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;
import java.math.BigInteger;
import java.util.Arrays;

public class Greed{
    public static void main(String []args){
        //For Storing Problem Data.
        int canCount = Console.nextInt();
        BigInteger [] colaVolume   = new BigInteger [canCount];
        BigInteger [] colaCapacity = new BigInteger [canCount];
        //Getting Cola for each Can.
        BigInteger totalColaVolume = new BigInteger("0");
        for(int x = 0;x<canCount;++x){
            totalColaVolume = totalColaVolume.add(colaVolume[x] = Console.nextBigInteger());
        }
        //Getting Total Capacity for each Can.
        for (int x = 0;x<canCount;++x){
            colaCapacity[x] = Console.nextBigInteger();
        }
        //Sorting to find Cans with Highest Capacity.
        Arrays.sort(colaCapacity);
        BigInteger maxTwoCanCapacity = colaCapacity[canCount-1].add(colaCapacity[canCount-2]);
        //Verdict.
        if(maxTwoCanCapacity.compareTo(totalColaVolume)>=0){
            System.out.println("YES");
        }
        else System.out.println("NO");
    }
    public static final Scanner Console = new Scanner(System.in);
}