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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		long sum=0;
		long [] cap=new long[100002];
		for(int i=0;i<n;i++) {
			sum+=in.nextLong();
		}
		for(int i=0;i<n;i++) {
			cap[i]=in.nextLong();
		}
		long max=0,smax=0;
		int count=0;
		for(int i=0;i<n;i++) {
			if(cap[i]>max) {
				max=cap[i];
				count=i;
			}
		}
		for(int i=0;i<n;i++) {
			if(cap[i]>smax&&i!=count) {
				smax=cap[i];
			}
		}
		System.out.println(sum<=smax+max?"YES":"NO");
	}

}