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.*;

public class A892 {
		
	public static void main(String[] args) 
	{
		Scanner sc=new Scanner(System.in);
		int len=sc.nextInt();
		long sum=0, max=-1;
		long[] a=new long[len];
		long[] b=new long[len];
		
		for(int i=0; i<len; i++)
		{
			a[i]=sc.nextLong();
			sum+=a[i];
		}
		
		int index=-1;
		for(int i=0; i<len; i++)
		{
			b[i]=sc.nextLong();
			if(b[i]>max)
			{
				max=b[i];
				index=i;
			}
		}
		
		long max2=-1;
		
		for(int i=0; i<len; i++)
		{
			if(b[i]>max2 && b[i]<=max && i!=index)
			{
				max2=b[i];
			}
			
		}
		
		if(sum>max2+max)
		{
			System.out.println("NO");
		}
		else
		{
			System.out.println("YES");
		}
		
		
		
		
	}
}