#include <bits/stdc++.h>
void merge(int arr[], int l, int m, int r) {
  int i, j, k;
  int n1 = m - l + 1;
  int n2 = r - m;
  int L[n1], R[n2];
  for (i = 0; i < n1; i++) L[i] = arr[l + i];
  for (j = 0; j < n2; j++) R[j] = arr[m + 1 + j];
  i = 0;
  j = 0;
  k = l;
  while (i < n1 && j < n2) {
    if (L[i] <= R[j]) {
      arr[k] = L[i];
      i++;
    } else {
      arr[k] = R[j];
      j++;
    }
    k++;
  }
  while (i < n1) {
    arr[k] = L[i];
    i++;
    k++;
  }
  while (j < n2) {
    arr[k] = R[j];
    j++;
    k++;
  }
}
void mergeSort(int arr[], int l, int r) {
  if (l < r) {
    int m = l + (r - l) / 2;
    mergeSort(arr, l, m);
    mergeSort(arr, m + 1, r);
    merge(arr, l, m, r);
  }
}
int hcf(int a, int b) {
  if (a == 0) {
    return b;
  }
  while (b != 0) {
    int t = b;
    b = a % b;
    a = t;
  }
  return a;
}
int main() {
  int n, i;
  scanf("%d", &n);
  int a[n + 1];
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  mergeSort(a, 0, n - 1);
  int mindis = 0;
  for (i = 1; i < n; i++) {
    mindis = hcf(mindis, a[i] - a[i - 1]);
  }
  int ans = 0;
  for (i = 1; i < n; i++) {
    ans += (a[i] - a[i - 1]) / mindis - 1;
  }
  printf("%d", ans);
}
