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.*;
import java.lang.*;

public class Main {
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static long MOD = (long) (1e9 + 7);
    //    static int MOD = 998244353;
    static long MOD2 = MOD * MOD;
    static FastReader sc = new FastReader();
    static int pInf = Integer.MAX_VALUE;
    static int nInf = Integer.MIN_VALUE;
    static long ded = (long)(1e17)+9;
    public static void main(String[] args) throws Exception {
        int test = 1;
//        test = sc.nextInt();
        for (int i = 1; i <= test; i++){
//            out.print("Case #"+i+": ");
            solve();
        }
        out.flush();
        out.close();
    }
    static void solve()throws Exception{
        int n = sc.nextInt();
        int[] a = new int[n];
        int g = 0;
        for(int i = 0 ; i < n; i++){
            a[i] = sc.nextInt();
            g = (int)gcd(g,a[i]);
        }
        int max = 0;
        for(int i = 0; i < n; i++){
            a[i] = a[i]/g;
            max = Math.max(max,a[i]);
        }
        linearSieve(max+1);
        HashMap<Integer,Integer> A = new HashMap<>();
        for(int i= 0; i < n; i++){
            int t = a[i];
            HashSet<Integer> fac = new HashSet<>();
            while(t!=1){
                fac.add(lp[t]);
                t = t/lp[t];
            }
            for(int x: fac){
                A.put(x,A.getOrDefault(x,0)+1);
            }
        }
        int ans = -1;
        for(int x: A.values()){
            ans = Math.max(ans,x);
        }
        ans = n-ans;
        if(ans>n){
            out.println(-1);
            return;
        }
        out.println(ans);
    }

    static int[] lp;
    static ArrayList<Integer> P;
    static void linearSieve(int n){
        lp = new int[n+1];
        P = new ArrayList<>();
        for(int i = 1; i <= n; i++){
            lp[i] = i;
        }
        for(int i= 2; i <= n; i++){
            if(lp[i]==i){
                P.add(i);
            }
            for(int j = 0; j < P.size()&&P.get(j)<=lp[i]&&i*P.get(j)<=n; j++){
                lp[i*P.get(j)] = P.get(j);
            }
        }
    }
    static class Pair implements Comparable<Pair> {
        int x;
        int y;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
//            this.idx = idx;
        }
        @Override
        public int compareTo(Pair o){
            if(this.x==o.x){
                return this.y-o.y;
            }
            return this.x-o.x;
        }
    }
    public static long mul(long a, long b) {
        return ((a % MOD) * (b % MOD)) % MOD;
    }
    public static long add(long a, long b) {
        return ((a % MOD) + (b % MOD)) % MOD;
    }
    public static long c2(long n) {
        if ((n & 1) == 0) {
            return mul(n / 2, n - 1);
        } else {
            return mul(n, (n - 1) / 2);
        }
    }
    //Shuffle Sort
    static final Random random = new Random();
    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n); int temp= a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }
    //Brian Kernighans Algorithm
    static long countSetBits(long n) {
        if (n == 0) return 0;
        return 1 + countSetBits(n & (n - 1));
    }
    //Euclidean Algorithm
    static long gcd(long A, long B) {
        if (B == 0) return A;
        return gcd(B, A % B);
    }
    //Modular Exponentiation
    static long fastExpo(long x, long n) {
        if (n == 0) return 1;
        if ((n & 1) == 0) return fastExpo((x * x) % MOD, n / 2) % MOD;
        return ((x % MOD) * fastExpo((x * x) % MOD, (n - 1) / 2)) % MOD;
    }
    //AKS Algorithm
    static boolean isPrime(long n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i <= Math.sqrt(n); i += 6)
            if (n % i == 0 || n % (i + 2) == 0) return false;
        return true;
    }
    public static long modinv(long x) {
        return modpow(x, MOD - 2);
    }
    public static long modpow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long x = modpow(a, b / 2);
        x = (x * x) % MOD;
        if (b % 2 == 1) {
            return (x * a) % MOD;
        }
        return x;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}