#include <bits/stdc++.h>
int nextInt() {
  int x;
  scanf("%d", &x);
  return x;
}
double nextDouble() {
  double x;
  scanf("%lf", &x);
  return x;
}
long long nextLong() {
  long long x;
  scanf("%I64d", &x);
  return x;
}
char nextChar() {
  char x;
  scanf("%c", &x);
  return x;
}
void newLine() { printf("\n"); }
long long powM(long long a, long long b, long long MOD) {
  long long x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y);
      if (x > MOD) x %= MOD;
    }
    y = (y * y);
    if (y > MOD) y %= MOD;
    b /= 2;
  }
  return x;
}
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
int countBitSet(long long n) {
  int ans = 0;
  while (n != 0) {
    n -= (n & -n);
    ++ans;
  }
  return ans;
}
long long mod = 1000000007;
long long mod2 = 1000000009;
const int N = 200100;
const int M = 1111;
const int LOG = 21;
const int INF = 1e9;
const long double EPS = 1e-6;
const long double PI = 2 * acos(0);
using namespace std;
long long a[N];
int main() {
  int n = nextInt();
  for (int i = 0; i < n; i++) {
    a[i] = nextLong();
  }
  sort(a, a + n);
  long long g = 0;
  for (int i = 1; i < n; i++) {
    long long dist = a[i] - a[i - 1];
    g = gcd(g, dist);
  }
  long long ans = 0;
  for (int i = 1; i < n; i++) {
    long long dist = a[i] - a[i - 1];
    ans += (dist / g) - 1;
  }
  cout << ans << endl;
  return 0;
}
