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.lang.reflect.Array;
import java.util.Arrays;
import java.util.StringTokenizer;

public class A {
	public static void main(String[] args) throws FileNotFoundException {
		int toFile = 0;
		InputStream inputStream;
		OutputStream outputStream;
		if (toFile == 0) {
			inputStream = System.in;
			outputStream = System.out;
		} else {
			inputStream = new FileInputStream(new File("A.in"));
			outputStream = new FileOutputStream(new File("A.out"));
		}
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(in, out);
		out.close();
	}

	static class TaskA {

		public void solve(InputReader in, PrintWriter out) {
			int n = in.nextInt();
			long a[] = new long[n];
			long b[] = new long[n];
			long c[] = new long[n];

			for (int i=0; i<n; i++)
				a[i] = in.nextInt();

			for (int i=0; i<n; i++) {
				b[i] = in.nextInt();
				c[i] = b[i];
			}

			Arrays.sort(c);

			long sum = 0;
			for (int i=0; i<n; i++)
				sum += a[i];

			if (sum > c[n - 1] + c[n - 2])
				out.print("NO");
			else
				out.print("YES");
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}
}