#include <bits/stdc++.h>
using namespace std;
inline char gc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline long long read() {
  long long x = 0;
  char ch = getchar();
  bool positive = 1;
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') positive = 0;
  for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
  return positive ? x : -x;
}
inline void write(long long a) {
  if (a < 0) {
    a = -a;
    putchar('-');
  }
  if (a >= 10) write(a / 10);
  putchar('0' + a % 10);
}
inline void writeln(long long a) {
  write(a);
  puts("");
}
inline void wri(long long a) {
  write(a);
  putchar(' ');
}
inline unsigned long long rnd() {
  return ((unsigned long long)rand() << 30 ^ rand()) << 4 | rand() % 4;
}
const int N = 150005;
long double l[N], r[N];
struct data {
  long long p, t, id;
} a[N], b[N];
int n;
long long T;
bool cmp(data a, data b) { return a.p < b.p; }
bool cmpt(data a, data b) {
  long long A = (long long)a.t * b.p, B = (long long)b.t * a.p;
  return A == B ? a.p < b.p : A < B;
}
bool check(long double c) {
  long long sum = 0;
  for (int i = 1, j; i <= n; i = j) {
    j = i + 1;
    while (j <= n && a[j].t * a[i].p == a[i].t * a[j].p) j++;
    for (int k = (int)(i); k <= (int)(j - 1); k++)
      r[a[k].id] = (1 - c * (sum + a[k].t) / T) * a[k].p;
    for (int k = (int)(i); k <= (int)(j - 1); k++) sum += a[k].t;
    for (int k = (int)(i); k <= (int)(j - 1); k++)
      l[a[k].id] = (1 - c * sum / T) * a[k].p;
  }
  int dq = n;
  long double mn = 1e100;
  for (int i = (int)(n); i >= (int)(1); i--) {
    while (b[dq].p > b[i].p) {
      mn = min(mn, l[b[dq--].id]);
    }
    if (mn <= r[b[i].id]) return 0;
  }
  return 1;
}
int main() {
  n = read();
  for (int i = (int)(1); i <= (int)(n); i++) a[a[i].id = i].p = read();
  for (int i = (int)(1); i <= (int)(n); i++) T += (a[i].t = read());
  for (int i = (int)(1); i <= (int)(n); i++) b[i] = a[i];
  sort(a + 1, a + n + 1, cmpt);
  sort(b + 1, b + n + 1, cmp);
  long double l = 0, r = 1;
  for (int i = (int)(1); i <= (int)(80); i++) {
    long double mid = (l + r) / 2;
    if (check(mid))
      l = mid;
    else
      r = mid;
  }
  printf("%.10f", (double)l);
}
