#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>

using namespace std;

class BarbarianInvasion2 {
public:
  double minimumTime(vector <int>, vector <int>, vector <int>, vector <int>);
};

const int N = 11111;

long double e[N], start[N], rs[9][N], rf[9][N];
int pe[N], nr[9];

double BarbarianInvasion2::minimumTime(vector <int> bx, vector <int> by, vector <int> xc, vector <int> yc) {
  int nb = bx.size(), nc = xc.size(), i, j, tt, it, ok, t, ke, kb, bal;
  bx.push_back(bx[0]);
  by.push_back(by[0]);
  long double ll = 0, rr = 1e5, mid, len = 0, dist, tmp, u, d, dx, dy, d1, d2, dd, left, right, cent, sum;
  for (i=0;i<nb;i++) {
    start[i] = len;
    len += sqrt(1.0*(bx[i]-bx[i+1])*(bx[i]-bx[i+1])+1.0*(by[i]-by[i+1])*(by[i]-by[i+1]));
  }
  long long a, b, c, aa, bb, cc;
  for (it=0;it<100;it++) {
    mid = 0.5*(ll+rr);
    for (i=0;i<nc;i++) {
      nr[i] = 0;
      for (j=0;j<nb;j++) {
        a = by[j+1]-by[j];
        b = bx[j]-bx[j+1];
        c = -a*bx[j]-b*by[j];
        dist = a*xc[i]+b*yc[i]+c;
        if (dist < 0) dist = -dist;
        dist /= sqrt(1.0*a*a+1.0*b*b);
        u = mid*mid-dist*dist;
        if (u < 0) continue;
        u = sqrt(u);
        aa = -b; bb = a;
        cc = -aa*xc[i]-bb*yc[i];
        d = a*bb-b*aa;
        dx = 1.0*(b*cc-c*bb)/d;
        dy = 1.0*(c*aa-a*cc)/d;
        d1 = sqrt((dx-bx[j])*(dx-bx[j])+(dy-by[j])*(dy-by[j]));
        d2 = sqrt((dx-bx[j+1])*(dx-bx[j+1])+(dy-by[j+1])*(dy-by[j+1]));
        dd = sqrt((bx[j]-bx[j+1])*(bx[j]-bx[j+1])+(by[j]-by[j+1])*(by[j]-by[j+1]));
        if (d1+d2 < dd+1e-9 || d2 < d1) cent = start[j]+d1;
        else cent = start[j]-d1;
        left = cent-u;
        right = cent+u;
        if (left < start[j]) left = start[j];
        if (right > start[j]+dd) right = start[j]+dd;
        if (left > right) continue;
        rs[i][nr[i]] = left;
        rf[i][nr[i]] = right;
        nr[i]++;
      }
    }
    ok = 1;
    for (t=1;t<(1<<nc);t++) {
      ke = 0; kb = 0;
      for (i=0;i<nc;i++)
        if (t & (1 << i)) {
          kb++;
          for (j=0;j<nr[i];j++) {
            e[ke] = rs[i][j];
            pe[ke] = 1;
            ke++;
            e[ke] = rf[i][j];
            pe[ke] = -1;
            ke++;
          }
        }
      for (i=0;i<ke;i++)
        for (j=i+1;j<ke;j++)
          if (e[i] > e[j]) {
            tmp = e[i]; e[i] = e[j]; e[j] = tmp;
            tt = pe[i]; pe[i] = pe[j]; pe[j] = tt;
          }
      sum = 0; bal = 0;
      for (i=0;i<ke;i++) {
        bal += pe[i];
        if (bal > 0) sum += e[i+1]-e[i];
      }
      if (sum < len*kb/nc-1e-9) {
        ok = 0;
        break;
      }
    }
    if (ok) rr = mid;
    else ll = mid;
  }
  return 0.5*(ll+rr);
}