Problem: The Kingdom of Neva is home to two ethnic groups, the Totata and the Tutete. The biggest feature of the Totata tribe is that they eat sweet and sour pork with pineapple. However, the Tutete tribe eats vinegared pork in pineapple. These two peoples couldn't get along with each other, and the Totata and Tutete have been in conflict for hundreds of years.

One day, a petition arrived from two ethnic groups under King Neva. According to it, the Totata tribe wants to build a road connecting the town A and the town B where they live. On the other hand, the Tutete tribe also wants to build a road connecting the town C and the town D where they live.

To prevent the two races from clashing, the roads of the Totata and Tutete cannot be crossed. Also, due to technical restrictions, it is only possible to build a road that connects the two cities in a straight line. In other words, if necessary, instead of connecting city A and city B directly with a road, it would indirectly connect city A and city B via some Totata towns (of course, of the Tutete tribe). Do not go through the city). At that time, the roads connecting the towns of the Totata tribe may intersect. The same applies to town C and town D.

Building a road costs proportional to its length. Therefore, I would like to make the total length of the roads to be constructed as short as possible while satisfying the conditions. Now, what is the minimum length?



Input

NA NB
xA, 1 yA, 1
xA, 2 yA, 2
..
..
..
xA, NA yA, NA
xB, 1 yB, 1
xB, 2 yB, 2
..
..
..
xB, NB yB, NB


The integer NA (2 ≤ NA ≤ 1,000) and the integer NB (2 ≤ NB ≤ 1,000) are written on the first line of the input, separated by blanks. This means that there are NA towns where the Totata tribe lives and NB towns where the Tutete tribe lives in the Kingdom of Neva. In the initial state, no road has been built anywhere.

The following NA line contains the integers xA, i (-10,000 ≤ xA, i ≤ 10,000) and the integers yA, i (-10,000 ≤ yA, i ≤ 10,000), separated by blanks. The geography of the Kingdom of Neva is represented by a two-dimensional Cartesian coordinate plane, and the integers xA, i and yA, i written on the 1 + i line are the position coordinates of the i-th city where the Totata tribe lives (xA, i, yA). , I). (xA, 1, yA, 1) and (xA, 2, yA, 2) are the coordinates of the two cities to be connected.

On the following NB line, the integers xB, i (-10,000 ≤ xB, i ≤ 10,000) and the integers yB, i (-10,000 ≤ yB, i ≤ 10,000) are written separated by blanks. The integers xB, i and yB, i written on the 1 + NA + i line indicate that the position coordinates of the i-th city where the Ytterbium live are (xB, i, yB, i). (xB, 1, yB, 1) and (xB, 2, yB, 2) are the coordinates of the two cities to be connected.

It can be assumed that the coordinates of the two cities are different and that none of the three cities are on the same straight line.

Output

When the road is constructed so as to meet the conditions of the problem statement, output the minimum value of the total length of the road. The "length" here is the Euclidean distance. However, if you cannot build a road that meets the conditions, output -1 instead. The output may contain errors, but the relative error to the true value must be less than 10-9.

Examples

Input

2 2
0 0
1 1
2 0
2 -1


Output

2.414213562373


Input

2 3
4 0
0 0
2 3
2 -2
3 1


Output

-1


Input

5 2
-2 1
1 2
-1 3
-1 5
1 4
0 4
0 0


Output

12.359173603117

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

//Roads on Towns
public class Main{

	int NA, NB;
	double INF = 1L<<50, res = INF;

	final double EPS = 1e-10;

	double dot(double[] a, double[] b){
		return a[0]*b[0]+a[1]*b[1];
	}
	double cross(double[] a, double[] b){
		return a[0]*b[1]-a[1]*b[0];
	}
	double norm(double[] a, double[] b){
		return Math.hypot(a[0]-b[0], a[1]-b[1]);
	}
	double[] sub(double[] a, double[] b){
		return new double[]{a[0]-b[0], a[1]-b[1]};
	}
	double area(double[] a, double[] b, double[] c){
		double res = cross(a, b)+cross(b, c)+cross(c, a);
		return Math.abs(res)/2;
	}
	double ex(double[] a, double[] b, double[] c){
		double[] s1 = sub(b, a), s2 = sub(c, a);
		return cross(s1, s2);
	}
	boolean crossing(double[] a, double[] b, double[] s, double[] t){
		if(Math.abs(cross(sub(b, a), sub(t, s)))<EPS){
			return Math.min(dist(a, b, s), Math.min(dist(a, b, t), Math.min(dist(s, t, a), dist(s, t, b))))<EPS;
		}
		if(ex(a, b, s)*ex(a, b, t)>0)return false;
		if(ex(b, a, s)*ex(b, a, t)>0)return false;
		if(ex(s, t, a)*ex(s, t, b)>0)return false;
		return ex(t, s, a)*ex(t, s, b)<EPS;
	}
	double dist(double[] a, double[] b, double[] p){
		if(dot(sub(b, a), sub(p, a))<EPS)return norm(a, p);
		if(dot(sub(a, b), sub(p, b))<EPS)return norm(b, p);
		return Math.abs(cross(sub(b, a), sub(p, a)))/norm(a, b);
	}

