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.util.Arrays;
import java.util.IntSummaryStatistics;
import java.util.LongSummaryStatistics;

public class prb1 {

	  private static final Scanner scanner = new Scanner(System.in);

	    public static void main(String[] args) {

	    	int number = scanner.nextInt();
	    	int[] volume_rem_l=new int[number];
	    	int [] capacity_l=new int[number];

	    	for (int i=0;i<number;i++){
//	    		String volume_rem = scanner.nextLine();
	    		int volume_rem=scanner.nextInt();
	    		volume_rem_l[i]=volume_rem;



	    	}
	    	for (int i=0;i<number;i++){
//	    		String capacity = scanner.nextLine();
//	    		capacity_l[i]=Long.parseLong(capacity);
	    		int capacity=scanner.nextInt();
	    		capacity_l[i]=capacity;


	    	}

//	    	System.out.print (max(capacity_l));
//	    	System.out.print (twoLargest(capacity_l)[0]+" "+twoLargest(capacity_l)[1] );

	    	if (twoLargest(capacity_l)[0]+twoLargest(capacity_l)[1]>= sum(volume_rem_l)){
	    		System.out.print("YES");
	    	}
	    	else System.out.print("NO");
//	    	if

//


	    }


static int max(int[] tab){

    IntSummaryStatistics stat = Arrays.stream(tab).summaryStatistics();
    int max = (int) stat.getMax();
//    System.out.println("Min = " + min);
//    System.out.println("Max = " + max);

    return max;
}

public static int[] twoLargest(int values[]){
    int largestA = Integer.MIN_VALUE, largestB = Integer.MIN_VALUE;

    for(int value : values) {
        if(value > largestA) {
            largestB = largestA;
            largestA = value;
        } else if (value > largestB) {
            largestB = value;
        }
    }
    return new int[] { largestA, largestB };
}
static long sum(int[] array ){
	long sum=0;
	for (int i=0;i<array.length;i++){
		sum+=array[i];
	}
	return sum;
}
}