/*
灏忓簾鐗╋紝杩欓兘涓嶄細 /cf
*/
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define inf (ll)1e9
#define pii pair <ll, ll>
#define fr first
#define se second
const ll mod = 1e9 + 7;
char buf[1 << 21], *p1 = buf, *p2 = buf;
#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 18, stdin), p1 == p2) ? EOF : *p1++)
inline ll read() {
	ll x = 0, f = 1;
	char ch = getchar();
	while(ch < '0' || ch > '9') f = ((ch == '-') ? -1 : f), ch = getchar();
	while(ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
	return x * f;
}
inline void write(ll x) {
	if(x < 0) x = -x, putchar('-');
	if(x >= 10) write(x / 10);
	putchar(x % 10 + '0');
}
ll n;
ll a[100005], s[100005], id[100005];
ll bs1[100005], bs2[100005];
ll ts1[100005], ts2[100005];
vector <ll> G;
struct BIT_TREE {
	inline ll lowbit(ll x) {
		return x & (-x);
	}
	ll bit[200005];
	inline void add(ll x, ll y) {
		for(ll i = x; i <= 2 * n; i += lowbit(i)) bit[i] += y;
	}
	inline ll Sum(ll x) {
		ll Ans = 0;
		for(ll i = x; i; i -= lowbit(i)) Ans += bit[i];
		return Ans;
	}
	inline ll get_sum(ll l, ll r) {
		return Sum(r) - Sum(l - 1);
	}
	inline void clear() {
		for(ll i = 0; i <= 2 * n; i++) bit[i] = 0;
	}
}Tr;
int main() {
//	freopen("circle.in", "r", stdin);
//	freopen("circle.out", "w", stdout);
	ll T = read();
	while(T--) {
		n = read();
		for(ll i = 1; i <= n; i++) a[i] = read(), s[i] = s[i-1] + a[i], id[i] = i;
		if(s[n] <= 0) {
			ll fl = 1;
			for(ll i = 1; i <= n; i++) fl &= !a[i];
			if(fl) puts("0");
			else puts("-1");
			continue;
		} 
		G.clear(), G.reserve(2 * n);
		for(ll i = 1; i <= n; i++) {
			bs1[i] = (ll)floor(1.0 * (s[i] - 1) / s[n]);
			bs2[i] = (ll)floor(1.0 * s[i] / s[n]);
			ts1[i] = s[i] - 1 - bs1[i] * s[n];
			ts2[i] = s[i] - bs2[i] * s[n];
			G.push_back(ts1[i]), G.push_back(ts2[i]);
		}
		sort(G.begin(), G.end()), G.erase(unique(G.begin(), G.end()), G.end());
		for(ll i = 1; i <= n; i++) {
			ts1[i] = lower_bound(G.begin(), G.end(), ts1[i]) - G.begin() + 1;
			ts2[i] = lower_bound(G.begin(), G.end(), ts2[i]) - G.begin() + 1;
		}
		ll Ans = 0;
//		for(ll i = 1; i <= n; i++) {
//			for(ll j = 1; j <= n; j++) {
//				if(s[i] <= s[j]) continue;
//				Ans += (i < j) + (s[i] - s[j] - 1) / s[n];
//			}
//		}
		sort(id + 1, id + 1 + n, [&] (ll A, ll B) {return s[A] < s[B];});
		//s[i] > s[j] && i < j 
		Tr.clear();
		for(ll i = 1, j; i <= n; i = j + 1) {
			j = i;
			while(j < n && s[id[j+1]] == s[id[j]]) j++;
			for(ll k = i; k <= j; k++) Ans += Tr.get_sum(id[k], 2 * n);
			for(ll k = i; k <= j; k++) Tr.add(id[k], 1);
		}
		//sum of bs1 - bs2
		for(ll i = 1, j; i <= n; i = j + 1) {
			j = i;
			while(j < n && s[id[j+1]] == s[id[j]]) j++;
			for(ll k = i; k <= j; k++) {
				Ans += bs1[id[k]] * (i - 1);
				Ans -= bs2[id[k]] * (n - j);
			}
		}
//		//ts1 < ts2
		Tr.clear();
		for(ll i = 1, j; i <= n; i = j + 1) {
			j = i;
			while(j < n && s[id[j+1]] == s[id[j]]) j++;
			for(ll k = i; k <= j; k++) Ans -= Tr.get_sum(ts1[id[k]] + 1, 2 * n);
			for(ll k = i; k <= j; k++) Tr.add(ts2[id[k]], 1);
		}
		write(Ans), putchar('\n');
	} 
	return 0;
}
/*
1
3
5 2 -2

5 7 5

0 1 0

*/