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 <bits/stdc++.h>

using namespace std;

#define all(v) (v).begin(), (v).end()
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define reps(i, f, n) for(int i = (int)(f); i < (int)(n); i++)

typedef pair<double, int> P;

const double inf = 1e9;

#define EPS (1e-10)
#define equals(a, b) (fabs((a)-(b)) < EPS)
#define lt(a, b) ((a) - (b) < -EPS)

// ???/????????????
struct Point {
  double x, y;
  Point(double x = 0.0, double y = 0.0):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(x * a, y * a); }
  Point operator / (double a) { return Point(x / a, y / a); }

  double abs() { return sqrt(norm()); }
  double norm() { return x*x + y*y; }

  bool operator < (const Point& p) const {
    return 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;
  }
};
typedef Point Vector;

// ???
struct Circle {
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0):c(c), r(r){}
};

// ????§???¢
typedef vector<Point> Polygon;

// ??????/??´???
struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()):p1(p1), p2(p2){}  
};
typedef Segment Line;

// ????????????????????????
double norm(Vector v)
{
  return v.x*v.x + v.y*v.y;
}
// ?????????????????§??????
double abs(Vector v)
{
  return sqrt(norm(v));
}
// ?????????????????????
double dot(Vector a, Vector b)
{
  return a.x*b.x + a.y*b.y;
}
// ??????????????????????????§??????
double cross(Vector a, Vector b)
{
  return a.x*b.y - a.y*b.x;
}
// ??´?????????
bool isOrthogonal(Vector a, Vector b)
{
  return equals(dot(a, b), 0.0);
}
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2)
{
  return isOrthogonal(a1 - a2, b1 - b2);
}
bool isOrthogonal(Segment s1, Segment s2)
{
  return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
// ????????????
bool isParallel(Vector a, Vector b)
{
  return equals(cross(a, b), 0.0);
}
bool isParallel(Point a1, Point a2, Point b1, Point b2)
{
  return isParallel(a1 - a2, b1 - b2);
}
bool isParallel(Segment s1, Segment s2)
{
  return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
// ?°???±
Point project(Segment s, Point p)
{
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / norm(base);
  return s.p1 + base * r;
}
// ????°?
Point reflect(Segment s, Point p)
{
  return p + (project(s, p) - p) * 2.0;
}
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE         = -1;
static const int ONLINE_BACK       = 2;
static const int ONLINE_FRONT      = -2;
static const int ON_SEGMENT        = 0;
// ???????¨???????
int ccw(Point p0, Point p1, Point p2)
{
  Vector a = p1 - p0;
  Vector 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(a.norm() < b.norm()) return ONLINE_FRONT;
  return ON_SEGMENT;
}
// ????????????
bool intersect(Point p1, Point p2, Point p3, Point p4)
{
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
	  ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment s1, Segment s2)
{
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
// ?????????????????¢
double getDistance(Point a, Point b)
{
  return abs(a - b);
}
// ??´?????¨?????¨????????¢
double getDistanceLP(Line l, Point p)
{
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}
// ????????¨?????¨????????¢
double getDistanceSP(Segment s, Point p)
{
  if(dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
  if(dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
  return getDistanceLP(s, p);
}
// ????????????????????¢
double getDistance(Segment s1, Segment s2)
{
  if(intersect(s1, s2)) return 0.0;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
	     min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}
// ???????????????
Point getCrossPoint(Segment s1, Segment s2)
{
  Vector base = s2.p2 - s2.p1;
  double d1 = abs(cross(base, s1.p1 - s2.p1));
  double d2 = abs(cross(base, s1.p2 - s2.p1));
  double t = d1 / (d1 + d2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}
Point getCrossPointLL(Line l1, Line l2)
{
  Vector v1 = l1.p2 - l1.p1, v2 = l2.p2 - l2.p1;
  double d = cross(v2, v1);
  if(abs(d) < EPS) return l2.p1;
  return l1.p1 + v1 * cross(v2, l2.p2 - l1.p1) * (1.0 / d);
}

