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.util.*;		
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.*;
import java.math.*;
public class Main12{
	static public void main(String args[])throws IOException{
		int tt=1;
		
		StringBuilder sb=new StringBuilder();
		for(int ttt=1;ttt<=tt;ttt++){
			Reader s=new Reader();
			int n=s.nextInt();
			int[] a=new int[n];
			long gcd=0;
			int max=0;
			for(int i=0;i<n;i++){
				a[i]=s.nextInt();
				if(i==0){
					gcd=a[i];
				}else{
					gcd=gcd(a[i],gcd);
				}
				max=Math.max(max,a[i]);
			}
			boolean[] prime=new boolean[max+1];
			int[] spf=new int[max+1];
			for(int i=1;i<=max;i++){
				spf[i]=i;
			}
			for(int i=2;i*i<=max;i++){
				if(prime[i]==false){
					spf[i]=i;
					for(int j=2*i;j<=max;j+=i){
						prime[j]=true;
						if(spf[j]==j){
							spf[j]=i;
						}
					}
				}
			}
			int[] count=new int[max+1];
			for(int i=0;i<n;i++){
				int num=a[i];
				if(spf[num]==num){
					count[num]++;
				}else{
					HashSet<Integer> hash=new HashSet<>();
					while(spf[num]!=num){
						hash.add(spf[num]);
						hash.add(num);
						num=num/spf[num];
					}
					hash.add(spf[num]);
					hash.add(num);
					Iterator itr=hash.iterator();
					while(itr.hasNext()){
						int tmp=(int)itr.next();
						count[tmp]++;
					}
				}
			}
			int ans=n;
			for(int i=(int)gcd+1;i<max+1;i++){
				int num=count[i];
				ans=Math.min(n-count[i],ans);
			}
			if(ans==n){
				sb.append("-1\n");
			}else{
				sb.append(ans+"\n");
			}
		}
		System.out.print(sb.toString());
	}
	
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	static ArrayList<ArrayList<Integer>> graph;
	static int mod=998244353;
	static class Pair{
		int x;
		int y;
		Pair(int x,int y,int z){
			this.x=x;
			this.y=y;
		}
		@Override
            public int hashCode() 
            { 
                final int temp = 14; 
                int ans = 1; 
                ans =x*31+y*13; 
                return ans; 
            } 
       @Override
        public boolean equals(Object o) 
        { 
            if (this == o) { 
                return true; 
            } 
            if (o == null) { 
                return false; 
            } 
            if (this.getClass() != o.getClass()) { 
                return false; 
            } 
            Pair other = (Pair)o; 
            if (this.x != other.x || this.y!=other.y) { 
                return false; 
            } 
            return true; 
        }
	}
	public static long[] sort(long[] a){
		int n=a.length;
		ArrayList<Long> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++){
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++){
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b){
        long result=1;
        while(b>0){
            if (b % 2 != 0){
                result=(result*a)%mod;
                b--;
            } 
            a=(a*a)%mod;
            b /= 2;
        }   
        return result;
    }
	public static long gcd(long a, long b){
        if (a == 0){
            return b;
		}
        return gcd(b%a, a);
    }
	public static long lcm(long a, long b){
		return a*(b/gcd(a,b));
	}
	public static long l(){
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value){
		System.out.println(value);
	}
	public static int i(){
		return in.Int();
	}
	public static String s(){
		return in.String();
	}
}
class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
class InputReader 
{
	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 int Int() {
		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 String String() {
		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 String();
	} 
	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}
class OutputWriter {
	private final PrintWriter writer;
	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}
	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}
	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}
	public void close() {
		writer.close();
	}
	public void flush() {
		writer.flush();
	}
 }
class IOUtils {
	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.Int();
		return array;
	}
} 
