#include<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
int T,n,a[N],s[N],c[N],st[N],L,p[N];
long long ans;
inline void add(int x,int y){ while(x<=L) c[x]+=y,x+=(x&-x); }
inline int ask(int x){int s=0;while(x){s+=c[x],x-=(x&-x);} return s;}
inline int F(int x){return (x>0?x:x-s[n]+1)/s[n];}
inline int G(int x){return (x%s[n]+s[n])%s[n];}
inline void solve(){
    scanf("%d",&n);ans=L=0;
    for(int i=1;i<=n;i++) scanf("%d",&a[i]),s[i]=s[i-1]+a[i];
    if(s[n]<0) return puts("-1"),void();
    if(s[n]==0){
        for(int i=1;i<=n;i++) if(s[i]) return puts("-1"),void();
        return puts("0"),void();
    }
    for(int i=1;i<=n;i++) st[++L]=s[i],st[++L]=G(s[i]);
    sort(st+1,st+1+L),L=unique(st+1,st+1+L)-st-1;
    for(int i=1;i<=L;i++) c[i]=0;
	for(int i=1;i<=n;i++) ans-=ask(lower_bound(st+1,st+L+1,s[i])-st-1),add(lower_bound(st+1,st+L+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<=L;++i) c[i]=0;
	for (int i=1;i<=n;++i) ans+=ask(lower_bound(st+1,st+L+1,G(p[i]))-st-1),add(lower_bound(st+1,st+L+1,G(p[i]))-st,1);
	printf("%lld\n",ans);
}
int main(){
    int T;scanf("%d",&T);
    while(T--) solve();
    return 0;
}