using System;
using System.Collections.Generic;
using System.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var t = consoleReader.Split.Double;
            var v = new List<double>(consoleReader.Split.Double) { 0 }.ToArray();
            for (int i = N - 1; i >= 0; i--)
                v[i] = Math.Min(v[i], v[i + 1] + t[i]);

            double distance = 0;
            double velocityStart = 0;
            double velocityEnd;
            for (int i = 0; i < t.Length; i++)
            {
                if (v[i] <= v[i + 1])
                {
                    if (velocityStart + t[i] < v[i])
                    {
                        velocityEnd = velocityStart + t[i];
                        distance += (velocityStart + velocityEnd) * t[i] / 2;
                    }
                    else
                    {
                        velocityEnd = v[i];
                        var accTime = velocityEnd - velocityStart;
                        distance += (velocityStart + velocityEnd) * accTime / 2 + (t[i] - accTime) * velocityEnd;
                    }
                }
                else
                {
                    if (velocityStart + t[i] < v[i + 1])
                    {
                        velocityEnd = velocityStart + t[i];
                        distance += (velocityStart + velocityEnd) * t[i] / 2;
                    }
                    else
                    {
                        var t1 = v[i] - velocityStart;
                        var t2 = t[i] + v[i + 1] - v[i];
                        velocityEnd = v[i + 1];
                        if (t1 <= t2)
                        {
                            distance += (velocityStart + v[i]) * t1 / 2;
                            distance += v[i] * (t2 - t1);
                            distance += (velocityEnd + v[i]) * (t[i] - t2) / 2;
                        }
                        else
                        {
                            var tx = (t[i] + velocityEnd - velocityStart) / 2;
                            var vx = velocityStart + tx;

                            distance += (velocityStart + vx) * tx / 2;
                            distance += (velocityEnd + vx) * (t[i] - tx) / 2;
                        }
                    }
                }
                velocityStart = velocityEnd;
            }
            return distance;
        }

        #region いつもの
#pragma warning disable
        private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    static class Ext
    {
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector)
            => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader
    {
        private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = ReadLineSplit();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            private string[] splited;
            public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String => splited;
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader : IEnumerable<ConsoleReader>
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator();
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator();

            public IEnumerable<string> String => this.Select(cr => cr.String);
            public IEnumerable<int> Int => this.Select(cr => cr.Int);
            public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1);
            public IEnumerable<long> Long => this.Select(cr => cr.Long);
            public IEnumerable<double> Double => this.Select(cr => cr.Double);
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
    #endregion
}

Measured memory_bytes: 13396