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.util.*;
/*
 * Heart beats fast
 * 		Colors and promises
 * 			How to be brave
 * 				How can I love when I am afraid...
 */
public class Main
{
	public static void main(String[]args) throws Exception
	{
		int n=ni();
		int[]a=nia(n);
		
//		long time=System.currentTimeMillis();
		int gcd=gcd(a);
		boolean bool=true;
		for(int i=0; i<n; i++)
			if(gcd!=a[i])
				bool=false;
		for(int i=0; i<n; i++)
			a[i]/=gcd;
		int[]smpf=new int[15_000_001];
		for(int i=2; i<=15_000_000; i++)
			if(smpf[i]==0)
				for(int j=i; j<=15_000_000; j+=i)
					smpf[j]=i;
		int[]te=new int[15_000_001];
		if(bool)
			pr(-1);
		else
		{
			int temp;
			for(int i=0; i<n; i++)
				while(a[i]!=1)
				{
					te[smpf[a[i]]]++;
					temp=smpf[a[i]];
					a[i]/=temp;
					while(a[i]%temp==0)
						a[i]/=temp;
				}
			int max=0;
			for(int i=0; i<=15_000_000; i++)
				max=max(te[i],max);
			pr(n-max);
		}
//		sop((System.currentTimeMillis()-time)/1e3);
		System.out.println(output);
	}
	///////////////////////////////////////////
	///////////////////////////////////////////
	///template from here
//	static final int mod=998_244_353;
	static final int mod=1000_000_007;
	static final double eps=1e-7;
	static final long inf=1000_000_000_000_000_000L;
	static class pair
	{
		int a,b;
		pair(){}
		pair(int c,int d){a=c;b=d;}
		@Override
		public int hashCode()
		{
			return (a+" "+b).hashCode();
		}
		public boolean equals(Object c)
		{
			return (a==(((pair)c).a)&&b==(((pair)c).b));
		}
	}
	public static void sort(int[][]a)
	{
		Arrays.sort(a, new Comparator<int[]>()
				{
			public int compare(int[]a,int[]b)
			{
				if(a[0]>b[0])
					return 1;
				if(a[0]<b[0])
					return -1;
				return 0;
			}
				});
	}
	static interface combiner
	{
		public int combine(int a, int b);
	}
	static void pr(Object a){output.append(a+"\n");}
	static void pr(){output.append("\n");}
	static void p(Object a){output.append(a);}
	static void pra(int[]a){for(int i:a)output.append(i+" ");output.append("\n");}
	static void pra(long[]a){for(long i:a)output.append(i+" ");output.append("\n");}
	static void pra(String[]a){for(String i:a)output.append(i+" ");output.append("\n");}
	static void pra(double[]a){for(double i:a)output.append(i+" ");output.append("\n");}
	static void sop(Object a){System.out.println(a);}
	static void flush(){System.out.print(output);output=new StringBuilder();}
	static int ni(){return Integer.parseInt(in.next());}
	static long nl(){return Long.parseLong(in.next());}
	static String ns(){return in.next();}
	static double nd(){return Double.parseDouble(in.next());}
	static int[] nia(int n){int a[]=new int[n];for(int i=0; i<n; i++)a[i]=ni();return a;}
	static int[] pnia(int n){int a[]=new int[n+1];for(int i=1; i<=n; i++)a[i]=ni();return a;}
	static long[] nla(int n){long a[]=new long[n];for(int i=0; i<n; i++)a[i]=nl();return a;}
	static String[] nsa(int n){String a[]=new String[n];for(int i=0; i<n; i++)a[i]=ns();return a;}
	static double[] nda(int n){double a[]=new double[n];for(int i=0; i<n; i++)a[i]=nd();return a;}
	static Reader in=new Reader();
	static StringBuilder output=new StringBuilder();
	static Random rn=new Random();
