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.Arrays;
import java.util.Scanner;
/**
 * 
 * 作者：张宇翔 创建日期：2017年10月23日 下午1:24:36 描述：
 */
public class AndroidTest {
	private static final int Max=(int) (2e5+10);
	private static final int MOD=(int) (1e9+7);
	private static int n;
	private static int []a;
	private static int []b;
	private static long sum;
	public static void main(String[] args) {
		InitData();
		GetAns();
	}
	private static void InitData(){
		Scanner cin=new Scanner(System.in);
		n=cin.nextInt();
		a=new int[Max];
		b=new int[Max];
		sum=0;
		for(int i=0;i<n;i++){
			a[i]=cin.nextInt();
			sum+=a[i];
		}
		for(int i=0;i<n;i++){
			b[i]=cin.nextInt();
		}
		Arrays.sort(b,0,n);
	};
	private static void GetAns(){
		if(b[n-2]+b[n-1]>=sum){
			System.out.println("YES");
		}else{
			System.out.println("NO");
		}
	};
}