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.
// Author @ BlackRise :) //

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class enlargeGCD {
    static Calendar ts, te;                                                  //For time calculation
    static int mod9 = (int) 1e9 + 7;
    static InputReader input = new InputReader(System.in);
    static PrintWriter pw = new PrintWriter(System.out, true);


    public static void main(String[] args) {                                 //threading has been used to increase the stack size.

        new Thread(null, null, "BlackRise", 1<<25)  //the last parameter is stack size which is desired,
        {
            public void run() {

                try {
                    Blackrise();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

    static void Blackrise() {                                                //The name Blackrise is my pen name... you can change the name according to your wish

        //tsc();                                                               //calculates the starting time of execution

        int n=ni();
        int ar[]=new int[n];ar[0]=ni();ar[1]=ni();
        int gcd=gcd(ar[0],ar[1]);
        for(int i=2;i<n;i++)
        {
            ar[i]=ni();
            gcd=gcd(gcd,ar[i]);
        }
        for(int i=0;i<n;i++)ar[i]/=gcd;
        int seive[]=new int[15000000+1];

        Seive(seive,15000000+1);

        int countDiv[]=new int[15000000+1];
        int ans=0;
        for(int i=0;i<n;i++) {
            int ele = ar[i];

            while (ele > 1) {
                int div = seive[ele];
                countDiv[div]++;
                ans = Integer.max(ans, countDiv[div]);

                while (ele % div == 0)ele /= div;
            }
        }
        pl(ans==0?-1:n-ans);

        tec();                  //calculates the ending time of execution
        //pwt();                //prints the time taken to execute the program
    }

    static int gcd(int a, int b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

   static void Seive(int prime[],int MAX)
    {
        for (int i = 2; i * i < MAX; ++i)
        {
            if (prime[i]==0)
                for (int j = i * i; j < MAX; j += i)
                    prime[j] = i;
        }

        // Prime number will have same divisor
        for (int i = 1; i < MAX; ++i)
            if (prime[i]==0)
                prime[i] = i;
    }

///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////


    static class InputReader {                                              //InputReader class for fast input
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        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 String nextLine() {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public 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;
        }

        public 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;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

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

    // functions to take input//
    static int ni() {
        return input.nextInt();
    }

    static long nl() {
        return input.nextLong();
    }

    static double nd() {
        return input.nextDouble();
    }

    static String ns() {
        return input.readString();
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o){
        pw.print(o+"");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    static void tsc()                                          //calculates the starting time of execution
    {
        ts = Calendar.getInstance();
        ts.setTime(new Date());
    }

    static void tec()                                          //calculates the ending time of execution
    {
        te = Calendar.getInstance();
        te.setTime(new Date());
    }

    static void pwt()                                          //prints the time taken for execution
    {
        pw.printf("\nExecution time was :- %f s\n", (te.getTimeInMillis() - ts.getTimeInMillis()) / 1000.00);
    }
}
