#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(b);i>=(a);i--)
#define lowbit(x) (x & (-x))

typedef long long ll;

using namespace std;

const int MAXN = 1e5+10;

int T,n;
ll a[MAXN],s[MAXN],sp[MAXN],ans,S;

typedef array<ll,2> pr;
pr arr[MAXN];

ll pre[MAXN];

ll b[MAXN],tot;

ll cdiv(ll x,ll z){
	if(x>=0)return (x+z-1)/z;
	else return x/z;
}
ll Cmod(ll x,ll z){
	return (x%z + z)%z;
}
ll cmod(ll x,ll z){
	return Cmod(x,z) ? Cmod(x,z) : (z);
}

struct BIT{
	ll t[MAXN],tot;
	void clr(int n){
		memset(t,0,sizeof t);
		tot = n;
	}
	void mdf(ll x,ll v){
		for(;x<=tot;x+=lowbit(x))t[x] += v;
	}
	ll qry(ll x,ll S=0){
		for(;x;x-=lowbit(x))S+=t[x];
		return S;
	}
}t,t2;

void solve(){
	cin>>n;
	rep(i,1,n)cin>>a[i];

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

	S = s[n];

	if(S < 0){
		cout<<-1<<endl;
		return;
	}
	if(S==0){
		rep(i,1,n)if(a[i] != 0){
			cout<<-1<<endl;
			return;
		}
		cout<<0<<endl;
		return;
	}

	ans = tot = 0;
	
	rep(i,1,n)arr[i] = {s[i],i},b[++tot] = cmod(s[i],S);
	sort(b+1,b+1+tot);unique(b+1,b+1+tot)-b-1;

	rep(i,1,n)sp[i] = lower_bound(b+1,b+1+tot,cmod(s[i],S)) - b;


	sort(arr+1,arr+1+n);

	rep(i,1,n)pre[i] = pre[i-1] + cdiv(arr[i][0],S);

	t.clr(tot);t2.clr(n);
	int cur = 0;

	rep(i,1,n){
		while(cur+1 <= n && arr[cur+1][0] < arr[i][0]){
			cur++;
			t.mdf(sp[arr[cur][1]],1);

			t2.mdf(arr[cur][1],1);
		}

		ans += cur * cdiv(arr[i][0],S) - pre[cur];

		ans += t.qry(sp[arr[i][1]] - 1);

		ans -= t2.qry(arr[i][1]-1);
	}


	cout<<ans<<endl;
}

int main(){
	ios::sync_with_stdio(false);

	cin>>T;
	while(T--)solve();

	return 0;
}