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 HelloWorld{

     public static void main(String []args)throws IOException{
        //System.out.println("Hello World");
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine());
        int a[]=new int[t];
        int b[]=new int[t];            StringTokenizer st=new StringTokenizer(br.readLine());
int max1,max2;long res;res=max1=max2=0;
        for(int i=0;i<t;i++)
        {
            a[i]=Integer.parseInt(st.nextToken());
                        res=res+(a[i]);

        }
                    StringTokenizer st1=new StringTokenizer(br.readLine());

        for(int i=0;i<t;i++)
        {
            b[i]=Integer.parseInt(st1.nextToken());
            if(b[i]>max1)
            {
                max2=max1;
                max1=b[i];
            }
            else if(b[i]>max2)
            {
                max2=b[i];
            }
            
        }
        //System.out.println(res+" "+max1+" "+max2);
        if((max1+max2)>=res)System.out.println("YES");
        else System.out.println("NO");
     }
}