i], P[(i+1)%N]);
			Point inte = segseg(s1, s2);
			if(inte != null)
				inter.add(inte);
		}
		Collections.sort(inter, new Comparator<Point>(){
			public int compare(Point p1, Point p2) {
				double d1 = st.dist(p1);
				double d2 = st.dist(p2);
				if(d1 < d2)
					return -1;
				if(d1 > d2)
					return 1;
				return 0;
			}});
		for(int i = 0; i < inter.size()-1;i++){
			if(inter.get(i).equals(inter.get(i+1))){
				inter.remove(i+1);
			}
		}
		if(inter.size() == 3)
			inter.remove(1);
		int stidx = -1, enidx = -1;
		for(int i = 0; i < inter.size(); i++){
			G.add(new ArrayList<Edge>());	
			Point p = inter.get(i);
			if(p.equals(st))
				stidx = i+N;
			if(p.equals(en))
				enidx = i+N;
			
			for(int j = 0; j < N;j++){
				if(onseg(new Line(P[j], P[(j+1)%N]), p)){
					G.get(i+N).add(new Edge(j, p.dist(P[j])));
					G.get(j).add(new Edge(i+N, p.dist(P[j])));
					G.get(i+N).add(new Edge((j+1)%N, p.dist(P[(j+1)%N])));
					G.get((j+1)%N).add(new Edge(i+N, p.dist(P[(j+1)%N])));
				}
			}
		}
		for(int i = 0; i < inter.size()-1; i++){
			int cost = i%2 == 0 ? 1 : 2;
			G.get(i+N).add(new Edge(i+N+1, cost*inter.get(i).dist(inter.get(i+1))));
			G.get(i+N+1).add(new Edge(i+N, cost*inter.get(i).dist(inter.get(i+1))));
		}
		double[] dist = new double[G.size()];
		Arrays.fill(dist, Long.MAX_VALUE);
		dist[stidx] = 0;
		PriorityQueue<State> pq = new PriorityQueue<State>();
		pq.add(new State(stidx, 0));
		while(pq.size() > 0){
			State at = pq.poll();
			if(dist[at.at] < at.dist)
				continue;
			for(Edge e: G.get(at.at)){
				if(at.dist+e.cost < dist[e.to]-eps){
					dist[e.to] = at.dist+e.cost;
					pq.add(new State(e.to, dist[e.to]));
				}
			}
		}
		System.out.format("%.15f\n", dist[enidx]);

	}
	static Point st, en;
	static class Edge{
		int to;
		double cost;
		public Edge(int to, double cost){
			this.to = to;
			this.cost = cost;
		}
	}
	static class State implements Comparable<State>{
		int at;
		double dist;
		public State(int at, double dist){
			this.at = at;
			this.dist = dist;
		}
		public int compareTo(State s){
			if(dist < s.dist)
				return -1;
			if(dist > s.dist)
				return 1;
			return 0;
		}
	}

