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.math.BigInteger;
import java.util.Scanner;

/**
 *
 * @author qqanyjuan
 *
 */
public final class A_892_Greed {

    /**
     * Private constructor so this utility class cannot be instantiated.
     */
    private A_892_Greed() {
    }

    /**
     * Main method.
     *
     * @param args
     *            the command line arguments
     */
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int cans = in.nextInt();
        BigInteger[] volume = new BigInteger[cans];
        for (int i = 0; i < cans; i++) {
            volume[i] = in.nextBigInteger();
        }
        BigInteger[] maxVol = new BigInteger[cans];
        for (int i = 0; i < cans; i++) {
            maxVol[i] = in.nextBigInteger();
        }
        BigInteger maxCan1 = BigInteger.ZERO;
        BigInteger maxCan2 = BigInteger.ZERO;
        int pos1 = 0;
        for (int i = 0; i < cans; i++) {
            if (maxVol[i].compareTo(maxCan1) > 0) {
                maxCan1 = maxVol[i];
                pos1 = i;
            }
        }
        for (int i = 0; i < cans; i++) {
            if (maxVol[i].compareTo(maxCan2) > 0 && pos1 != i) {
                maxCan2 = maxVol[i];
            }
        }

        BigInteger volumeTot = BigInteger.ZERO;
        for (int i = 0; i < volume.length; i++) {
            volumeTot = volumeTot.add(volume[i]);
        }

        if (volumeTot.compareTo(maxCan1.add(maxCan2)) <= 0) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }

        in.close();

    }

}