#include <bits/stdc++.h>
#define pb emplace_back
#define fst first
#define scd second
#define mkp make_pair
#define mems(a, x) memset((a), (x), sizeof(a))

using namespace std;
typedef long long ll;
typedef double db;
typedef unsigned long long ull;
typedef long double ldb;
typedef pair<ll, ll> pii;
typedef vector<ll> vl;

const int maxn = 1000100;

ll n, a[maxn], lsh[maxn], tot;

namespace BIT {
	ll c[maxn];
	
	inline void init() {
		mems(c, 0);
	}
	
	inline void update(ll x, ll d) {
		for (int i = x; i <= tot; i += (i & (-i))) {
			c[i] += d;
		}
	}
	
	inline ll query(int x) {
		ll res = 0;
		for (int i = x; i; i -= (i & (-i))) {
			res += c[i];
		}
		return res;
	}
}

struct node {
	ll s, p, q, id;
} b[maxn];

inline int ID(ll x) {
	return lower_bound(lsh + 1, lsh + tot + 1, x) - lsh;
}

void solve() {
	scanf("%lld", &n);
	for (int i = 1; i <= n; ++i) {
		scanf("%lld", &a[i]);
		b[i].s = b[i - 1].s + a[i];
		b[i].id = i;
	}
	if (b[n].s < 0) {
		puts("-1");
		return;
	} else if (b[n].s == 0) {
		for (int i = 1; i <= n; ++i) {
			if (a[i] < 0) {
				puts("-1");
				return;
			}
		}
		puts("0");
		return;
	}
	for (int i = 1; i <= n; ++i) {
		b[i].p = (b[i].s >= 0 ? b[i].s / b[n].s : -((-b[i].s + b[n].s - 1) / b[n].s));
		b[i].q = b[i].s - b[i].p * b[n].s;
	}
	sort(b + 1, b + n + 1, [&](const node &a, const node &b) {
		return a.s < b.s;
	});
	tot = 0;
	for (int i = 1; i <= n; ++i) {
		lsh[++tot] = b[i].q;
	}
	sort(lsh + 1, lsh + tot + 1);
	tot = unique(lsh + 1, lsh + tot + 1) - lsh - 1;
	ll ans = 0, s = 0;
	BIT::init();
	for (int i = 1, j = 1; i <= n; i = (++j)) {
		while (j < n && b[j + 1].s == b[i].s) {
			++j;
		}
		for (int k = i; k <= j; ++k) {
			ans += b[k].p * (i - 1) - s + BIT::query(ID(b[k].q) - 1);
		}
		for (int k = i; k <= j; ++k) {
			s += b[k].p;
			BIT::update(ID(b[k].q), 1);
		}
	}
	sort(b + 1, b + n + 1, [&](const node &a, const node &b) {
		return a.id < b.id;
	});
	tot = 0;
	for (int i = 1; i <= n; ++i) {
		lsh[++tot] = b[i].s;
	}
	sort(lsh + 1, lsh + tot + 1);
	tot = unique(lsh + 1, lsh + tot + 1) - lsh - 1;
	BIT::init();
	for (int i = 1, j = 1; i <= n; i = (++j)) {
		while (j < n && b[j + 1].id == b[i].id) {
			++j;
		}
		for (int k = i; k <= j; ++k) {
			ans -= BIT::query(ID(b[k].s) - 1);
		}
		for (int k = i; k <= j; ++k) {
			BIT::update(ID(b[k].s), 1);
		}
	}
	printf("%lld\n", ans);
}

int main() {
	int T = 1;
	scanf("%d", &T);
	while (T--) {
		solve();
	}
	return 0;
}