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 CPP):

Solution:
#include <stdio.h>
#include <cmath>
#include <algorithm>
#include <cfloat>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
#include <set>
#include <map>
#include <time.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;


enum Type{
	A,
	B,
};

struct Data{
	Data(int arg_node_id,double arg_sum_dist){
		node_id = arg_node_id;
		sum_dist = arg_sum_dist;
	}
	bool operator<(const struct Data &arg) const{
		return sum_dist > arg.sum_dist;
	}
	int node_id;
	double sum_dist;
};


struct Point{
	double x,y;
};

struct Line{
	Point p[2];
};

double calc_dist(Line a){
	return sqrt((a.p[0].x-a.p[1].x)*(a.p[0].x-a.p[1].x)+(a.p[0].y-a.p[1].y)*(a.p[0].y-a.p[1].y));
}


int func(double x1,double y1,double x2, double y2, double xp, double yp){
	double naiseki,norm1,norm2,gaiseki;
	norm1 = sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
	norm2 = sqrt((xp-x1)*(xp-x1)+(yp-y1)*(yp-y1));
	naiseki = (xp-x1)*(x2-x1)+(yp-y1)*(y2-y1);
	gaiseki = (x2-x1)*(yp-y1)-(xp-x1)*(y2-y1);
	if(gaiseki > EPS){
		return 1;
	}else if(gaiseki < -EPS){
		return -1;
	}
	if(naiseki < -EPS){
		return 2;
	}

	if(norm1 < norm2){
		return -2;
	}
	return 0;
}

bool is_Cross(Line a,Line b){

	if(func(a.p[0].x,a.p[0].y,a.p[1].x,a.p[1].y,b.p[0].x,b.p[0].y)*
			func(a.p[0].x,a.p[0].y,a.p[1].x,a.p[1].y,b.p[1].x,b.p[1].y) <= 0 &&
			func(b.p[0].x,b.p[0].y,b.p[1].x,b.p[1].y,a.p[0].x,a.p[0].y)*
			func(b.p[0].x,b.p[0].y,b.p[1].x,b.p[1].y,a.p[1].x,a.p[1].y) <= 0){
		return true;
	}
	return false;
}


Point point[2][1000];
double min_dist[1000],DIST[2][1000][1000];
int start = 0,goal = 1;
Line base_line;


double dijkstra(int data_num,Type type){

	min_dist[start] = 0;
	for(int i = 1; i < data_num; i++)min_dist[i] = DBL_MAX;

	priority_queue<Data> Q;
	Q.push(Data(start,0));

	double tmp_dist;

	Line line;

	while(!Q.empty()){

		if(Q.top().node_id == goal){
			Q.pop();
		}else if(Q.top().sum_dist > min_dist[Q.top().node_id]){
			Q.pop();
		}else{

			line.p[0] = point[type][Q.top().node_id];

			for(int next_node = 0; next_node < data_num; next_node++){
				if(next_node == Q.top().node_id)continue;

				line.p[1] = point[type][next_node];

				if(is_Cross(line,base_line))continue;

				tmp_dist = DIST[type][Q.top().node_id][next_node];

				if(min_dist[next_node] > Q.top().sum_dist+tmp_dist){
					min_dist[next_node] = Q.top().sum_dist+tmp_dist;
					Q.push(Data(next_node,min_dist[next_node]));
				}
			}
			Q.pop();
		}
	}

	return min_dist[goal];
}

int main(){

	int N_A,N_B;
	scanf("%d %d",&N_A,&N_B);

	for(int i = 0; i < N_A; i++){
		scanf("%lf %lf",&point[A][i].x,&point[A][i].y);
	}

	Line calc_line;
	double tmp_dist;

	for(int i = 0; i < N_A-1; i++){
		calc_line.p[0] = point[A][i];
		for(int k = i+1; k < N_A; k++){
			calc_line.p[1] = point[A][k];
			tmp_dist = calc_dist(calc_line);
			DIST[A][i][k] = tmp_dist;
			DIST[A][k][i] = tmp_dist;
		}
	}

	for(int i = 0; i < N_B; i++){
		scanf("%lf %lf",&point[B][i].x,&point[B][i].y);
	}

	for(int i = 0; i < N_B-1; i++){
		calc_line.p[0] = point[B][i];
		for(int k = i+1; k < N_B; k++){
			calc_line.p[1] = point[B][k];
			tmp_dist = calc_dist(calc_line);
			DIST[B][i][k] = tmp_dist;
			DIST[B][k][i] = tmp_dist;
		}
	}

	double dist_1,dist_2;

	base_line.p[0] = point[A][0];
	base_line.p[1] = point[A][1];

	dist_1 = dijkstra(N_B,B);

	if(fabs(dist_1-DBL_MAX)<EPS){
		//Do nothing
	}else{
		dist_1 += calc_dist(base_line);
	}

	base_line.p[0] = point[B][0];
	base_line.p[1] = point[B][1];

	dist_2 = dijkstra(N_A,A);

	if(fabs(dist_2-DBL_MAX)<EPS){
		//Do nothing
	}else{
		dist_2 += calc_dist(base_line);
	}

	double ans = min(dist_1,dist_2);

	if(fabs(ans-DBL_MAX) < EPS){
		printf("-1\n");
	}else{
		printf("%.12lf\n",ans);
	}

	return 0;
}