using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var p = Enumerate(n, x => sc.Double() / 1000); var q = Enumerate(n, x => sc.Double() / 100); var pq = new PriorityQueue>((l, r) => r.Value.CompareTo(l.Value)); for (int i = 0; i < n; i++) pq.Enqueue(new KeyValuePair(i, p[i] * q[i])); var ans = 0.0; for (int _ = 1; _ <= 100000; _++) { var x = pq.Dequeue(); ans += _ * x.Value; pq.Enqueue(new KeyValuePair(x.Key, (1 - q[x.Key]) * x.Value)); } IO.Printer.Out.WriteLine("{0:0.000000000000}",ans); } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, IEnumerable source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, IEnumerable source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region PriorityQueue and PairingHeap public class PriorityQueue { PairingHeap top; Comparison compare; int size; public int Count { get { return size; } } public PriorityQueue() : this(Comparer.Default) { } public PriorityQueue(Comparison comparison) { compare = comparison; } public PriorityQueue(IComparer comparer) { compare = comparer.Compare; } public void Enqueue(T item) { var heap = new PairingHeap(item); top = PairingHeap.Merge(top, heap, compare); size++; } public T Dequeue() { var ret = top.Key; size--; top = PairingHeap.Pop(top, compare); return ret; } public bool Any() { return size > 0; } public T Peek() { return top.Key; } } #region PairingHeap public class PairingHeap { public PairingHeap(T k) { key = k; } private readonly T key; public T Key { get { return key; } } private PairingHeap head; private PairingHeap next; static public PairingHeap Pop(PairingHeap s, Comparison compare) { return MergeLst(s.head, compare); } static public PairingHeap Merge(PairingHeap l, PairingHeap r, Comparison compare) { if (l == null || r == null) return l == null ? r : l; if (compare(l.key, r.key) > 0) Swap(ref l, ref r); r.next = l.head; l.head = r; return l; } static public PairingHeap MergeLst(PairingHeap s, Comparison compare) { var n = new PairingHeap(default(T)); while (s != null) { PairingHeap a = s, b = null; s = s.next; a.next = null; if (s != null) { b = s; s = s.next; b.next = null; } a = Merge(a, b, compare); a.next = n.next; n.next = a; } while (n.next != null) { var j = n.next; n.next = n.next.next; s = Merge(j, s, compare); } return s; } static void Swap(ref PairingHeap l, ref PairingHeap r) { var t = l; l = r; r = t; } } #endregion #endregion