# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int a[100010],b[100010],id[100010],rr[100010],r[100010];
struct BIT
{
	int n,s[100010];
	void init(int _n){n=_n;memset(s+1,0,sizeof(int)*n);}
	void update(int x){for(int i=x;i<=n;i+=i&(-i)) s[i]++;}
	int query(int x)
	{
		int ans=0;
		for(int i=x;i;i-=i&(-i)) ans+=s[i];
		return ans;
	}
}B;
int main()
{
	int T;
	cin>>T;
	while(T--)
	{
		int n,S=0;
		ll ans=0,sum=0;
		scanf("%d",&n);
		for(int i=1;i<=n;i++) scanf("%d",&a[i]),a[i]+=a[i-1];
		S=a[n];
		if(S<0){puts("-1");continue;}
		else if(!S)
		{
			bool ok=1;
			for(int i=1;i<=n;i++) ok&=(!a[i]);
			puts(ok?"0":"-1");
			continue;
		}
		iota(id+1,id+n+1,1);
		sort(id+1,id+n+1,[](int i,int j){return a[i]<a[j] || (a[i]==a[j] && i>j);});
		B.init(n);
		for(int i=1;i<=n;i++) ans-=B.query(id[i]),B.update(id[i]);
		for(int i=1;i<=n;i++) rr[i]=r[i]=(a[i]%S+S)%S,b[i]=(a[i]-r[i])/S;
		sort(rr+1,rr+n+1);
		int len=unique(rr+1,rr+n+1)-rr-1;
		for(int i=1;i<=n;i++) r[i]=lower_bound(rr+1,rr+len+1,r[i])-rr;
		B.init(len);
		for(int i=1;i<=n;i++) sum+=b[id[i]],ans+=(ll)i*b[id[i]]-sum+B.query(r[id[i]]-1),B.update(r[id[i]]);
		printf("%lld\n",ans);
	}
	return 0;
}