#include <stdio.h>
#include <stdlib.h>

int GCD(int a, int b);

int main() {
    int N;
    scanf("%d",&N);
    int* tree = (int*)malloc(sizeof(int)*N);
    for(int i=0; i<N; i++) scanf("%d", &tree[i]);

    int* diff = (int*)malloc(sizeof(int)*(N-1));
    for(int i=0; i<N-1; i++) diff[i] = tree[i+1] - tree[i];
    
    int gcd = diff[0];
    for(int i=1; i<N-1; i++) gcd = GCD(diff[i], gcd);

    int result = 0;
    for(int i=0; i<N-1; i++) {
        result += diff[i]/gcd - 1;
    }

    printf("%d\n", result);

    free(tree);
    free(diff);
    return 0;
}

int GCD(int a, int b) {
    while(b!=0) {
        int r = a%b;
        a = b;
        b = r;
    }

    return a;
}