#pragma GCC optimize(2)

#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define op(x) ((x&1)?x+1:x-1)
#define odd(x) (x&1)
#define even(x) (!odd(x))
#define lc(x) (x<<1)
#define rc(x) (lc(x)|1)
#define lowbit(x) (x&-x)
#define mp(x,y) make_pair(x,y)
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
using namespace std;
const int MAXN=1e5+10;

int T,n,a[MAXN],mn;
ll S,ans,cnt,pos[MAXN],val[MAXN];
ll s[MAXN];

typedef array<ll,3> pr;
pr p[MAXN];

struct B{
	ll b[MAXN],tot;
	void init(){tot=0;}
	void add(ll x){b[++tot]=x;}
	void pr(){sort(b+1,b+1+tot);tot=unique(b+1,b+1+tot)-b-1;}
	ll qry(ll x){return lower_bound(b+1,b+1+tot,x)-b;}
}bp,bv;
struct BIT{
	ll t[MAXN],n;
	void init(ll n){
		this->n=n;
		rep(i,1,n)t[i] = 0;
	}
	void mdf(ll x,ll v){
		for(;x<=n;x+=lowbit(x))t[x] += v;
 	}
 	ll qry(ll x,ll S=0){
 		for(;x;x-=lowbit(x))S+=t[x];
 		return S;
 	}
}t;

pr arr[MAXN];
int cur;

void cdq(int L,int R){
	if(L==R)return;
	int mid=(L+R)>>1;
	cdq(L,mid);
	cdq(mid+1,R);

	cur=0;
	rep(i,L,mid)arr[++cur] = {p[i][0],-1,p[i][2]};
	rep(i,mid+1,R)arr[++cur] = {p[i][0],1,p[i][2]};
	sort(arr+1,arr+1+cur);

	rep(i,1,cur){
		if(arr[i][1] == -1)t.mdf(bv.tot-arr[i][2]+1,1);else{
			cnt += t.qry(bv.tot-arr[i][2]);
		}
	}
	rep(i,1,cur)if(arr[i][1] == -1)t.mdf(bv.tot-arr[i][2]+1,-1);
}

void solve(){
	cin>>n;S=0;mn=1e9;
	rep(i,1,n)cin>>a[i],S+=a[i],mn = min(mn,a[i]);
	if(S<0 || (S==0 && mn < 0)){
		cout<<"-1\n";
		return;
	}
	if(S==0){
		cout<<"0\n";
		return;
	}

	ans=0;
	rep(i,1,n)s[i] = s[i-1] + a[i];

	bp.init();bv.init();

	rep(i,1,n)pos[i] = (s[i] >= 0) ? (-s[i] / S) : ((-s[i] + S-1)/S),val[i] = (s[i] % S + S)%S;
	rep(i,1,n)bp.add(pos[i]),bv.add(val[i]);
	bp.pr();bv.pr();

	rep(i,1,n)p[i] = {pos[i],i,val[i]};
	
	t.init(bv.tot);

	rep(i,1,n)p[i][2] = bv.qry(val[i]);
 	rep(i,1,n){
		int cnt = (i-1) - t.qry(p[i][2]);
		ans -= cnt;
		t.mdf(p[i][2],1);
	}
	rep(i,1,n)t.mdf(p[i][2],-1);

	cnt=0;

	cdq(1,n);

	ans+=cnt*2;
	//

	rep(i,1,n)p[i][0] = pos[i],p[i][2] = bv.qry(val[i]),p[i][1] = i;

	sort(p+1,p+1+n); 
	ll preS=0;
	rep(i,1,n){
		ans += (p[i][0] * (i-1) - preS);
		preS += p[i][0];
	}

	rep(i,1,n)p[i][0] = bp.qry(p[i][0]),swap(p[i][0],p[i][2]);
	sort(p+1,p+1+n);

	t.init(bp.tot);

	for(int l=1,r;l<=n;l=r+1){
		r=l;while(r+1<=n && p[r+1][0] == p[l][0])r++;
		rep(i,l,r){
			int cnt = (i-l) - t.qry(p[i][2]);
			ans -= cnt;
			t.mdf(p[i][2],1);	
		}
		rep(i,l,r)t.mdf(p[i][2],-1);
	}
	//
	cout<<ans<<"\n";
}

int main(){
	ios::sync_with_stdio(false);
	cin>>T;
	while(T--)solve();

    return 0;
}