	static void reverse(int[]a){for(int i=0; i<a.length/2; i++){a[i]^=a[a.length-i-1];a[a.length-i-1]^=a[i];a[i]^=a[a.length-i-1];}}
	static int log2n(long a)
	{
		int te=0;
		while(a>0)
		{
			a>>=1;
			++te;
		}
		return te;
	}
	static class vectorl implements Iterable<Long>
	{
		long a[];
		int size;
		vectorl(){a=new long[10];size=0;}
		vectorl(int n){a=new long[n];size=0;}
		public void add(long b){if(++size==a.length)a=Arrays.copyOf(a, 2*size);a[size-1]=b;}
		public void sort(){Arrays.sort(a, 0, size);}
		public void sort(int l, int r){Arrays.sort(a, l, r);}
		@Override
		public Iterator<Long> iterator() {
			Iterator<Long> hola=new Iterator<Long>()
					{
				int cur=0;
						@Override
						public boolean hasNext() {
							return cur<size;
						}
						@Override
						public Long next() {
							return a[cur++];
						}				
					};
			return hola;
		}
	}
	static class vector implements Iterable<Integer>
	{
		int a[],size;
		vector(){a=new int[10];}
		vector(int n){a=new int[n];}
		public void add(int b){if(++size==a.length)a=Arrays.copyOf(a, 2*size);a[size-1]=b;}
		public void sort(){Arrays.sort(a, 0, size);}
		public void sort(int l, int r){Arrays.sort(a, l, r);}
		@Override
		public Iterator<Integer> iterator() {
			Iterator<Integer> hola=new Iterator<Integer>()
					{
				int cur=0;
						@Override
						public boolean hasNext() {
							return cur<size;
						}
						@Override
						public Integer next() {
							return a[cur++];
						}				
					};
			return hola;
		}
	}
	static class deque {
		int a[];
		int head,tail;
		deque(){a=new int[8];}
		void clear()
		{
			head=0;tail=0;
		}
		void add(int i)
		{	
			head=(head+1)&(a.length-1);
			if(tail==head)
			{
				int[]b=new int[2*a.length];
				System.arraycopy(a, tail, b, 0, a.length-tail);
				System.arraycopy(a, 0, b, a.length-tail, head);
				tail=0;
				a=b;
				head=(a.length>>>1);
			}
			a[(head-1)&(a.length-1)]=i;
		}
		int poll()
		{
			tail=(tail+1)&(a.length-1);
			return a[(tail-1)&(a.length-1)];
		}
		boolean notempty()
		{
			return head!=tail;
		}
	}
	static void exit(){System.out.print(output);System.exit(0);}
	static int min(int... a){int min=a[0];for(int i:a)min=Math.min(min, i);return min;}
	static int max(int... a){int max=a[0];for(int i:a)max=Math.max(max, i);return max;}	
	static int gcd(int... a){int gcd=a[0];for(int i:a)gcd=gcd(gcd, i);return gcd;}	
	static long min(long... a){long min=a[0];for(long i:a)min=Math.min(min, i);return min;}
	static long max(long... a){long max=a[0];for(long i:a)max=Math.max(max, i);return max;}	
	static long gcd(long... a){long gcd=a[0];for(long i:a)gcd=gcd(gcd, i);return gcd;}	
	static String pr(String a, long b){String c="";while(b>0){if(b%2==1)c=c.concat(a);a=a.concat(a);b>>=1;}return c;}
	static long powm(long a, long b, long mod2){long an=1;long c=a%mod2;while(b>0){if(b%2==1)an=(an*c)%mod2;c=(c*c)%mod2;b>>=1;}return an;}
	static long pow(long a, long b){long an=1;long c=a;while(b>0){if(b%2==1)an*=c;c*=c;b>>=1;}return an;}
	static int gcd(int a, int b){if(b==0)return a;return gcd(b, a%b);}
	static long gcd(long a, long b){if(b==0)return a;return gcd(b, a%b);}
	static class Reader{
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
    }
} 