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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

// http://codeforces.com/contest/890/problem/A
public class ProblemA {
	static Scanner sc = new Scanner(System.in);
	static int a[];

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		Long a[] = new Long[n];
		long sum = 0;
		for (int i = 0; i < n; i++) {
			sum += 1L * sc.nextInt();
		}
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextLong();
		}
		Arrays.sort(a);
		long x = a[a.length - 1] + a[a.length - 2];

		System.out.println(x >= sum ? "YES" : "NO");
		pw.flush();
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			// TODO Auto-generated constructor stub
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreElements())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public Long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}