Problem:
Score : 300 points

Problem Statement

There are N+1 towns. The i-th town is being attacked by A_i monsters.

We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.

What is the maximum total number of monsters the heroes can cooperate to defeat?

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N

Output

Print the maximum total number of monsters the heroes can defeat.

Sample Input 1

2
3 5 2
4 5

Sample Output 1

9

If the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result.

The first hero defeats two monsters attacking the first town and two monsters attacking the second town.

The second hero defeats three monsters attacking the second town and two monsters attacking the third town.

Sample Input 2

3
5 6 3 8
5 100 8

Sample Output 2

22

Sample Input 3

2
100 1 1
1 100

Sample Output 3

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

#if true
//#if false
#define UTAKA_DEBUG
#endif

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using static System.Math;


namespace UtakaApp
{
    public class Program
    {
        public const string ContestName = "abc135";
        public const string ProblemName = "C";

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
            new TestCaseChecker().TestProblems();
#else
            new Program().Solve(Console.In, new ConsoleWriter());
#endif
        }

        public void Solve(TextReader textReader, IConsoleWriter consoleWriter)
        {
            var cin = new ConsoleInput(textReader, ' ');

            var n = cin.ReadInt;
            var a = cin.ReadIntArray(n + 1);
            var b = cin.ReadIntArray(n);

            var total = 0;

            var killedByFormer = Min(b[0], a[0]);

            total += killedByFormer;

            var remainPowerOfFormer = b[0] - killedByFormer;

            Dbg.WriteLine($"{0} {0} {killedByFormer}");

            for (int i = 1; i < n; i++)
            {
                killedByFormer = Min(remainPowerOfFormer, a[i]);

                total += killedByFormer;

                var rest = a[i] - killedByFormer;

                var killedByLatter = Min(rest, b[i]);

                total += killedByLatter;

                remainPowerOfFormer = b[i] - killedByLatter;

                Dbg.WriteLine($"{i} {killedByFormer} {killedByLatter}");
            }

            var lastKill = Min(remainPowerOfFormer, a[n]);
            
            Dbg.WriteLine($"{n} {lastKill} -");

            total += lastKill;

            consoleWriter.WriteLine(total.ToString());
        }
    }

    public class ConsoleInput
    {
        private readonly TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;

        public ConsoleInput(TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                {
                    inputStream.Enqueue(tmp[i]);
                }

                return inputStream.Dequeue();
            }
        }

        public string ReadLine => _stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => double.Parse(Read);

        public string[] ReadStrArray(long N)
        {
            var ret = new string[N];
            for (long i = 0; i < N; ++i) ret[i] = Read;
            return ret;
        }

        public int[] ReadIntArray(long N)
        {
            var ret = new int[N];
            for (long i = 0; i < N; ++i) ret[i] = ReadInt;
            return ret;
        }

        public long[] ReadLongArray(long N)
        {
            var ret = new long[N];
            for (long i = 0; i < N; ++i) ret[i] = ReadLong;
            return ret;
        }
    }

    public interface IConsoleWriter
    {
        void Write(string str);
        void WriteLine(string str);
    }

    public class ConsoleWriter : IConsoleWriter
    {
        public void Write(string str)
        {
            Console.Write(str);
        }

        public void WriteLine(string str)
        {
            Console.WriteLine(str);
        }
    }

#if UTAKA_LOCAL

    public class DebugConsoleWriter : IConsoleWriter
    {
        private StringBuilder mSb;

        public DebugConsoleWriter()
        {
            mSb = new StringBuilder();
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

    public class TestCaseChecker
    {
        private string DirectoryPath => $"../../../../{Program.ContestName}/{Program.ProblemName}";

        private string GetInputFilePath(int testCaseNumber)
        {
            return $"{DirectoryPath}/in_{testCaseNumber}.txt";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            return $"{DirectoryPath}/out_{testCaseNumber}.txt";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);

            var debugConsoleWriter = new DebugConsoleWriter();

            new Program().Solve(inputStream, debugConsoleWriter);

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var outputAnswer = outputStream.ReadToEnd();

#if UTAKA_DEBUG
            Console.Write(output);
            Console.Write(outputAnswer);
#endif

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems()
        {
            var isSuccessAll = true;

            var testCaseNumber = 1;
            while (true)
            {
                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    Console.WriteLine($"Success");
                }
                else
                {
                    isSuccessAll = false;
                    Console.WriteLine($"Failure *****");
                }

                testCaseNumber++;
            }

            if (isSuccessAll)
            {
                Console.WriteLine($"!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}