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.*;
import java.util.*;

public class Solution{ 

	
 public static void main(String[] args) {
     
     Scanner in = new Scanner(System.in);
     
     int n,i,max1_index=0,max1=-1,max2=-1;
     long sum=0;
     int[] a,b;
     boolean work=false;
     
     n=in.nextInt();
     
     a=new int[n+1];
     b=new int[n+1];
     
     
     for(i=1;i<=n;i++){
    	 a[i]=in.nextInt();
    	 sum+=(long)a[i];
     }
     
     for(i=1;i<=n;i++){
    	 b[i]=in.nextInt();
     }
     
     for(i=1;i<=n;i++){
    	 if(b[i]>max1){
    		 max1=b[i];
    		 max1_index=i;
    	 }
     }
     
   
     
     for(i=1;i<=n;i++){
    	 if(i==max1_index)continue;
    	 if(b[i]>max2){
    		 max2=b[i];
    	 }
     }
     
     if(sum<=max1+max2) work=true;
     
     
     if(work){
    	 System.out.println("YES");
     }
     else{
    	 System.out.println("NO");
     }
     
     
     
     
     
 }
}