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 A {
        public static void main(String[] args) {
            
            String salida = "";
            Scanner scan = new Scanner(System.in);
            int numberOfCans = scan.nextInt();
            int actualCan = 0;
            int firstMayor = 0;
            int secondMayor = 0;
            long capacityCans = 0;          
            for (int i = 0; i < numberOfCans; i++) {
                capacityCans += scan.nextInt();
            }
            //System.out.println(capacityCans);
            for (int i = 0; i < numberOfCans; i++) {
               actualCan = scan.nextInt(); 
                //System.out.println(actualCan + "-*-");
                if (actualCan >= firstMayor) {
                    secondMayor = firstMayor;
                    firstMayor = actualCan;
                    //System.out.println(actualCan + "-1-" + firstMayor);
                }else if(actualCan >= secondMayor){
                     //System.out.println(actualCan + "-2-" + secondMayor);
                    secondMayor = actualCan;
                }
            }
            //System.out.println(firstMayor + "--" + secondMayor);
            if (capacityCans <= (firstMayor + secondMayor)) {
                salida = "YES";
            }else{
                salida = "NO";
            }
            System.out.print(salida);        
        } 
    
}