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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class MainClarss
{
	public const long Giri = 1000000007;
	private static long r;
	private static void KillImpl(long[] a, Hero h, int target)
	{
		if(a[target]==0)
			return;
		
		if(h.AP == 0)
			return;
			
		if(h.AP-a[target]<0)
		{
			a[target]-=h.AP;
			r+=h.AP;
			//Console.WriteLine(h.ID+":+"+h.AP);
			h.AP=0;
		}
		else
		{
			h.AP-=a[target];
			r+=a[target];
			//Console.WriteLine(h.ID+":+"+a[target]);
			a[target]=0;
		}
	}
	
	private static void KillMax(long[] a, Hero h, int before, int next)
	{
		if(a[before] == 0)
		{
			KillImpl(a, h, next);
			return;
		}
		
		if(a[next] == 0)
		{
			KillImpl(a, h, before);
			return;
		}
		
		if(a[before] > a[before])
		{
			KillImpl(a, h, before);
		}
		else
		{
			KillImpl(a, h, next);
		}

	}
	
	private static void KillMin(long[] a, Hero h, int before, int next)
	{
		if(a[before] == 0)
		{
			KillImpl(a, h, next);
			return;
		}
		
		if(a[next]==0)
		{
			KillImpl(a, h, before);
			return;
		}
		
		if(h.ID-1<0)//左端
		{
			KillImpl(a,h,before);
			return;
		}
		
		if(h.ID+1>=a.Length)//右端
		{
			KillImpl(a,h,next);
			return;
		}
		
		long mae = a[h.ID-1];
		long usiro = a[h.ID+1];
		
		if(mae==usiro)
		{
			if(a[before] < a[before])
		{
			KillImpl(a, h, before);
		}
		else
		{
			KillImpl(a, h, next);
		}
		return;
		}
		if(mae>usiro)
		{
			KillImpl(a,h,next);
		}
		else
		{
			KillImpl(a,h,before);
		}
		
	}
	
	public static void Main(string[] args)
	{
		int n = int.Parse(Console.ReadLine());
		string[] io = Input();
		long[] a = new long[n+1];
		long[] a2 = new long[n+1];
		List<Hero> heros = new List<Hero>(n);
		List<Hero> heros2 = new List<Hero>(n);
		
		for(int i = 0; i < n+1; i++)
		{
			a[i] = long.Parse(io[i]);
			a2[i] = long.Parse(io[i]);
		}
		io = Input();
		for(int i = 0; i < n; i++)
		{
			long ap = long.Parse(io[i]);
			heros.Add(new Hero(){ ID=i, AP=ap});
			heros2.Add(new Hero(){ ID=i, AP=ap});
		}
		
		//heros.Sort((_a,b)=>(int)(b.AP-_a.AP));
		
		r = 0;
		for(int i = 0; i < n;i++)
		{
			Hero h = heros[i];
			int bf = h.ID;
			int ne = h.ID+1;
			
			//11kaime
			//tiisaihou
			/*
			KillMin(a, h, bf, ne);

			if(h.AP > 0)
			{
				KillMax(a, h, bf, ne);
			}
			*/
			
			KillImpl(a, h, bf);
			KillImpl(a, h, ne);
			
		}
		long maeR = r;
		for(int i = n-1; i >= 0;i--)
		{
			Hero h = heros[i];
			int bf = h.ID;
			int ne = h.ID+1;
			
			//11kaime
			//tiisaihou
			/*
			KillMin(a, h, bf, ne);

			if(h.AP > 0)
			{
				KillMax(a, h, bf, ne);
			}
			*/
			
			KillImpl(a, h, bf);
			KillImpl(a, h, ne);
			
		}
		
		
		Console.WriteLine(Math.Max(maeR,r));
	}
	
	class Hero
	{
		public int ID{get;set;}
		public long AP{get;set;}
	}
	
	
	public static long GCD(long a, long b)
	{
		if(b == 1)
			return a;
		long p = b / a;
		return GCD(a, b - a*p);
	}
	
	public static string[] Input()
	{
		return Console.ReadLine().Split(' ');
	}

	
	public static int Clamp(int val, int max, int min = 0)
	{
		return Math.Min(max, Math.Max(min, val));
	}

}