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 NewMain2 {

    public static void main(String[] args) {
        // TODO code application logic here
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        long[] volume = new long[n];
        long[] capacity = new long[n];
        long volume_sum = 0, capacity_two_sum = 0;
        String ans = "";
        for (int i = 0; i < n; i++) {
            volume[i] = s.nextLong();
            volume_sum += volume[i];
        }
        for (int i = 0; i < n; i++) {
            capacity[i] = s.nextLong();
        }
        if (n == 2) {
            System.out.println("YES");
        } else {
            Arrays.sort(capacity);
            capacity_two_sum += capacity[n - 1] + capacity[n - 2];
            if (capacity_two_sum < volume_sum) {
                System.out.println("NO");
            } else {
                System.out.println("YES");
            }
            //System.out.println(Arrays.toString(capacity) + "\n" + capacity_two_sum);
        }
    }

}