import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }




void main() {
  try {
    for (; ; ) {
      const N = readInt;
      auto A = new real[N];
      foreach (i; 0 .. N) {
        A[i] = readReal;
      }
      auto B = new real[N];
      foreach (i; 0 .. N) {
        B[i] = readReal;
      }
      
      int len;
      auto as = new real[N];
      auto bs = new real[N];
      auto xs = new real[N];
      foreach (i; 0 .. N) {
        real a = A[i];
        real b = B[i];
        real x = max(sqrt(a / b), 1.0L);
        for (; len >= 1 && xs[len - 1] > x; ) {
          --len;
          a += as[len];
          b += bs[len];
          x = max(sqrt(a / b), 1.0L);
        }
        as[len] = a;
        bs[len] = b;
        xs[len] = x;
        ++len;
      }
      debug {
        writeln("as = ", as[0 .. len]);
        writeln("bs = ", bs[0 .. len]);
        writeln("xs = ", xs[0 .. len]);
      }
      
      real ans = 0.0L;
      foreach (j; 0 .. len) {
        ans += as[j] / xs[j] + bs[j] * xs[j];
      }
      writefln("%.12f", ans);
    }
  } catch (EOFException e) {
  }
}