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;
import java.util.Arrays;

/**
 * Created by Kowshika Sarker on 11/26/2017.
 */
public class A892 {
    public static void main(String[] args) {
        int i, j, can, left[], size[];
        long allLeft=0;
        Scanner scanner = new Scanner(System.in);
        can = scanner.nextInt();
        if(can == 2)
        {
            System.out.println("YES");
            System.exit(0);
        }
        left = new int[can];
        size = new int[can];
        for(i=0; i<can; i++)
        {
            left[i] = scanner.nextInt();
            //left[i] = 1000000000;
            allLeft += left[i];
        }
        for(i=0; i<can; i++)
        {
            size[i] = scanner.nextInt();
            //size[i] = 1000000000;
        }
        //int j;
        Arrays.sort(size);
        if((size[can-1] + size[can-2]) >= allLeft)
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}