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 sun.nio.cs.ext.MacThai;

import java.io.*;
import java.util.*;

public final class Main {

    static int log(int x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

//    public void solveB(){
//        int n = in.nextInt();
//        PriorityQueue<Integer> q = new PriorityQueue<>();
//        for (int i = 0; i < n; i++){
//
//        }
//    }

    public void solve() {
        int n = in.nextInt();
        long sumB = 0;
        int tmp;
        for (int i = 0; i < n; i++){
            tmp = in.nextInt();
            sumB += tmp;
        }
        int maxA1 = 0, maxA2 = 0;
        for (int i = 0; i < n; i++){
            tmp = in.nextInt();
            if (tmp > maxA1){
                if (maxA1 > maxA2)
                    maxA2 = maxA1;
                maxA1 = tmp;
            }else if (tmp > maxA2)
                maxA2 = tmp;
        }

        if (sumB > maxA1 + maxA2)
            out.print("NO");
        else
            out.print("YES");
    }

    // —-----------I/O-----------— \\

    void run() {
        try {
            in = new FScanner(new File("input.txt"));
            out = new PrintWriter(new BufferedWriter(new FileWriter(new File("output.txt"))));
            solve();
            out.close();
            in.close();
        } catch (IOException ex) {
            ex.printStackTrace();
        }
    }

    void runIO() {
        in = new FScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        solve();
        out.close();
        in.close();
    }

    public static void main(String[] args) {
        new Main().runIO();
    }

    private FScanner in;
    private PrintWriter out;

    class FScanner {

        private BufferedReader br;
        private StringTokenizer st;

        public FScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException ex) {
                ex.printStackTrace();
            }
        }

        void useString(String s) {
            if (s != null) {
                st = new StringTokenizer(s);
            }
        }

        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 s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

        void close() {
            try {
                br.close();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
        }

    }

    class Pair<X, Y> implements Comparable<Pair<X, Y>> {

        public X first;
        public Y second;

        public Pair(X first, Y second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public int hashCode() {
            int hash = 7;
            hash = 11 * hash + Objects.hashCode(this.first);
            hash = 11 * hash + Objects.hashCode(this.second);
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj) {
                return true;
            }
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Pair<?, ?> other = (Pair<?, ?>) obj;
            if (!Objects.equals(this.first, other.first)) {
                return false;
            }
            if (!Objects.equals(this.second, other.second)) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Pair<X, Y> p) {
            return -((Comparable<X>) first).compareTo(p.first);
        }

        @Override
        public String toString() {
            return first + " " + second;
        }
    }

    static class Library {
        public static boolean isPrime(int n) {
            for (int i = 2; i * i <= n; i++)
                if (n % i == 0)
                    return false;
            return true;
        }


        public static long gcd(long a, long b) {
            if (b == 0) return a;
            return gcd(b, a % b);
        }

        public static long lcm(long a, long b) {
            return a / gcd(a, b) * b;
        }


    }
}