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.*;
import java.io.*;

public class Codeforces{

	static class MyScanner{
		BufferedReader br;
		StringTokenizer st;

		MyScanner(){
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nn(){
			while(st == null || !st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				}catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int ni(){
			return Integer.parseInt(nn());
		}

		long nl(){
			return Long.parseLong(nn());
		}

		double nd(){
			return Double.parseDouble(nn());
		}
	}

	private static PrintWriter out;

	public static void main(String[] args) throws FileNotFoundException{

		MyScanner sc = new MyScanner();
		out = new PrintWriter(new BufferedOutputStream(System.out));

		int n = sc.ni();
		long coke = 0;
		for(int i = 0; i < n; i++){
			coke += sc.nl();
		}

		long max1 = 0, max2 = 0;

		for(int i = 0; i < n; i++){
			long a = sc.nl();
			if(a > max1){
				max2 = max1;
				max1 = a;
			}else if(a > max2){
				max2 = a;
			}
		}

		out.println(max1 + max2 >= coke? "YES": "NO");

		out.close();
	}
}