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 final class Main {


    public static void main(String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);

        StringTokenizer st = new StringTokenizer(br.readLine());

        int n = Integer.parseInt(st.nextToken());

        st = new StringTokenizer(br.readLine());

        long colaVolume = 0;
        for(int i = 0; i<n; i++){
            colaVolume += Integer.parseInt(st.nextToken());
        }


        st = new StringTokenizer(br.readLine());

        int maxCan = 0;
        int secondMaxCan = 0;
        for(int i = 0; i<n; i++){
            int bi = Integer.parseInt(st.nextToken());
            if(bi >= maxCan){
                secondMaxCan = maxCan;
                maxCan = bi;
            }else if(bi > secondMaxCan){
                secondMaxCan = bi;
            }
        }


        System.out.println(colaVolume-(maxCan+secondMaxCan) <= 0 ? "YES" : "NO");
    }
}