package Practice;

import java.io.BufferedReader;

import java.io.InputStreamReader;

public class B2485 { //°¡·Î¼ö

static int N;

static int[] trees;

public static void main(String[] args) throws Exception {

// TODO Auto-generated method stub

BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

N = Integer.parseInt(br.readLine());

trees = new int[N];

for(int i = 0; i < N; i++) trees[i] = Integer.parseInt(br.readLine());

int dis = trees[1] - trees[0];

for(int i = 2; i < N; i++) dis = find_gcd(trees[i] - trees[0], dis);

System.out.println((trees[N - 1] - trees[0]) / dis + 1 - N);

}

static int find_gcd(int a, int b) {

while(a % b != 0) {

int temp = b;

b = a % b;

a = temp;

}

return b;

}

}