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.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

/**
 */
public class MainA {
	public static void main(String[] args) {
		run(System.in, System.out);
	}

	public static void run(InputStream in, PrintStream out) {

		try (Scanner sc = new Scanner(in)) {
			int n = sc.nextInt();
			long a = 0;
			for (int i = 0; i < n; i++) {
				a += sc.nextInt();
			}
			long b1 = 0;
			long b2 = 0;
			for (int i = 0; i < n; i++) {
				int b = sc.nextInt();
				if (b > b1 && b > b2) {
					b2 = b1;
					b1 = b;
				} else if (b > b2) {
					b2 = b;
				}
			}

			if (a <= (b1 + b2)) out.print("YES");
			else out.print("NO");

			out.print("");
		}
	}

}