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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.TreeMap;
import java.util.TreeSet;


		    
		    
		    
		                                                public class Solution1 implements Runnable
		                                                {
		                                                    static final long MAX = 464897L;
		                                                    static class InputReader
		                                                    {
		                                                        private InputStream stream;
		                                                        private byte[] buf = new byte[1024];
		                                                        private int curChar;
		                                                        private int numChars;
		                                                        private SpaceCharFilter filter;
		                                                        private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		                                                 
		                                                        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()
		                                                        {
		                                                            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);
		                                                        }
		                                                    }
		                                                     
		                                                    public static void main(String args[]) throws Exception
		                                                    {
		                                                        new Thread(null, new Solution1(),"Solution",1<<26).start();
		                                                    }   
		                                                    static int gcd(int a, int b) 
		                                                    { 
		                                                      if (b == 0) 
		                                                        return a; 
		                                                      return gcd(b, a % b);  
		                                                    } 
		                                                    
		                                                    long MOD = 1000000007;
		                                                    
		                                                    ArrayList<Integer> adj[];
		                                                    ArrayList<Pair> adj2[];
		                                                    public void run() 
		                                                    {
		                                                        
		                                                            //InputReader sc= new InputReader(new FileInputStream("input.txt"));
		                                                            //PrintWriter w= new PrintWriter(new FileWriter("output.txt"));
		                                                            InputReader sc = new InputReader(System.in);
		                                                            PrintWriter w = new PrintWriter(System.out);
		                                                            int n = sc.nextInt();
		                                                            int[] arr = new int[n];
		                                                            for(int i = 0;i < n;i++) {
		                                                            	arr[i] = sc.nextInt();
		                                                            }
		                                                            int gcd = arr[0];
		                                                            for(int i = 1;i < n;i++) {
		                                                            	gcd = gcd(arr[i],gcd);
		                                                            }
		                                                            for(int i = 0;i < n;i++) {
		                                                            	arr[i] = arr[i]/gcd;
		                                                            }
		                                                            sieve();
		                                                            for(int i = 0;i < n;i++) {
		                                                            	getFactorization(arr[i]);
		                                                            }
		                                                            int fans = -1;
		                                                            int max = Integer.MIN_VALUE;
		                                                            for(Integer val: ans.keySet()) {
		                                                            	max = Math.max(max,ans.get(val));
		                                                            }
		                                                            if(max == Integer.MIN_VALUE) {
		                                                            	w.println("-1");
		                                                            }else {
		                                                            	w.println(n - max);
		                                                            }
		                                                            w.close();
		                                                     }
		                                                    static final int MAXN = 15000001; 
		                                                    
		                                                    // stores smallest prime factor for every number 
		                                                    static int spf[] = new int[MAXN]; 
		                                                       
		                                                    // Calculating SPF (Smallest Prime Factor) for every 
		                                                    // number till MAXN. 
		                                                    // Time Complexity : O(nloglogn) 
		                                                    static void sieve() 
		                                                    { 
		                                                        spf[1] = 1; 
		                                                        for (int i=2; i<MAXN; i++) 
		                                                       
		                                                            // marking smallest prime factor for every 
		                                                            // number to be itself. 
		                                                            spf[i] = i; 
		                                                       
		                                                        // separately marking spf for every even 
		                                                        // number as 2 
		                                                        for (int i=4; i<MAXN; i+=2) 
		                                                            spf[i] = 2; 
		                                                       
		                                                        for (int i=3; i*i<MAXN; i++) 
		                                                        { 
		                                                            // checking if i is prime 
		                                                            if (spf[i] == i) 
		                                                            { 
		                                                                // marking SPF for all numbers divisible by i 
		                                                                for (int j=i*i; j<MAXN; j+=i) 
		                                                       
		                                                                    // marking spf[j] if it is not  
		                                                                    // previously marked 
		                                                                    if (spf[j]==j) 
		                                                                        spf[j] = i; 
		                                                            } 
		                                                        } 
		                                                    } 
		                                                       
		                                                    static TreeMap<Integer,Integer> ans = new TreeMap();
		                                                    // A O(log n) function returning primefactorization 
		                                                    // by dividing by smallest prime factor at every step 
		                                                    static void getFactorization(int x) 
		                                                    { 
		                                                        TreeSet<Integer> ret = new TreeSet<>(); 
		                                                        while (x != 1) 
		                                                        { 
		                                                            ret.add(spf[x]); 
		                                                            x = x / spf[x]; 
		                                                        } 
		                                                        for(Integer val: ret) {
		                                                        	if(ans.containsKey(val)) {
		                                                        		ans.put(val, ans.get(val) + 1);
		                                                        	}else {
		                                                        		ans.put(val, 1);
		                                                        	}
		                                                        }
		                                                    } 
		                                                    class Pair implements Comparable<Pair>{
		                                                        long a;
		                                                        int b;
		                                                        //int c;
		                                                        Pair(long a,int b){
		                                                            this.b = b;
		                                                            this.a = a;
		                                                        }
		                                                        public boolean equals(Object o) {
		                                                            Pair p = (Pair)o;
		                                                            return this.a == p.a && this.b == p.b;
		                                                        }
		                                                        public int hashCode(){
		                                                            return Long.hashCode(a)*27 + Long.hashCode(b)* 31;
		                                                        }
		                                                        public int compareTo(Pair p) {
		                                                            return Long.compare(this.a,p.a);
		                                                        }
		                                                    }
		                                    }