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.*;
public class Card {
	public static void main(String [] args) {
	      Scanner in = new Scanner(System.in);
	      long n = in.nextLong();
	      long amount = 0;
	      long max=0;
	      long max2 = 0;
	      for(int i=0;i<n;i++) {
	    	  amount+=in.nextLong();
	    }
	      
	      for(int i=0;i<n;i++) {
	    	  long c = in.nextLong();

	    	  
	    	  if(max<c) {
	    		  long t = max;
	    		  max=c;
	    		  max2=t;
	    	  }
	    	  else if(max2<c) {
	    		  max2=c;
	    	  
	      }
	      
	}
	      System.out.println(max+max2>=amount ? "YES" : "NO");


}

}