	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	static double eps = 1e-9;
	static boolean EQ(double a, double b){return abs(a-b) < eps;}
	static double SQ(double d){return d*d;}
	static double normang(double t){ return ((t % (2*PI)) + 2*PI) % (2*PI); }
	static double angdiff(double t1, double t2){ return normang(t1 - t2 + PI) - PI; }
	static ArrayList<Point> makeVec(Point...P){
		ArrayList<Point> ans = new ArrayList<Point>();
		for(Point p:P)
			ans.add(p);
		return ans;
	}
	static class Point{
		double x, y;
		public Point(double x, double y){this.x = x;this.y = y;}
		Point add(Point p){return new Point(x+p.x, y+p.y);}
		Point sub(Point p){return new Point(x-p.x, y-p.y);}
		Point mult(double d){return new Point(x*d, y*d);}
		double dot(Point p){return x*p.x+ y*p.y;}
		double cross(Point p){return x*p.y - y*p.x;}
		double len(){return hypot(x, y);}
		Point scale(double d){return mult(d/len());}
		double dist(Point p){return sub(p).len();}
		double ang(){return atan2(y, x);}
		static Point polar(double r, double theta){return new Point(r*cos(theta), r*sin(theta));}
		Point rot(double theta){return new Point(x*cos(theta)-y*sin(theta), x*sin(theta)+y*cos(theta));}
		Point perp(){return new Point(-y, x);}
		boolean equals(Point p){return EQ(0, dist(p));}
		double norm(){return dot(this);}
		public String toString(){return String.format("(%.03f, %.03f)", x, y);}
	}	
	static class Line{
		Point a, b;
		Line(Point a, Point b){this.a = a;this.b = b;}
		public String toString(){return String.format("{%s -> %s}", a, b);}
	}
	static class Circle{
		Point p;double r;
		public Circle(Point p, double r){this.p = p;this.r = r;}
		public Circle(Point a, Point b, Point c){
			Point p1 = a.add(b).mult(0.5);
			Line l1 = new Line(p1, p1.add(a.sub(b).perp()));
			Point p2 = b.add(c).mult(0.5);
			Line l2 = new Line(p2, p2.add(b.sub(c).perp()));
			p = lineline(l1, l2);
			assert(p != null);
			r = p.dist(a);
		}
	}
	static double ccw(Point p1, Point p2, Point p3){
		return p2.sub(p1).cross(p3.sub(p1));
	}
	static Point lineline(Line a, Line b){//tested
		double d = a.b.sub(a.a).cross(b.b.sub(b.a));
		if(EQ(d, 0))
			return null;
		return a.a.add((a.b.sub(a.a)).mult(b.b.sub(b.a).cross(a.a.sub(b.a))/d));
	}
	static Point segline(Line a, Line b){
		Point inter = lineline(a, b);
		if(inter == null || !onseg(a, inter))
			return null;
		return inter;
	}
	static Point segseg(Line a, Line b){//tested
		Point inter = lineline(a, b);
		if(inter == null || !onseg(a, inter) || !onseg(b, inter))
			return null;
		return inter;
	}
	static boolean onseg(Line l, Point p){ //tested
		Point delta = l.b.sub(l.a);
		return online(l, p) && delta.dot(l.a)-eps <= delta.dot(p) && delta.dot(p) <= delta.dot(l.b)+eps;
	}
	static boolean online(Line l, Point p){ //tested
		return EQ(ccw(l.a, l.b, p), 0);
	}
	static Point pointline(Point p, Line l){
		Point v = l.b.sub(l.a).scale(1);
		double dot = p.sub(l.a).dot(v);
		return l.a.add(v.mult(dot));
	}
	static Point pointseg(Point p, Line l){
		Point v = l.b.sub(l.a).scale(1);
		double dot = p.sub(l.a).dot(v);
		dot = max(dot, 0);
		dot = min(dot, l.b.dist(l.a));
		return l.a.add(v.mult(dot));
	}
	static double pointsegdist(Point p, Line l){
		return pointseg(p, l).dist(p);
	}
	static double pointlinedist(Point p, Line l){
		return pointline(p, l).dist(p);
	}

	static double polyarea(Point[] poly){
		double area = 0;
		for(int i = 0; i < poly.length; i++)
			area += poly[i].cross(poly[(i+1)%poly.length]);
		return abs(area)/2.0;
	}
	static int pointinpoly(Point[] poly, Point p){
		double ang = 0.0;
		for(int i = 0; i < poly.length; i++){
			Point a = poly[i];
			Point b = poly[(i+1)%poly.length];
			if(onseg(new Line(a, b), p))
				return 0;
			ang += angdiff(a.sub(p).ang(), b.sub(p).ang());
		}
		return EQ(ang, 0) ? -1 : 1;
	}

	static Point v0;
	static ArrayList<Point> convexhull(ArrayList<Point> P){//tested
		v0 = null;
		for(Point p:P)
			if(v0 == null || p.x < v0.x - eps || (EQ(p.x, v0.x) && p.y < v0.y))
				v0 = p;
		Collections.sort(P, new Comparator<Point>(){
			public int compare(Point a, Point b){
				if(a == v0) return -1;
				if(b == v0) return 1;
				double ccw = ccw(v0, a, b);
				if(EQ(ccw, 0)){
					double d1 = v0.dist(a);
					double d2 = v0.dist(b);
					if(d1 < d2) return -1;
					if(d1 > d2) return 1;
					return 0;
				}
				return (int) -signum(ccw);
			}});
		ArrayList<Point> ch = new ArrayList<Point>();
		for(Point p:P){
			while(ch.size() >= 2 && ccw(ch.get(ch.size()-2), ch.get(ch.size()-1), p) <= 0)
				ch.remove(ch.size()-1);
			ch.add(p);
		}
		return ch;
	}
	//add half space intersection

