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.InputStreamReader;
import java.util.*;
import java.io.*;
import java.util.StringTokenizer;
 
public class cocacola{
    public static void main(String[] args){
        FastReader scan=new FastReader();
        PrintStream p = System.out;
        int n = scan.nextInt();
        long arr[] = new long[n];
        long sum=0;
        for(int i=0;i<n;i++){
            sum += scan.nextInt();
        }
        for(int i=0;i<n;i++){
            arr[i] = scan.nextLong();  
        }
        Arrays.sort(arr);
        long cap = arr[n-1]+arr[n-2];
        if(cap>=sum){
            p.println("YES");
        }else{
            p.println("NO");
        }
        //p.println(sum+" "+cap);
    }
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader(){
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt(){
            return Integer.parseInt(next());
        }
 
        long nextLong(){
            return Long.parseLong(next());
        }
 
        double nextDouble(){
            return Double.parseDouble(next());
        }
 
        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }
            catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }
    }
}