#include <bits/stdc++.h>
#define int long long
using namespace std;
int a[100005];
struct qwq
{
	int op,x,y,z;
}c[1000005];
int ans;
bool cmp(qwq x,qwq y)
{
	return x.x>y.x||x.x==y.x&&x.op<y.op;
}
bool cmpy(qwq x,qwq y)
{
	return x.y<y.y||x.y==y.y&&x.op<y.op;
}
int cntop=0;
struct BIT
{
	int tree[500005];
	void init()
	{
		memset(tree,0,sizeof tree);
	}
	int lowbit(int x)
	{
		return x&-x;
	}
	void add(int x,int y)
	{
		for(x+=5;x<=500000;x+=lowbit(x)) tree[x]+=y;
	}
	int ask(int x)
	{
		int rtn=0;
		for(x+=5;x;x^=lowbit(x)) rtn+=tree[x];
		return rtn;
	}
}T;
const int inf=8e18;
int Div(int x,int d)
{
	return (x+inf/d*d)/d-inf/d;
}
vector<int> S;
int rk(int x)
{
	return lower_bound(S.begin(),S.end(),x)-S.begin();
}
void SOLVE(int l,int r)
{
	if(l>=r) return ;
	int mid=(l+r)/2;
	SOLVE(l,mid),SOLVE(mid+1,r);
	vector<qwq> v;
	for(int i=l;i<=mid;i++)
		if(c[i].op==0) v.push_back(c[i]);
	for(int i=mid+1;i<=r;i++)
		if(c[i].op!=0) v.push_back(c[i]);
	sort(v.begin(),v.end(),cmpy);
	vector<int> clr;
	for(auto t:v)
	{
		int R=rk(t.z);
		if(t.op==0) T.add(R,1),clr.push_back(R);
		else ans+=T.ask(R);
	}
	for(auto t:clr) T.add(t,-1);
}
void solve()
{
	cntop=0;
	int n;
	cin >> n;
	for(int i=1;i<=n;i++) cin >> a[i];
	for(int i=1;i<=n;i++) a[i]+=a[i-1];
	if(a[n]<0)
	{
		cout << "-1\n";
		return ;
	}
	if(a[n]==0)
	{
		int flag=0;
		for(int i=1;i<=n;i++) if(a[i]) flag=1;
		if(flag)
		{
			cout << "-1\n";
			return ;
		}
		cout << "0\n";
		return ;
	}
	int d=a[n];
	ans=0;
	int MN=0;
	for(int i=1;i<=n;i++) MN=min(MN,a[i]);
	for(int i=1;i<=n;i++) a[i]-=MN;
	for(int i=1;i<=n;i++)
		c[++cntop]={0,i,a[i]%d,a[i]};
	for(int i=1;i<=n;i++) S.push_back(a[i]-1),S.push_back(a[i]),S.push_back(a[i]-2),S.push_back(a[i]+1);
	sort(S.begin(),S.end());
	BIT T,TT;
	T.init(),TT.init();
	for(int i=n;i>=1;i--)
	{
		//y<x
		int x=a[i]+d-1;
		int k=(x)%d;
		if(k<0) k+=d;
		int w=Div((x),d);
		c[++cntop]={2,i+1,k,a[i]-1};
		ans+=T.ask(rk(a[i]-1))*(w-1);
		ans+=TT.ask(rk(a[i]-1));
		T.add(rk(a[i]),1);
		TT.add(rk(a[i]),-(a[i])/d);
	}
	T.init(),TT.init();
	for(int i=n;i>=1;i--)
	{
		//y>x+d
		int x=a[i];
		int k=(x+1)%d;
		if(k<0) k+=d;
		int w=Div((x+1),d)+1;
		c[++cntop]={1,i+1,k,x+1};
		ans-=(T.ask(400000)-T.ask(rk(a[i])))*(w);
		ans+=(TT.ask(400000)-TT.ask(rk(a[i])));
		T.add(rk(a[i]),1);
		TT.add(rk(a[i]),(a[i])/d);
	}
	int qwq=0;
	sort(c+1,c+cntop+1,cmp);
	int nw=n;
	T.init(),TT.init();
	for(int i=cntop;i>=1;i--)
	{
		if(c[i].op==1)
		{
			ans+=n-c[i].x+1;
			for(int j=c[i].x;j<=n;j++)
			{
				if(a[j]%d<c[i].y) --ans;
			}
			for(int j=c[i].x;j<=n;j++)
			{
				if(a[j]<c[i].z) --ans;
			}
			c[i].op=2,c[i].y--,c[i].z--;
		}
	}
/*	for(int i=1;i<=cntop;i++)
	{
		if(c[i].op==2) --c[i].x;
	}*/
/*	for(int i=1;i<=cntop;i++)
	{
		if(c[i].op==2)
		{
			for(int j=c[i].x;j<=n;j++)
			{
				if((a[j]%d<=c[i].y)&&(a[j]<=c[i].z)) ++ans;
			}
		}
	}*/
	sort(c+1,c+cntop+1,cmp);
	SOLVE(1,cntop);
	cout << ans << "\n";
}
signed main()
{
//	freopen("circle4.in","r",stdin);
//	freopen("circle.out","w",stdout);
	ios::sync_with_stdio(false);
	cin.tie(0);
	int greg;
	cin >> greg;
	while(greg--) solve();
	return 0;
}