#include<bits/stdc++.h>
#define int long long 
using namespace std;
inline int read()
{
	int n=0,f=1,ch=getchar();
	while(ch<'0'||ch>'9')
	{
		if(ch=='-')f=-1;
		ch=getchar();
	}
	while(ch>='0'&&ch<='9')
	{
		n=n*10+ch-'0';
		ch=getchar();
	}
	return n*f;
}
int a[200005],pos[200005],qz[200005];
int n;
int f[200005];
void insert(int k,int x)
{
	while(k<=n)
	{
		f[k]+=x;
		k+=((k)&(-k));
	}
}
int query(int k)
{
	int ans=0; 
	while(k>=1)
	{
		ans+=f[k];
		k-=((k)&(-k));
	}
	return ans;
}
bool bi(int x,int y)
{
	if(a[x]!=a[y])return a[x]<a[y];
	return x>y;
}
int posq[200005],lsh[200005];
bool bibi(int x,int y)
{
	return qz[x]<qz[y];
 } 
signed main()
{
	int t;
	t=read();
	for(int greg=1;greg<=t;greg++)
	{
		n=read();
		int het=0;
		for(int i=1;i<=n;i++)
		{
			a[i]=read();
			het+=a[i];
		}
		if(het<0)
		{
			printf("-1\n");
			continue;
		}
		else if(het==0)
		{
			bool flag=true;
			for(int i=1;i<=n;i++)if(a[i]!=0)
			{
				flag=false;
				break;
			}
			if(flag==true)printf("0\n");
			else printf("-1\n");
			continue;
		}
		for(int i=1;i<=n;i++)a[i]+=a[i-1];
		for(int i=1;i<=n;i++)pos[i]=i;
		sort(pos+1,pos+n+1,bi);
		int ans=0;
		for(int i=1;i<=n;i++)
		{
			ans-=query(pos[i]);
			insert(pos[i],1);
		}
		for(int i=1;i<=n;i++)f[i]=0;
		for(int i=1;i<=n;i++)qz[i]=(a[i]%het+het)%het;
		for(int i=1;i<=n;i++)posq[i]=i;
		sort(posq+1,posq+n+1,bibi);
		lsh[posq[1]]=1;
		for(int i=2;i<=n;i++)
		{
			if(qz[posq[i]]==qz[posq[i-1]])lsh[posq[i]]=lsh[posq[i-1]];
			else lsh[posq[i]]=lsh[posq[i-1]]+1;
		}
		for(int i=1;i<=n;i++)
		{
			int sth=(a[pos[i]]-qz[pos[i]])/het;
			//printf("%lld %lld\n",pos[i],sth);
			ans+=(i-1)*sth;
			ans-=(n-i)*sth;
			ans+=query(lsh[pos[i]]-1);
			insert(lsh[pos[i]],1);
		}
		for(int i=1;i<=n;i++)f[i]=0;
		printf("%lld\n",ans);
	}
	return 0;
}