	//circle
	static ArrayList<Point> circline(Circle c, Line l){
		Point x = pointline(c.p, l);
		double d = x.dist(c.p);
		if(d > c.r + eps) return new ArrayList<Point>();
		double h = sqrt(SQ(c.r) - SQ(d));
		Point v = x.sub(c.p);
		return makeVec(c.p.add(v.scale(d)).add(v.scale(h)), c.p.add(v.scale(d)).add(v.scale(-h)));
	}
	static ArrayList<Point> circcirc(Circle a, Circle b){
		double d = a.p.dist(b.p);
		if(d > a.r + b.r + eps) return new ArrayList<Point>();
		if(d < abs(a.r - b.r) - eps) return new ArrayList<Point>();
		double x = (SQ(d) - SQ(b.r) + SQ(a.r)) / 2*d;
		double y = sqrt(SQ(a.r) - SQ(x));
		Point v = b.p.sub(a.p);
		return makeVec(a.p.add(v.scale(x)).add(v.perp().scale(y)), a.p.add(v.scale(x)).add(v.perp().scale(-y)));
	}
	static ArrayList<Line> circcirctan(Circle a, Circle b){//tested
		if(a.r < b.r)
			return circcirctan(b, a);
		ArrayList<Line> res = new ArrayList<Line>();
		double d = a.p.dist(b.p);
		double d1 = a.r*d/(a.r + b.r);
		double t = acos(a.r/d1);
		Point v = b.p.sub(a.p);
		res.add(new Line(a.p.add(v.scale(a.r).rot(t)), b.p.add(v.scale(-b.r).rot(t))));
		res.add(new Line(a.p.add(v.scale(a.r).rot(-t)), b.p.add(v.scale(-b.r).rot(-t))));   
		t = asin((a.r-b.r)/d)+PI/2;
		v = a.p.sub(b.p);
		res.add(new Line(a.p.add(v.scale(a.r).rot(t)), b.p.add(v.scale(b.r).rot(t))));
		res.add(new Line(a.p.add(v.scale(a.r).rot(-t)), b.p.add(v.scale(b.r).rot(-t)))); 
		return res;
	}

	//3d
	static class Point3{
		double x, y, z;
		Point3(double x, double y, double z) {  this.x = x; this.y = y; this.z = z; }
		static Point3 sphere(double theta, double phi, double r){
			return new Point3(r*cos(theta)*sin(phi),r*sin(theta)*sin(phi),r*cos(theta));
		}
		double[] ang(){ return new double[]{atan(y/x), acos(z/len())}; }
		Point proj(){ return new Point(x, y); }
		Point3 add(Point3 p){ return new Point3(x+p.x, y+p.y, z+p.z); }
		Point3 sub(Point3 p){ return new Point3(x-p.x, y-p.y, z-p.z); }
		double dot(Point3 p){ return x*p.x+ y*p.y+ z*p.z; }
		Point3 cross(Point3 p){ return new Point3(y*p.z-p.y*z, z*p.x-p.z*x, x*p.y-p.x*y); }
		Point3 mult(double d){ return new Point3(x*d, y*d, z*d); }
		double len(){ return sqrt(x*x+y*y+z*z); }
		Point3 scale(double d){ return mult(d/len()); }
		double dist(Point3 p){ return sub(p).len(); } 
		boolean equals(Point3 p){ return EQ(dist(p), 0); }
	}
	static Point3[] getbasis(Point3 z){
		z = z.scale(1);
		Point3 t = new Point3(1, 0, 0);
		Point3 y = z.cross(t);
		if(EQ(y.len(), 0)){
			t = new Point3(0, 1, 0);
			y = z.cross(t);
		}
		Point3 x = y.cross(z);
		assert(x.cross(y).equals(z));
		return new Point3[]{x, y, z};
	}
	static Point3 trans(Point3[] B, Point3 p){
		return new Point3(B[0].dot(p), B[1].dot(p), B[2].dot(p));
	}
	static Point3 invtrans(Point3[] B, Point3 p){
		return B[0].mult(p.x).add(B[1].mult(p.y)).add(B[2].mult(p.z));
	}
}