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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Demo {

    public static void main(String[] args) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());

        String[] tmp = br.readLine().split(" ");
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = Long.parseLong(tmp[i]);

        tmp = br.readLine().split(" ");
        long[] b = new long[n];
        for (int i = 0; i < n; i++)
            b[i] = Long.parseLong(tmp[i]);

        long total = 0;
        for (int i = 0; i < n; i++)
            total += a[i];

        Arrays.sort(b);

        if ((b[b.length-1] + b[b.length-2]) >= total)
            System.out.println("YES");
        else
            System.out.println("NO");

    }
}