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.lang.reflect.Array;
import java.util.*;
import java.lang.*;
import java.math.*;
import java.util.concurrent.Callable;

public class MainA1 {

    static class TaskG {

        private void solve(int test, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            long sum = 0;
            for(int i = 0; i < n; i++){
                sum += in.nextInt();
            }
            ArrayList<Integer> arr = new ArrayList<>();
            for(int i = 0; i < n; i++){
                arr.add(in.nextInt());
            }
            Collections.sort(arr);
            if(arr.get(arr.size()-1) + arr.get(arr.size()-2) >= sum){
                out.println("Yes");
            }else{
                out.println("No");
            }
        }
    }

    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
//        FastScanner in = new FastScanner("eatpuz.in");
//        PrintWriter out = new PrintWriter(new FileWriter("eatpuz.out"));
        new TaskG().solve(1, in, out);
        out.close();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer token;

        public FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

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

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}