There are n kangaroos with pockets. Each kangaroo has a size (integer number). A kangaroo can go into another kangaroo's pocket if and only if the size of kangaroo who hold the kangaroo is at least twice as large as the size of kangaroo who is held.

Each kangaroo can hold at most one kangaroo, and the kangaroo who is held by another kangaroo cannot hold any kangaroos.

The kangaroo who is held by another kangaroo cannot be visible from outside. Please, find a plan of holding kangaroos with the minimal number of kangaroos who is visible.

Input

The first line contains a single integer — n (1 ≤ n ≤ 5·105). Each of the next n lines contains an integer si — the size of the i-th kangaroo (1 ≤ si ≤ 105).

Output

Output a single integer — the optimal number of visible kangaroos.

Examples

Input

8
2
5
7
6
9
8
4
2


Output

5


Input

8
9
1
6
2
6
5
8
3


Output

5
import java.util.*;

import java.io.*;


public class CF_373_C_COUNTING_KANGAROOS_IS_FUN {

	static boolean canTake(int [] a , int mid )
	{
		
		for(int i = 0 ; i < mid ; i++)
			if(a[i]<<1 > a[a.length - mid + i ])
				return false; 
		
		return true ;
		
	}

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		
		
		int []  a = new int [n];
		
		for(int i = 0 ; i < n ; i++)
			a[i] = sc.nextInt();
		
		shuffle(a);
		
		Arrays.sort(a);
		
		int start = 0 ; 
		int end = n/2;
		int ans = 0 ; 
		
		while(start <= end)
		{
			int mid = (start + end) >> 1 ;
			
			if(canTake(a, mid))
			{
				start = mid + 1 ; 
				ans = mid ;
			}else 
				end = mid - 1;
			
		}
		
		System.out.println(n - ans);
		
	}
	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 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();
		}

	}

}