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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution {
    public static void main(String arg[]){
        int n;
        Scanner sc=new Scanner(System.in);
      n=sc.nextInt();
        int max1=0,max2=0;
        int a,b;
        int A[]=new int [n];
        int B[]=new int[n];
       
        long count=0;
        for(int i=0;i<n;i++){
            a=sc.nextInt();
            A[i]=a;
            count+=a;
        }
        for(int i=0;i<n;i++){
            b=sc.nextInt();
            B[i]=b;
        }
        Arrays.sort(B);
        //System.out.println(Arrays.toString(B));
        if(B[n-1]+B[n-2]>=count){
            System.out.println("YES");
        }
        else{
            System.out.println("NO");
        }
    }
}