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.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;

public class A {

	public static void main(String[] args) {
		FS in = new FS();
		int n = in.nextInt();
		long vol = 0;
		long cap[] = new long[n];
		for(int i = 0; i < n; i++) {
			vol+=in.nextLong();
		}
		for(int i = 0; i < n; i++) {
			cap[i] = in.nextLong();
		}
		Arrays.sort(cap);
		if(vol <= cap[n-1]+cap[n-2]) System.out.println("YES");
		else System.out.println("NO");
		
		
	}
	
	
	
	
	static class FS{
		BufferedReader br;
		StringTokenizer st;
		public FS() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String nextToken() {
			while(st == null || !st.hasMoreElements()) {
				try {st = new StringTokenizer(br.readLine());}
				catch(IOException e) { e.printStackTrace();}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
		long nextLong() {return Long.parseLong(nextToken());}
		double nextDouble() {return Double.parseDouble(nextToken());}
		String next() {
			return nextToken();
		}
	}
}