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.Scanner;

public class A892 {
    public static void main(String ... args)
    {
        Scanner sc = new Scanner(System.in);
        int i, n=sc.nextInt();
        long max1=0, max2=0, total=0;
        long[] remain = new long[n];
        long[] capacity = new long[n];

        for (i=0; i<n; i++)
        {
            remain[i]=sc.nextLong();
            total+=remain[i];
        }

        for (i=0; i<n; i++)
        {
            capacity[i]=sc.nextInt();
            if (capacity[i]>max2)
            {
                if (capacity[i]>max1)
                {
                    max2=max1;
                    max1=capacity[i];
                }
                else
                    max2=capacity[i];
            }
        }

        if ((max1+max2)<total)
            System.out.println("NO");
        else
            System.out.println("YES");
    }
}