#include<bits/stdc++.h>
#define ll long long
using namespace std;
//a_1 a_2  ... v a_1 ... v
//v a_2 ... a_n | v a_2 ...  a_n 
//-v        a_n | v 
int n;
ll a[101000];
ll mo(ll x){return (x%a[n]+a[n])%a[n];}
ll xc(ll x){return (x-mo(x))/a[n];}
ll qc[201000];int cn;ll tr[201000];
struct qq{int ty,id;ll z;}e[201000];
bool cmp(qq a,qq b){
	if(a.z==b.z)return a.ty>b.ty;
	return a.z<b.z;
}
void ad(int x,ll z){for(;x<=cn;x+=(x&-x))tr[x]+=z;}
ll ask(int x){ll s=0;for(;x;x-=(x&-x))s+=tr[x];return s;}
void sol(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lld",&a[i]),a[i]+=a[i-1];
	if(a[n]<0){puts("-1");return;}
	if(a[n]==0){
		bool fl=1;for(int i=1;i<=n;i++)fl&=(a[i]==0);
		if(fl)puts("0");
		else puts("-1");return;
	}
	ll ans=0;
	for(int i=1;i<=n;i++)e[2*i-1]=(qq){0,i,a[i]},e[2*i]=(qq){1,i,a[i]+1};
	sort(e+1,e+n*2+1,cmp);
	cn=n;
	for(int i=1;i<=cn;i++)tr[i]=0;
	ll s1=0,s2=0;
	for(int i=1;i<=n*2;i++){
		if(!e[i].ty)ans+=ask(n-e[i].id),ans+=s1*xc(e[i].z),ans-=s2;
		else s1++,s2+=xc(e[i].z),ad(n-e[i].id+1,1);
	}
	cn=0;
	for(int i=1;i<=n*2;i++)qc[++cn]=mo(e[i].z);
	sort(qc+1,qc+cn+1);cn=unique(qc+1,qc+cn+1)-qc-1;
	for(int i=1;i<=cn;i++)tr[i]=0;
	for(int i=1;i<=n*2;i++){
		int X=lower_bound(qc+1,qc+cn+1,mo(e[i].z))-qc;
		if(!e[i].ty)ans-=ask(cn-X);
		else ad(cn-X+1,1);
	}
	/*for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)if(i!=j){
		ll v1=a[i],v2=a[j];
		if(v1>v2)ans+=xc(v1),ans-=xc(v2+1),ans-=(mo(v1)<mo(v2+1));
		if(j>i&&v1>v2)ans++;
	}*/
	printf("%lld\n",ans);
}
int main(){
	int T;cin>>T;while(T--)sol();
	return 0;
}