Problem: Jafar has n cans of cola. Each can is described by two integers: remaining volume of cola ai and can's capacity bi (ai ≤  bi).

Jafar has decided to pour all remaining cola into just 2 cans, determine if he can do this or not!

Input

The first line of the input contains one integer n (2 ≤ n ≤ 100 000) — number of cola cans.

The second line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 109) — volume of remaining cola in cans.

The third line contains n space-separated integers that b1, b2, ..., bn (ai ≤ bi ≤ 109) — capacities of the cans.

Output

Print "YES" (without quotes) if it is possible to pour all remaining cola in 2 cans. Otherwise print "NO" (without quotes).

You can print each letter in any case (upper or lower).

Examples

Input

2
3 5
3 6


Output

YES


Input

3
6 8 9
6 10 12


Output

NO


Input

5
0 0 5 0 0
1 1 8 10 5


Output

YES


Input

4
4 1 0 3
5 2 2 3


Output

YES

Note

In the first sample, there are already 2 cans, so the answer is "YES".

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Rough {
	
	public static void main(String[] args) 
	{   Scanner sc= new Scanner(System.in);
		int n=sc.nextInt();
		long cap[]= new long[n];
		long total=0;
		
		for(int i=0;i<n;i++)
			total+=sc.nextLong();
		for(int i=0;i<n;i++)
			cap[i]=sc.nextLong();
		
		
		System.out.println(TwoSum(cap,total));
	    sc.close();		
	}
	
	public static String TwoSum(long a[], long x)
    { Arrays.sort(a);
    
      
	  int j=a.length-1;
	  if(j==1)
		  return "YES";
	  
      int i=0;
       
       while(i<j)
        {
            if(a[i]+a[j]<x)
              i++;
            else if(a[i]+a[j]>=x)
              return "YES";
        }
        
        return "NO";
       
    }
}