#include<iostream>
#include<cstdio>
#include<algorithm>
#define N 200000
using namespace std;
int read()
{
    char c=0;
    int sum=0,f=1;
    while (c!='-'&&(c<'0'||c>'9')) c=getchar();
    if (c=='-') c=getchar(),f=-1;
    while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
    return sum*f;
}
int T,n,length,a[N+1],s[N+1],p[N+1],st[N+1],c[N+1];
long long ans;
int lowbit(int x)
{
    return x&(-x);
}
void add(int x,int d)
{
    for (;x<=length;x+=lowbit(x)) c[x]+=d;
    return;
}
int query(int x)
{
    int res=0;
    for (;x>=1;x-=lowbit(x)) res+=c[x];
    return res;
}
int F(int x)
{
    if (x>0) return (x+s[n]-1)/s[n];
    else return -(-x)/s[n];
}
int main()
{
    bool op;
    T=read();
    while (T--)
    {
	n=read(),ans=length=0;
	for (int i=1;i<=n;++i) a[i]=read(),s[i]=s[i-1]+a[i];
	if (s[n]<0)
	{
	    puts("-1");
	    continue;
	}
	if (s[n]==0)
	{
	    op=1;
	    for (int i=1;i<=n;++i) op&=(s[i]==0);
	    if (!op)
	    {
		puts("-1");
		continue;
	    }
	    else
	    {
		puts("0");
		continue;
	    }
	}
	for (int i=1;i<=n;++i) st[++length]=s[i],st[++length]=s[i]%s[n];
	sort(st+1,st+length+1),length=unique(st+1,st+length+1)-st-1;
	for (int i=1;i<=length;++i) c[i]=0;
	for (int i=1;i<=n;++i) ans-=query(lower_bound(st+1,st+length+1,s[i])-st-1),add(lower_bound(st+1,st+length+1,s[i])-st,1);
	for (int i=1;i<=n;++i) p[i]=s[i];
	sort(p+1,p+n+1);
	for (int i=1;i<=n;++i) ans+=1ll*((i-1)-(n-i))*F(p[i]);
	for (int i=1;i<=length;++i) c[i]=0;
	for (int i=n;i>=1;--i) ans-=query(lower_bound(st+1,st+length+1,p[i]%s[n])-st-1)*n,add(lower_bound(st+1,st+length+1,p[i]%s[n])-st,1);
	printf("%lld\n",ans);
    }
    return 0;
}