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 JavaApplication173 {

   

    public static void main(String[] args){
     Scanner sc = new Scanner(System.in);

     int n = sc.nextInt();
     int a[] = new int[n];
     int max1 = 0;
     int max2 = 0;
     for(int i=0; i<n; i++){
         a[i]= sc.nextInt();
         }
     for(int i=0; i<n; i++){
         int x = sc.nextInt();
         if(i%2 == 0){
             max1 = Math.max(x, max1);
         }else{
             max2 = Math.max(max2, x);
         }
     }
     long s = (max2 + max1);

     for(int i=0; i<n; i++){
         s -= a[i];
         if(s < 0){
             System.out.println("NO"); return;
         }
     }
     System.out.println("YES");
     

     
    }
}