Mr. F has n positive integers, a_1, a_2, …, a_n.

He thinks the greatest common divisor of these integers is too small. So he wants to enlarge it by removing some of the integers.

But this problem is too simple for him, so he does not want to do it by himself. If you help him, he will give you some scores in reward.

Your task is to calculate the minimum number of integers you need to remove so that the greatest common divisor of the remaining integers is bigger than that of all integers.

Input

The first line contains an integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of integers Mr. F has.

The second line contains n integers, a_1, a_2, …, a_n (1 ≤ a_i ≤ 1.5 ⋅ 10^7).

Output

Print an integer — the minimum number of integers you need to remove so that the greatest common divisor of the remaining integers is bigger than that of all integers.

You should not remove all of the integers.

If there is no solution, print «-1» (without quotes).

Examples

Input

3
1 2 4


Output

1

Input

4
6 9 15 30


Output

2

Input

3
1 1 1


Output

-1

Note

In the first example, the greatest common divisor is 1 in the beginning. You can remove 1 so that the greatest common divisor is enlarged to 2. The answer is 1.

In the second example, the greatest common divisor is 3 in the beginning. You can remove 6 and 9 so that the greatest common divisor is enlarged to 15. There is no solution which removes only one integer. So the answer is 2.

In the third example, there is no solution to enlarge the greatest common divisor. So the answer is -1.
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.Map.Entry;

public class Main
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod1 = 1000000000 + 7;
	private long mod = 1000000000 + 7;

	private StringBuilder ans_sb;

	private void soln()
	{
		int n = nextInt();
		int max = 15000000;
		int[] arr = new int[n];
		int[] freq = new int[max + 1];
		long gcd = -1;
		for (int i = 0; i < n; i++) {
			int x = nextInt();
			freq[x]++;
			if (gcd == -1)
				gcd = x;
			else
				gcd = gcd(gcd, x);
		}
		boolean[] s = new boolean[max + 1];
		int ans1 = 0;
		for (int i = 2 * (int) gcd; i <= max; i++) {
			if (!s[i]) {
				int ans = 0;
				for (int j = i; j <= max; j += i) {
					s[j] = true;
					ans += freq[j];
				}
				ans1 = Math.max(ans, ans1);
			}
		}
		ans1 = n - ans1;
		if (ans1 == n)
			ans1 = -1;
		pw.println(ans1);
	}

	private class Pair implements Comparable<Pair>
	{

		public Pair()
		{

		}

		@Override
		public int compareTo(Pair arg0)
		{
			return 0;
		}

	}

	public class Segment
	{
		private long[] tree;
		// private boolean[] lazy;
		private int size;
		private int n;

		public Segment(int n)
		{
			// this.base=arr;
			int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
			size = 2 * (int) Math.pow(2, x) - 1;
			tree = new long[size];
			// lazy = new boolean[size];
			this.n = n;
			// this.set = set1;
			// build(0, 0, n - 1);
		}

		public long query(int l, int r)
		{
			return queryUtil(l, r, 0, 0, n - 1);
		}

		private long queryUtil(int x, int y, int id, int l, int r)
		{
			if (l > y || x > r)
				return 0;
			if (x <= l && r <= y) {
				return tree[id];
			}
			int mid = ((l + r) >> 1);
			// shift(id);
			long q1 = queryUtil(x, y, (id << 1) | 1, l, mid);
			long q2 = queryUtil(x, y, (id << 1) + 2, mid + 1, r);
			return (q1 + q2) % mod;
		}

		public void update(int x, int y, long c)
		{
			update1(x, y, c, 0, 0, n - 1);
		}

		private void update1(int x, int y, long colour, int id, int l, int r)
		{
			// System.out.println(l+" "+r+" "+x);
			if (x > r || y < l)
				return;
			if (x <= l && r <= y) {
				tree[id] = colour;
				return;
			}
			int mid = ((l + r) >> 1);
			// shift(id);
			if (y <= mid)
				update1(x, y, colour, (id << 1) | 1, l, mid);
			else if (x > mid)
				update1(x, y, colour, (id << 1) + 2, mid + 1, r);
			else {
				update1(x, y, colour, (id << 1) | 1, l, mid);
				update1(x, y, colour, (id << 1) + 2, mid + 1, r);
			}
			tree[id] = (tree[(id << 1) | 1] + tree[(id << 1) + 2]) % mod;
		}

	}

	private String solveEqn(long a, long b)
	{
		long x = 0, y = 1, lastx = 1, lasty = 0, temp;
		while (b != 0) {
			long q = a / b;
			long r = a % b;
			a = b;
			b = r;
			temp = x;
			x = lastx - q * x;
			lastx = temp;
			temp = y;
			y = lasty - q * y;
			lasty = temp;
		}
		return lastx + " " + lasty;
	}

	private void debug(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}

	private long pow(long a, long b, long c)
	{
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}

	private long gcd(long n, long l)
	{
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}

	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable()
		{
			@Override
			public void run()
			{
				new Main().solve();
			}
		}, "1", 1 << 25).start();
		// new Main().solve();
	}

	public StringBuilder solve()
	{
		InputReader(System.in);
		/*
		 * try { InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
		 * } catch(FileNotFoundException e) {}
		 */
		pw = new PrintWriter(System.out);
		// ans_sb = new StringBuilder();
		soln();

		pw.close();
		// System.out.println(ans_sb);
		return ans_sb;
	}

	public void InputReader(InputStream stream1)
	{
		stream = stream1;
	}

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

	private boolean isEndOfLine(int c)
	{
		return c == '\n' || c == '\r' || c == -1;
	}

	private 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++];
	}

	private int nextInt()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private long nextLong()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private String nextToken()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private String nextLine()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private int[] nextIntArray(int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(int[] arr)
	{
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private void pArray(long[] arr)
	{
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private boolean isSpaceChar(int c)
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private char nextChar()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}