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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class A {
	
	public static void main(String[] args) throws IOException{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		long sum = 0;
		for(int i = 0; i < n; i++)
			sum += sc.nextInt();
		
		int[] b = new int[n];
		for(int i = 0; i < n; i++)
			b[i] = sc.nextInt();
		Arrays.sort(b);
		
		out.println(sum <= b[n-1] + b[n-2]? "YES" : "NO");
		out.flush();
		out.close();
	}
	
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
		Scanner(String file) throws FileNotFoundException {br = new BufferedReader(new FileReader(file));}
		String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		String nextLine()throws IOException{return br.readLine();}
		int nextInt() throws IOException {return Integer.parseInt(next());}
		double nextDouble() throws IOException {return Double.parseDouble(next());}
		char nextChar()throws IOException{return next().charAt(0);}
		Long nextLong()throws IOException{return Long.parseLong(next());}
		boolean ready() throws IOException{return br.ready();}
		void waitForInput(){for(long i = 0; i < 3e9; i++);}
	}
}