#include<stdio.h>
    long long int gcd(long long int n1,long long int n2);
    int main()
    {long long int n,i,g,sum;
    scanf("%lld",&n);
    long long int a[1000000];
    for(i=0;i<n;i++)
    {scanf("%lld",&a[i]);}
    for(i=0;i<n-1;i++)
    {g=a[1]-a[0];
    g=gcd(g,a[i+1]-a[i]);}
    sum=0;
    for(i=0;i<n-1;i++)
    {sum += ((a[i+1]-a[i])/g) -1;
    }
    printf("%lld\n",sum);
    return 0;
    }
    long long int gcd(long long int n1,long long int n2)
    {long long int i,gc=0;
    for(i=1;i<=n1||i<=n2;i++)
    {if(n1%i==0&&n2%i==0)
    gc=i;}
    return gc;
    }
 
 
 
 
 
 

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