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;

public class Greed {
public static void main(String[] args) {
	Scanner scan = new Scanner(System.in);
	int colas = scan.nextInt();
	long sumRemaining = 0;
	for(int i = 0;i<colas;i++)
	{
		sumRemaining+=scan.nextInt();
	}
	int num = scan.nextInt();
	long max1 = num;
	long max2 = num;
	long num2 = num;
	for(int i = 1;i<colas;i++)
	{
		num = scan.nextInt();
		max1 = Math.max(num, max1);
		if(num2<max1)
			max2 = Math.max(num2, max2);
		num2 = num;
	}
	
	
	System.out.print((max1+max2)>=sumRemaining?"YES":"NO");
	return;
}
}