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:
/* package whatever; // don't place package name! */
 
import java.util.*;
import java.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class bbg
{
	public static int result;
 
public static ArrayList<Integer> [] graph;
 
public static int[]cats;
 
public static int vizitat[];
public static int x;
//public static HashMap<String, Integer> map2;
 
 
	public static void main (String[] args) throws java.lang.Exception
{
 
Scanner input=new Scanner(System.in);
 
HashMap<Integer, Integer> contor1= new HashMap<Integer, Integer>();
HashMap<Integer, Integer> contor2= new HashMap<Integer, Integer>();


HashMap<Integer, Integer> map= new HashMap<Integer, Integer>();
HashMap<String, Integer> map2= new HashMap<String, Integer>();
HashMap<String, Integer> combinari= new HashMap<String, Integer>();
 
		
		int n=input.nextInt();
		
		int []v=new int[n];
		int []r=new int[n];
		
		Long sum=0L;
		
		for(int i=0;i<n;i++) {v[i]=input.nextInt();
		
		sum+=v[i];
		
		}
		
		for(int i=0;i<n;i++) r[i]=input.nextInt();
		
		Arrays.sort(r);
		
		Long tot=1l*(r[n-1]+r[n-2]);
		
		if(tot>=sum) System.out.println("YES");
		else 
		System.out.println("NO");
		
		
		
		}
		
		
		
		
		
		
		
	
		}