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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		int cnt = 0,can;
		long totalcola =0;
		long sum=0;
		Scanner sc = new Scanner(System.in);
		can = sc.nextInt();
		int[] rem = new int[can];
		int[] cap = new int[can];
		for(int i=0;i<can;i++)
		{
		    rem[i] = sc.nextInt();
		    totalcola = totalcola + rem[i];
		}
		for(int i=0;i<can;i++)
		{
		    cap[i] = sc.nextInt();
		}
		Arrays.sort(cap);
		sum = cap[can-1] + cap[can-2];
		if(sum>= totalcola)
		{
		    System.out.println("Yes");
		}
		else 
		{
		    System.out.println("No");
		}
	}
}