#include <bits/stdc++.h>

using namespace std;

#define rep(i, s, e) for (int i = s; i <= e; ++i)
#define drep(i, s, e) for (int i = s; i >= e; --i)
#define file(a) freopen(#a".in", "r", stdin), freopen(#a".out", "w", stdout)
#define pv(a) cout << #a << " = " << a << endl
#define pa(a, l, r) cout << #a " : "; rep(_, l, r) cout << a[_] << ' '; cout << endl

using i64 = long long;

const int N = 1e5 + 10;

int read() {
  int x = 0, f = 1; char c = getchar();
  for (; c < '0' || c > '9'; c = getchar()) if (c == '-') f = -1;
  for (; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - 48;
  return x * f;
}

namespace bit {
  int c[N], lim;
  void reset(int n) { lim = n, fill(c + 1, c + n + 1, 0); }
  void add(int u, int k) { for (; u <= lim; u += u & -u) c[u] += k; }
  int ask(int u) { int res = 0; for (; u; u -= u & -u) res += c[u]; return res; }
}

using bit::reset;
using bit::add;
using bit::ask;

int n, a[N], s, id[N], x[N], y[N], val[N], cnt;
i64 ans;

i64 solve() {
  n = read();
  rep(i, 1, n) a[i] = a[i - 1] + read(), id[i] = i;
  s = a[n];
  if (s <= 0) {
    return *min_element(a + 1, a + n + 1) >= 0 ? 0 : -1;
  }
  ans = 0;
  sort(id + 1, id + n + 1, [&](int i, int j) {
    return a[i] == a[j] ? i > j : a[i] < a[j];
  });
  reset(n), cnt = 0;
  rep(i, 1, n) {
    ans -= ask(id[i]), add(id[i], 1);
    x[i] = (a[i] % s + s) % s, y[i] = (a[i] - x[i]) / s;
    val[++ cnt] = x[i];
  }
  rep(i, 1, n) {
    ans += 1ll * ((i - 1) - (n - i)) * y[id[i]];
  }
  sort(val + 1, val + cnt + 1);
  cnt = unique(val + 1, val + cnt + 1) - val - 1;
  reset(cnt);
  rep(i, 1, n) {
    x[i] = lower_bound(val + 1, val + cnt + 1, x[i]) - val;
    ans += ask(x[i] - 1), add(x[i], 1);
  }
  return ans;
}

int main() {
  for (int tc = read(); tc; -- tc) {
    printf("%lld\n", solve());
  }
  return 0;
}