	double[][][] p;
	int[] ua, ub;
	int ka, kb;
	double[][] pd;
	
	double[] d;
	double dijkstraA(double D){
		if(res + EPS < D + pd[0][1])return INF;
		Arrays.fill(d, INF);
		d[0] = 0;
		PriorityQueue<Integer> q = new PriorityQueue<Integer>(NB, new Comparator<Integer>() {
			public int compare(Integer o1, Integer o2) {
				return (int)Math.signum(d[o1]-d[o2]);
			}
		});
		q.add(0);
		while(!q.isEmpty()){
			int v = q.poll();
			if(v==1)return d[1];
			for(int i=1;i<NA;i++){
				double w = d[v] + pd[v][i];
				if(res+EPS < w+D)continue;
				boolean ok = true;
				for(int j=0;j+1<=kb&&ok;j++)if(crossing(p[1][ub[j]], p[1][ub[j+1]], p[0][v], p[0][i]))ok = false;
				if(ok && w < d[i]){
					d[i] = w; q.add(i);
				}
			}
		}
		return INF;
	}
	double dijkstraB(double D){
		if(res+EPS < D+pd[NA][NA+1])return INF;
		Arrays.fill(d, INF);
		d[0] = 0;
		PriorityQueue<Integer> q = new PriorityQueue<Integer>(NB, new Comparator<Integer>() {
			public int compare(Integer o1, Integer o2) {
				return (int)Math.signum(d[o1]-d[o2]);
			}
		});
		q.add(0);
		while(!q.isEmpty()){
			int v = q.poll();
			if(v==1)return d[1];
			for(int i=1;i<NB;i++){
				double w = d[v] + pd[NA+v][NA+i];
				if(res+EPS < w+D)continue;
				boolean ok = true;
				for(int j=0;j+1<=ka&&ok;j++)if(crossing(p[0][ua[j]], p[0][ua[j+1]], p[1][v], p[1][i]))ok = false;
				if(ok && w < d[i]){
					d[i] = w; q.add(i);
				}
			}
		}
		return INF;
	}
	
	void fa(){
		for(int k=2;k<NA;k++){
			double d = pd[0][k] + pd[k][1];
			ka = 2;
			ua[1] = k; ua[2] = 1;
			res = Math.min(res, d+dijkstraB(d));
		}
	}
	void fb(){
		for(int k=2;k<NB;k++){
			double d = pd[NA][NA+k] + pd[NA+k][NA+1];
			kb = 2;
			ub[1] = k; ub[2] = 1;
			res = Math.min(res, d+dijkstraA(d));
		}
	}
	
	void run(){
		Scanner sc = new Scanner(System.in);
		NA = sc.nextInt(); NB = sc.nextInt();
		p = new double[2][][];
		p[0] = new double[NA][2]; p[1] = new double[NB][2];
		for(int i=0;i<NA;i++)for(int j=0;j<2;j++)p[0][i][j]=sc.nextDouble();
		for(int i=0;i<NB;i++)for(int j=0;j<2;j++)p[1][i][j]=sc.nextDouble();
		ua = new int[NA]; ub = new int[NB];
		d = new double[1000];
		pd = new double[NA+NB][NA+NB];
		for(int i=0;i<NA;i++){
			for(int j=i;j<NA;j++)pd[i][j] = pd[j][i] = norm(p[0][i], p[0][j]);
			for(int j=0;j<NB;j++)pd[i][NA+j] = pd[NA+j][i] = norm(p[0][i], p[1][j]);
		}
		for(int i=0;i<NB;i++){
			for(int j=i;j<NB;j++)pd[NA+i][NA+j] = pd[NA+j][NA+i] = norm(p[1][i], p[1][j]);
		}
		double d = pd[0][1];
		ua[1] = 1;
		ka = 1;
		res = Math.min(res, d+dijkstraB(d));
		d = pd[NA][NA+1];
		ub[1] = 1;
		kb = 1;
		res = Math.min(res, d+dijkstraA(d));
//		fa(); fb();
		if(res==INF)System.out.println(-1);
		else System.out.printf("%.10f\n", res);
	}

	public static void main(String[] args) {
		new Main().run();
	}
}