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.util.Arrays;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.Random;
import java.util.StringTokenizer;
 
public class ProblemB {
	public static void main(String[] args) throws IOException {
		solve();
 
	}
 
 
 
	public static void solve() throws IOException {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int vol [] = new int[n];
		int cap[] = new int[n];
		long sum=0;
		for(int i=0;i<n;i++) {
			sum+=sc.nextLong();
		}
		for(int i=0;i<n;i++) {
			cap[i]=sc.nextInt();
		}
		shuffle(cap);
		Arrays.sort(cap);
		if(sum<=cap[cap.length-1]+cap[cap.length-2]) {
			System.out.println("YES");
		}else {
			System.out.println("NO");
		}
		
		
		
		
		
		
		
		
		
		
		}
	
	
	

		
	
	
	
	
	
	
	
	static void shuffle(int[] a)
	{
		int n = a.length;
		for(int i = 0; i < n; i++)
		{
			int r = i + (int)(Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}
	static class Pair{
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + end;
			result = prime * result + start;
			return result;
		}
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (end != other.end)
				return false;
			if (start != other.start)
				return false;
			return true;
		}
		int start;
		int end;
		public Pair(int s,int e) {
			start=s;
			end=e;
		}
	}
 
 
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s){
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		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());}
 
		public String nextLine() throws IOException {return br.readLine();}
 
		public double nextDouble() throws IOException
		{
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if(x.charAt(0) == '-')
			{
				neg = true;
				start++;
			}
			for(int i = start; i < x.length(); i++)
				if(x.charAt(i) == '.')
				{
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				}
				else
				{
					sb.append(x.charAt(i));
					if(dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg?-1:1);
		}
 
		public boolean ready() throws IOException {return br.ready();}
	}
 
}