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.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {
  public static FastScanner in=new FastScanner();
  final static int N=15000000+10;
  static int[]r=new int[N];
  static int []zzh=new int[N];
  public static void main(String[] args) throws IOException {
    seive();
    //for(int i=0; i<101; ++i) System.out.print(r[i]+" ");
    //System.out.println();
    Arrays.fill(zzh,0);
    int n=ri();
    int[] a = new int[n];
    a=ria(n);
    Long MAX=-1L;
    int gcd=a[0];
    int cr=0;
    for(int i=0; i<n; ++i){
      MAX=max(MAX,a[i]);
      gcd=gcf(gcd,a[i]);
      if(a[i]%a[0]==0) ++cr;
    }
    sort(a);
    if(MAX<=gcd){
      System.out.println(-1);
      System.exit(0);
    }
    for(int i=0; i<n; ++i) a[i]/=gcd;
    for(int i=0; i<n; ++i){
      MAX=max(MAX,a[i]);
      gcd=gcf(gcd,a[i]);
    }
    //System.out.println(gcd);
    for(int x:a){
      solve(x);
    }
    Long MIN=n-1L;
    for(int i=gcd+1; i<N; ++i){
      MIN=min(MIN,n-zzh[i]);
    }
    System.out.println(MIN);
    close();
  }

  static void seive(){
    for(int i=1; i<N; ++i){
      r[i]=i;
    }
    for(int i=2; i<N; i+=2) r[i]=2;
    for(int i=3; i*i<N; ++i){
      if(r[i]!=i) continue;
      for(int j=i*i; j<N; j+=i){
        if(r[j]==j) r[j]=i;
      }
    }
  }

  static void solve(int n){
    int fact=r[n];
    //System.out.println(n);
    while(n>1){
      //System.out.print(fact+" ");
      zzh[fact]++;
      while(n%fact==0) n/=fact;
      fact=r[n];
    }
    //System.out.println();
  }

  static class FastScanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    String next() {
      while (!st.hasMoreTokens())
        try { st = new StringTokenizer(br.readLine()); }
        catch (IOException e) { e.printStackTrace(); }
      return st.nextToken();
    }
    int nextInt() { return Integer.parseInt(next()); }
    int[] readArray(int n) {
      int[] a = new int[n];
      for (int i = 0; i < n; i++) a[i] = nextInt();
      return a;
    }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
  }

  static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
  static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
  static StringTokenizer input;
  static Random __rand = new Random();

// references
// IBIG = 1e9 + 7
// IMAX ~= 2e9
// LMAX ~= 9e18

  // constants
  static final int IBIG = 1000000007;
  static final int IMAX = 2147483647;
  static final int IMIN = -2147483648;
  static final long LMAX = 9223372036854775807L;
  static final long LMIN = -9223372036854775808L;
  // math util
  static int minof(int a, int b, int c) {return min(a, min(b, c));}
  static int minof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
  static long minof(long a, long b, long c) {return min(a, min(b, c));}
  static long minof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
  static int maxof(int a, int b, int c) {return max(a, max(b, c));}
  static int maxof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
  static long maxof(long a, long b, long c) {return max(a, max(b, c));}
  static long maxof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
  static int powi(int a, int b) {if(a == 0) return 0; int ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
  static long powl(long a, int b) {if(a == 0) return 0; long ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
  static int fli(double d) {return (int)d;}
  static int cei(double d) {return (int)ceil(d);}
  static long fll(double d) {return (long)d;}
  static long cel(double d) {return (long)ceil(d);}
  static int gcf(int a, int b) {return b == 0 ? a : gcf(b, a % b);}
  static long gcf(long a, long b) {return b == 0 ? a : gcf(b, a % b);}
  static int lcm(int a, int b) {return a * b / gcf(a, b);}
  static long lcm(long a, long b) {return a * b / gcf(a, b);}
  static int randInt(int min, int max) {return __rand.nextInt(max - min + 1) + min;}
  static long hash(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
  // array util
  static void reverse(int[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
  static void reverse(long[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
  static void reverse(char[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
  static void shuffle(int[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
  static void shuffle(long[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
  static void rsort(int[] a) {shuffle(a); sort(a);}
  static void rsort(long[] a) {shuffle(a); sort(a);}
  static int[] copy(int[] a) {int[] ans = new int[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
  static long[] copy(long[] a) {long[] ans = new long[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
  static char[] copy(char[] a) {char[] ans = new char[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
  // graph util
  static List<List<Integer>> g(int n) {List<List<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
  static List<Set<Integer>> sg(int n) {List<Set<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new HashSet<>()); return g;}
  static void c(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
  static void cto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v);}
  static void dc(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v); g.get(v).remove(u);}
  static void dcto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v);}
  // input
  static void r() throws IOException {input = new StringTokenizer(__in.readLine());}
  static int ri() throws IOException {return Integer.parseInt(__in.readLine());}
  static long rl() throws IOException {return Long.parseLong(__in.readLine());}
  static int[] ria(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()); return a;}
  static int[] riam1(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()) - 1; return a;}
  static long[] rla(int n) throws IOException {long[] a = new long[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Long.parseLong(input.nextToken()); return a;}
  static char[] rcha() throws IOException {return __in.readLine().toCharArray();}
  static String rline() throws IOException {return __in.readLine();}
  static int rni() throws IOException {input = new StringTokenizer(__in.readLine()); return Integer.parseInt(input.nextToken());}
  static int ni() {return Integer.parseInt(input.nextToken());}
  static long rnl() throws IOException {input = new StringTokenizer(__in.readLine()); return Long.parseLong(input.nextToken());}
  static long nl() {return Long.parseLong(input.nextToken());}
  static List<List<Integer>> rg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for(int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
  static void rg(List<List<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
  static List<List<Integer>> rdg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for(int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
  static void rdg(List<List<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
  static List<Set<Integer>> rsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for(int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
  static void rsg(List<Set<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
  static List<Set<Integer>> rdsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for(int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
  static void rdsg(List<Set<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
  // output
  static void pr(int i) {__out.print(i);}
  static void prln(int i) {__out.println(i);}
  static void pr(long l) {__out.print(l);}
  static void prln(long l) {__out.println(l);}
  static void pr(double d) {__out.print(d);}
  static void prln(double d) {__out.println(d);}
  static void pr(char c) {__out.print(c);}
  static void prln(char c) {__out.println(c);}
  static void pr(char[] s) {__out.print(new String(s));}
  static void prln(char[] s) {__out.println(new String(s));}
  static void pr(String s) {__out.print(s);}
  static void prln(String s) {__out.println(s);}
  static void pr(Object o) {__out.print(o);}
  static void prln(Object o) {__out.println(o);}
  static void prln() {__out.println();}
  static void pryes() {__out.println("yes");}
  static void pry() {__out.println("Yes");}
  static void prY() {__out.println("YES");}
  static void prno() {__out.println("no");}
  static void prn() {__out.println("No");}
  static void prN() {__out.println("NO");}
  static void pryesno(boolean b) {__out.println(b ? "yes" : "no");};
  static void pryn(boolean b) {__out.println(b ? "Yes" : "No");}
  static void prYN(boolean b) {__out.println(b ? "YES" : "NO");}
  static void prln(int... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
  static void prln(long... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
  static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for(int i = 0; i < n; __out.print(iter.next()), __out.print(' '), ++i); if(n >= 0) __out.println(iter.next()); else __out.println();}
  static void h() {__out.println("hlfd"); flush();}
  static void flush() {__out.flush();}
  static void close() {__out.close();}
}