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.*;
import java.io.*;

    


public class Main
{
   static  class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            try {
                br = new BufferedReader(new InputStreamReader(f));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        
    }
    public static void main(String args[])
    {
         InputStream in=System.in;
       //  OutputStream out=System.out;
        FastScanner fs=new FastScanner(in);
        PrintWriter out=new PrintWriter(System.out);
       
         int n=fs.nextInt();
        int arr[]=new int[n];
        long rem=0;
        for(int i=0;i<n;i++)
        {
        arr[i]=fs.nextInt();
        rem=rem+arr[i];
        }
        arr[0]=fs.nextInt();
        long max=arr[0];
        long max1=0;
         for(int i=1;i<n;i++)
        {
        arr[i]=fs.nextInt();
         if(arr[i]>=max)
           { max1=max;
            max=arr[i];
        }
        if(arr[i]<max&&arr[i]>max1)
            max1=arr[i];

       
        }
        max=max+max1;
        if(max>=rem)
            out.println("YES");
        else
            out.println("NO");

    //   for(int i=0;i<n;i++)
      // System.out.println(arr[i]);
    out.close();
    }

}