血与泪。

//t4 interval rp++
#include<bits/stdc++.h>
//#define Freopen
using namespace std;

const int N=1e6+10;
int ans,n,t,a[N];
int gcd,s[N];

int GCD(int x,int y)
{
	if(y!=0&&x%y==0)return y;
	return GCD(y,x%y);
}

int main()
{
    #ifdef Freopen
	freopen("interval.in","r",stdin);
	freopen("interval.out","w",stdout);
    #endif
    
	scanf("%d",&t);
	while(t--)
	{
		memset(s,0,sizeof(s));
		bool fg=0,flg=1;
		ans=0;
		
		scanf("%d",&n);
		for(int i=1;i<=n;++i)
		{
			scanf("%d",&a[i]);
			s[i]=a[i]-a[i-1];
			if(s[i]==0&&i>1)fg=1;//wa1
		}
		for(int i=3;i<=n;++i)//wa2
		{
			if(s[i]!=s[2])
			{
				flg=0;
			}
		}
		if(flg||n<=2)//wa3
		{
			printf("0\n");
			continue;
		}
		else if(fg)
		{
			printf("-1\n");
			continue;
	    }
	    
		gcd=s[2];//wa4
		for(int i=3;i<=n;++i)
		{
			gcd=GCD(gcd,s[i]);
		}
		for(int i=2;i<=n;++i)
		{
			ans+=max(0,(s[i])/gcd-1);
		}
		printf("%d\n",ans);
		end:;
	}
	return 0;
}