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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class A {

	public static void main(String[] args) {
		try (Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
				PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)))) {
			final int n = in.nextInt();
			final int[] a = new int[n], b = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = in.nextInt();
			}
			for (int i = 0; i < n; i++) {
				b[i] = in.nextInt();
			}
			out.println(solve(a, b));
		}
	}

	private static String solve(int[] a, int[] b) {
		long c = Arrays.stream(a).asLongStream().sum();
		int m1 = -1, m2 = 0, j = -1;
		for (int i = 0; i < b.length; i++) {
			if (b[i] > m1) {
				m1 = b[i];
				j = i;
			}
		}
		for (int i = 0; i < b.length; i++) {
			if (i != j) {
				m2 = Math.max(m2, b[i]);
			}
		}
		if (c <= m1 + m2) {
			return "YES";
		}
		return "NO";
	}

}