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.HashSet;
import java.util.Iterator;
import java.util.StringTokenizer;

public class P {

	static class Pair implements Comparable<Pair> {
		int r, c;

		Pair(int i, int j) {
			r = i;
			c = j;
		}

		@Override
		public int compareTo(Pair o) {
			if (c == o.c)
				return r - o.r;
			return c - o.c;
		}
	}

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

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int N = sc.nextInt();
		Pair[] c = new Pair[N];
		int[] a = new int[N], b = new int[N];
		for (int i = 0; i < N; ++i) {
			a[i] = sc.nextInt();
		}
		for (int i = 0; i < N; ++i) {
			b[i] = sc.nextInt();
		}
		for (int i = 0; i < N; ++i) {
			c[i] = new Pair(a[i], b[i]);
		}
		Arrays.sort(c);
		long rem = 0;
		for (int i = 0; i < N - 2; ++i)
			rem += c[i].r;
		if ((long) (c[N - 1].c + c[N - 2].c - c[N - 1].r - c[N - 2].r) >= rem)
			System.out.println("YES");
		else
			System.out.println("NO");
		out.flush();
		out.close();

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String file) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(file));
		}

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

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

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

}