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:
/*
 * Remember a 7.0 student can know more than a 9.8 student.
 * Grades don't determine intelligence, they test obedience. 
 * I Never Give Up.
 */
import java.util.*;
import java.io.*;
import java.util.Comparator.*;

import static java.lang.System.out;
import static java.util.Arrays.sort;
//import static java.lang.Math.pow;
//import static java.lang.Math.sqrt;
//import static java.lang.Math.ceil;
//import static java.lang.Math.abs;
import static java.lang.Math.min;
import static java.lang.Math.max;
//import static java.lang.Math.floor;
public class ContestMain {
	private static long MOD=1000000007;//10^9+7 
	private static final int N=(int)200005; //20006
	private static ArrayList<Integer> v[]=new ArrayList[N];
	private static long color[]=new long[2];
	private static boolean mark[]=new boolean [N];
//	static int choice=Integer.MAX_VALUE,trav=Integer.MAX_VALUE;
	static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	
	public static void solve(int ar[],int n){
	}
	
	public static void main(String[] args) throws IOException{
		int n=Integer.parseInt(br.readLine());
		long ar[]=new long[n];
		long cp[]=new long[n];
		long v=0l;
		String s[]=br.readLine().split(" ");
		for(int i=0;i<n;i++)
			v+=Long.parseLong(s[i]);
		s=br.readLine().split(" ");
		for(int i=0;i<n;i++){
			cp[i]=Long.parseLong(s[i]);
		}
		Arrays.sort(cp);
		//out.println(cp[n-1]+" "+cp[n-2]);
		if(cp[n-1]+cp[n-2]>=v)out.println("YES");
		else out.println("NO");
	}
}