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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.stream.Stream;

/**
 * Success is not final, failure is not fatal. The courage to continue is what counts.
 * @author bodmas
 */
public class ProblemA {

    private boolean solve(int[] a, int[] b) {
        long remaining = 0;
        for (int i = 0; i < a.length; i++)
            remaining += a[i];
        Arrays.sort(b);
        return remaining <= 0L + b[b.length - 1] + b[b.length - 2];
    }

    public static void main(String[] args) throws IOException {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out))) {
            in.readLine();
            int[] a = Stream.of(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            int[] b = Stream.of(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            out.println(new ProblemA().solve(a, b) ? "YES" : "NO");
        }
    }
}