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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author Lotfi
 */
public class Train {
     public static void main(String[] arg) throws IOException{
        FastScanner sc = new FastScanner(System.in);
        long t= sc.nextLong();
        long rem=0;
        long capa=0;
        long cap[]= new long[(int)t];
        for(int i=0;i<t;i++){
            rem+=sc.nextLong();
        }
        for(int j=0;j<t;j++){
            cap[j]=sc.nextLong();
        }
        Arrays.sort(cap);
           capa=cap[cap.length-1]+cap[cap.length-2];
           if(capa>=rem){
               System.out.println("YES");
           }
           else{
               System.out.println("NO");
           }
     }
     
 public  static class FastScanner {
  private BufferedReader br;
  private StringTokenizer st;
  public FastScanner(InputStream inputStream){
    br = new BufferedReader(new InputStreamReader(inputStream));
  }
  public String nextLine() throws IOException{
      return br.readLine();
  }
  public String next() {
    while (st == null || !st.hasMoreTokens()){
      try {
        st = new StringTokenizer(br.readLine());
      } catch (IOException ignored){}
    }
    return st.nextToken();
  }
  public int nextInt() {
    return Integer.parseInt(next());
  }
  public long nextLong() {
    return Long.parseLong(next());
  }
 
}  
}