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<iostream>
#include<vector>
#include<algorithm>
#include<cmath>
#include<cassert>
#include<iomanip>
#include<cstdio>
#include<cassert>
#include<queue>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define inf (1<<29)
#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define MAX 2000
#define pow2(a) ((a)*(a))
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0


using namespace std;

//


class Point
{
  public:
  double x,y;

  Point(double x = -inf,double y = -inf): x(x),y(y){}

  Point operator + (Point p){return Point(x+p.x,y+p.y);}
  Point operator - (Point p){return Point(x-p.x,y-p.y);}
  Point operator * (double a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}

  bool operator < (const Point& p) const
  {
    return !equals(x,p.x)?x<p.x:y<p.y;
  }

  bool operator == (const Point& p)const
  {
    return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
  }

};

struct Segment
{
  Point p1,p2;
  Segment(Point p1 = Point(-inf,-inf),Point p2 = Point(-inf,-inf)):p1(p1),p2(p2){}
  bool operator == (const Segment& p)const
  {
    return p.p1 == p1 && p.p2 == p2;
  }
};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream& operator << (ostream& os,const Point& a)
{
  os << "(" << a.x << "," << a.y << ")";
}

ostream& operator << (ostream& os,const Segment& a)
{
  os << "( " << a.p1 << " , " << a.p2 << " )";
}

double dot(Point a,Point b){ return a.x*b.x + a.y*b.y; }

double cross(Point a,Point b){ return a.x*b.y - a.y*b.x; }

double norm(Point a){ return a.x*a.x+a.y*a.y; }

double abs(Point a){ return sqrt(norm(a)); }

//rad は角度をラジアンで持たせること
Point rotate(Point a,double rad){ return Point(cos(rad)*a.x - sin(rad)*a.y,sin(rad)*a.x + cos(rad)*a.y); }

// 度をラジアンに変換
double toRad(double agl){ return agl*M_PI/180.0; }

int ccw(Point p0,Point p1,Point p2)
{
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2-l.p1, m.p2-m.p1)) > EPS || // non-parallel
         abs(cross(l.p2-l.p1, m.p1-l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2-l.p1, s.p1-l.p1)*       // s[0] is left of l
         cross(l.p2-l.p1, s.p2-l.p1) < EPS; // s[1] is right of l
}
bool intersectLP(Line l,Point p) {
  return abs(cross(l.p2-p, l.p1-p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}

Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}
Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}
double distanceLP(Line l, Point p) {
  return abs(p - projection(l, p));
}
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}
Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) return m.p1; // same line
  if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
  return m.p1 +   (m.p2 - m.p1) * (B / A);
}

//

struct Poxas7
{
  int cur;
  double cost;
  Poxas7(int cur=inf,double cost=inf):cur(cur),cost(cost){}
  bool operator < (const Poxas7 &a)const
  {
    return cost > a.cost;
  }
};

int path[MAX],AN,BN,N;
double mincost[MAX];
vector<Point> vec[2];

double dijkstra(vector<Point> &vec,int s,int t,vector<Segment> &ban)
{
  N = vec.size();
  rep(i,N)path[i] = -1,mincost[i] = inf;
  priority_queue<Poxas7> Q;
  Q.push(Poxas7(s,0));
  mincost[s] = 0;
  while(!Q.empty())
    {
      Poxas7 pox = Q.top(); Q.pop();

      if(pox.cur == t)
	{
	  return pox.cost;
	}

      rep(next,N)
	{
	  if(s == next)continue;
	  Segment seg = Segment(vec[pox.cur],vec[next]);	  
	  bool out = false;
	  rep(i,ban.size())
	    if(intersectSS(ban[i],seg))
	      {
		out = true;
		break;
	      }
	  if(out)continue;

	  if(mincost[next] > pox.cost + abs(vec[pox.cur]-vec[next]))
	    {
	      path[next] = pox.cur;
	      mincost[next] = pox.cost + abs(vec[pox.cur]-vec[next]);
	      Q.push(Poxas7(next,mincost[next]));
	    }
	}

    }
  return -1;
}

int main()
{
  while(scanf("%d %d",&AN,&BN) != EOF)
    {
      rep(i,2)vec[i].clear();
      vec[0].resize(AN);
      vec[1].resize(BN);
      rep(i,AN)cin >> vec[0][i].x >> vec[0][i].y;
      rep(i,BN)cin >> vec[1][i].x >> vec[1][i].y;      

      double ans = inf;
      rep(i,2)
	{
	  vector<Segment> ban;
	  double cost = dijkstra(vec[i],0,1,ban);
	  if(cost == -1)continue;
	  int cur = 1;

	  for(int next=path[cur];cur != 0;cur=next,next=path[cur])
	    {
	      ban.push_back(Segment(vec[i][cur],vec[i][next]));
	    }

	  double cost2 = dijkstra(vec[(i+1)%2],0,1,ban);
	  if(cost2 == -1)continue;
	  ans = min(ans,cost+cost2);
	}

      if(ans == inf)cout << "-1" << endl;      
      else          cout << setiosflags(ios::fixed) << setprecision(15) << ans << endl;
    }
  return 0;
}