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.Scanner;

/**
 * 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!
 */
public class GreedCola {

	/**
	 * Test cases:
	 * 
	 * 2 3 5 3 6 -> YES
	 * 
	 * 3 6 8 9 6 10 12 -> NO
	 * 
	 * 5 0 0 5 0 0 1 1 8 10 5 -> YES
	 * 
	 * 4 4 1 0 3 5 2 2 3 -> YES
	 * 
	 */
	public static void main(String[] args) {
		try (Scanner s = new Scanner(System.in)) {
			int numCans = s.nextInt();
			long sumCola = 0;
			// Find the total amount of Cola we need to distribute.
			for (int i = 0; i < numCans; i++) {
				sumCola += s.nextInt();
			}
			// Find the two biggest can holders.
			int max = 0;
			int max2 = 0;
			for (int i = 0; i < numCans; i++) {
				int currentCan = s.nextInt();
				if (currentCan > max) {
					max2 = max;
					max = currentCan;
				} else if (currentCan > max2) {
					max2 = currentCan;
				}
			}
			if (max + max2 >= sumCola) {
				System.out.println("YES");
			} else {
				System.out.println("NO");
			}
		}
	}

}