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.*;
import java.util.*;
public class a {
	public static void main(String[] arg) throws IOException {
		new a();
	}
	public a() throws IOException {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int[] vs = new int[n];
		long total = 0;
		for(int i = 0; i < n; i++) {
			total += in.nextInt();
		}
		for(int i = 0; i < n; i++) {
			vs[i] = in.nextInt();
		}
		Arrays.sort(vs);
		if(total <= vs[n-1]+vs[n-2]) out.println("YES");
		else out.println("NO");
		in.close(); out.close();
	}
	class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer("");
		}
		public void close() throws IOException {
			br.close();
		}
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		public String next() throws IOException {
			while(!st.hasMoreElements()) st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
	}
}