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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author MaxHeap
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n];
            int[] b = new int[n];
            TaskA.Can[] cans = new TaskA.Can[n];
            long sum = 0;
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
                sum += a[i];
            }
            for (int i = 0; i < n; i++) {
                b[i] = in.nextInt();
            }
            if (n <= 2) {
                out.println("YES");
                return;
            }
            ArrayUtils.sort(b);
            if (sum <= b[n - 2] + b[n - 1]) {
                out.println("YES");
            } else {
                out.println("NO");
            }
        }

        static class Can implements Comparable<TaskA.Can> {
            int cap;
            int value;

            public Can(int cap, int value) {
                this.cap = cap;
                this.value = value;
            }


            public int compareTo(TaskA.Can o) {
                return Integer.compare(value, o.value);
            }

        }

    }

    static class ArrayUtils {
        public static void sort(int[] arr) {
            int n = arr.length;
            Random r = new Random();
            for (int i = 0; i < n; i++) {
                int p = r.nextInt(n + 1);
                if (p < n) {
                    int temp = arr[i];
                    arr[i] = arr[p];
                    arr[p] = temp;
                }
            }
            Arrays.sort(arr);
        }

    }

    static class FastReader {
        BufferedReader reader;
        StringTokenizer st;

        public FastReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            st = null;
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if (line == null) {
                        return null;
                    }
                    st = new StringTokenizer(line);
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

    }
}