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.io.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    static int primes[];
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        int n=input.scanInt();
        int arr[]=new int[n];
        for(int i=0;i<n;i++) {
            arr[i]=input.scanInt();
        }
        sieve();
        int min[]=new int[primes.length];
        int min_cnt[]=new int[primes.length];
        Arrays.fill(min, Integer.MAX_VALUE);
        for(int i=0;i<n;i++) {
            for(int j=0;j<primes.length;j++) {
                int cnt=0;
                while(arr[i]%primes[j]==0) {
                    arr[i]/=primes[j];
                    cnt++;
                }
                if(cnt<min[j]) {
                    min[j]=cnt;
                    min_cnt[j]=1;
                }
                else if(cnt==min[j]) {
                    min_cnt[j]++;
                }
            }
        }
        int ans=Integer.MAX_VALUE;
        for(int i=0;i<primes.length;i++) {
//            System.out.println(primes[i]+" "+min[i]+" "+min_cnt[i]);
            if(min_cnt[i]==n) {
                continue;
            }
            else {
                ans=Math.min(ans,min_cnt[i]);
            }
        }
//        merge_sort(arr,0,n-1);
        Arrays.sort(arr);
        for(int i=0;i<n;i++) {
            if(arr[i]==1) {
                continue;
            }
            int j=i,cnt=0;
            while(j<n && arr[j]==arr[i]) {
                j++;
                cnt++;
            }
            j--;
            i=j;
            if(cnt==n) {
                continue;
            }
            ans=Math.min(ans,n-cnt);
        }
        if(ans==Integer.MAX_VALUE) {
            ans=-1;
        }
        System.out.println(ans);
    }
    public static void sieve() {
        boolean sieve[]=new boolean[4000];
        int indx=0;
        primes=new int[550];
        for(int i=2;i<sieve.length;i++) {
            if(!sieve[i]) {
                primes[indx]=i;
                indx++;
                for(int j=2;i*j<sieve.length;j++) {
                    sieve[i*j]=true;
                }
            }
        }
//        System.out.println(indx);
    }
    
    
    public static void merge_sort(int arr[],int l,int r) {
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        merge_sort(arr,l,mid);
        merge_sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(int arr[],int l1,int r1,int l2,int r2) {
        int tmp[]=new int[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
}
