One day Vasya was on a physics practical, performing the task on measuring the capacitance. He followed the teacher's advice and did as much as n measurements, and recorded the results in the notebook. After that he was about to show the results to the teacher, but he remembered that at the last lesson, the teacher had made his friend Petya redo the experiment because the largest and the smallest results differed by more than two times. Vasya is lazy, and he does not want to redo the experiment. He wants to do the task and go home play computer games. So he decided to cheat: before Vasya shows the measurements to the teacher, he will erase some of them, so as to make the largest and the smallest results of the remaining measurements differ in no more than two times. In other words, if the remaining measurements have the smallest result x, and the largest result y, then the inequality y ≤ 2·x must fulfill. Of course, to avoid the teacher's suspicion, Vasya wants to remove as few measurement results as possible from his notes.

Help Vasya, find what minimum number of measurement results he will have to erase from his notes so that the largest and the smallest of the remaining results of the measurements differed in no more than two times.

Input

The first line contains integer n (2 ≤ n ≤ 105) — the number of measurements Vasya made. The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 5000) — the results of the measurements. The numbers on the second line are separated by single spaces.

Output

Print a single integer — the minimum number of results Vasya will have to remove.

Examples

Input

6
4 5 3 8 3 7


Output

2


Input

4
4 3 2 4


Output

0

Note

In the first sample you can remove the fourth and the sixth measurement results (values 8 and 7). Then the maximum of the remaining values will be 5, and the minimum one will be 3. Or else, you can remove the third and fifth results (both equal 3). After that the largest remaining result will be 8, and the smallest one will be 4.
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.OutputStream;
import java.io.FileOutputStream;
import java.io.PrintWriter;
import java.io.FileInputStream;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author George Marcus
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream;
		try {
			inputStream = new FileInputStream("input.txt");
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
		OutputStream outputStream;
		try {
			outputStream = new FileOutputStream("output.txt");
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
	public void solve(int testNumber, InputReader in, PrintWriter out) {
        int N = in.nextInt();
        Integer[] c = new Integer[N];
        for(int i = 0; i < N; i++)
            c[i] = in.nextInt();
        Arrays.sort(c);

        int[] num = new int[5005];
        num[0] = 0;
        for(int i = 0; i < N; i++)
            num[c[i]]++;
        for(int i = 1; i <= 5000; i++)
            num[i] += num[i - 1];

        int min = Integer.MAX_VALUE;
        for(int i = 0; i <= 5000; i++) {
            int left = (i > 0 ? num[i - 1] : 0);
            int right = (2 * i <= 5000 ? num[5000] - num[2 * i] : 0);
            int crt = left + right;
            min = Math.min(min, crt);
        }

        out.println(min);
	}
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        return Integer.parseInt(nextString());
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    private boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    }