// ???????????????????????¢??¬?????????????????????????????????
bool mergeIfAble(Segment &s1, Segment s2)
{
  if(abs(cross(s1.p2 - s1.p1, s2.p2 - s2.p1)) > EPS) return false;
  if(ccw(s1.p1, s2.p1, s1.p2) == COUNTER_CLOCKWISE ||
     ccw(s1.p1, s2.p1, s1.p2) == CLOCKWISE) return false;
  if(ccw(s1.p1, s1.p2, s2.p1) == ONLINE_FRONT ||
     ccw(s2.p1, s2.p2, s1.p1) == ONLINE_FRONT) return false;
  s1 = Segment(min(s1.p1, s2.p1), max(s1.p2, s2.p2));
  return true;
}
void mergeSegments(vector<Segment>& segs)
{
  for(int i = 0; i < segs.size(); i++) {
    if(segs[i].p2 < segs[i].p1) swap(segs[i].p1, segs[i].p2);
  }
  for(int i = 0; i < segs.size(); i++) {
    for(int j = i+1; j < segs.size(); j++) {
      if(mergeIfAble(segs[i], segs[j])) {
	segs[j--] = segs.back(), segs.pop_back();
      }
    }
  }
}

// ????????¢??¬???????????????
struct edge
{
  int to;
  double cost;
  edge(){}
  edge(int to, double cost):to(to), cost(cost){}

  bool operator < (const edge& e) const {
    return lt(cost, e.cost);
  }
};
typedef vector< vector<edge> > Graph;

Graph segmentArrangement(vector<Segment>& segs, vector<Point>& ps)
{
  for(int i = 0; i < segs.size(); i++) {
    ps.push_back(segs[i].p1);
    ps.push_back(segs[i].p2);
    for(int j = i+1; j < segs.size(); j++) {
      if(intersect(segs[i], segs[j])) ps.push_back(getCrossPoint(segs[i], segs[j]));
    }
  }
  sort(ps.begin(), ps.end());
  ps.erase(unique(ps.begin(), ps.end()), ps.end());
  Graph graph(ps.size());
  for(int i = 0; i < segs.size(); i++) {
    vector< pair<double, int> > ls;
    for(int j = 0; j < ps.size(); j++) {
      if(intersect(segs[i], ps[j])) {
	ls.emplace_back(getDistanceSP(segs[i], ps[j]), j);
      }
    }
    sort(ls.begin(), ls.end());
    for(int j = 0; j+1 < ls.size(); j++) {
      int u = ls[j].second, v = ls[j+1].second;
      graph[u].emplace_back(v, getDistance(ps[u], ps[v]));
      graph[v].emplace_back(u, getDistance(ps[u], ps[v]));
    }
  }
  return graph;
}

double dijkstra(vector<Point> p, Point a, Point b)
{
  priority_queue<P, vector<P>, greater<P> > que;
  vector<double> mincost(p.size(), inf);  
  que.push(P(0.0, 0));
  mincost[0] = 0.0;
  while(!que.empty()) {
    double c; int now;
    tie(c, now) = que.top(); que.pop();
    if(now == 1) return c + getDistance(a, b);
    if(mincost[now] < c) continue;
    for(int i = 0; i < p.size(); i++) {
      if(intersect(p[now], p[i], a, b)) continue;
      if(getDistance(p[now], p[i]) + c < mincost[i]) {
	mincost[i] = getDistance(p[now], p[i]) + c;
	que.push(P(mincost[i], i));
      }
    }
  }
  return inf;
}

signed main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  int Na, Nb;
  cin >> Na >> Nb;
  vector<Point> pa(Na), pb(Nb);
  rep(i, Na) cin >> pa[i].x >> pa[i].y;
  rep(i, Nb) cin >> pb[i].x >> pb[i].y;

  double a_st = dijkstra(pb, pa[0], pa[1]);
  double b_st = dijkstra(pa, pb[0], pb[1]);

  if(a_st != inf || b_st != inf) cout << min(a_st, b_st) << endl;
  else cout << -1 << endl;
  
  return 0;
}