#include <algorithm>
#include <array>
#include <cstddef>
#include <cstdint>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/detail/container_base_dispatch.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <fstream>
#include <functional>
#include <iostream>
#include <string>

namespace __gnu_pbds {
struct null_type;
struct rb_tree_tag;
}  // namespace __gnu_pbds

namespace {
using std::cin;
using std::cout;
using std::int64_t;
using std::size_t;
using Tree = __gnu_pbds::tree<int64_t, __gnu_pbds::null_type, std::less<>,
                              __gnu_pbds::rb_tree_tag,
                              __gnu_pbds::tree_order_statistics_node_update>;

namespace base {
template <typename T, size_t... sizes>
struct NestedArray {};

template <typename T, size_t size, size_t... sizes>
struct NestedArray<T, size, sizes...> {
  using Type = std::array<typename NestedArray<T, sizes...>::Type, size>;
};

template <typename T>
struct NestedArray<T> {
  using Type = T;
};

template <typename T, size_t... sizes>
using Array = typename NestedArray<T, sizes...>::Type;

void OptimizeIO() {
  std::ios::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
}

void OptimizeIO(const std::string &input_file, const std::string &output_file) {
  static std::ifstream input_stream(input_file);
  static std::ofstream output_stream(output_file);
  cin.rdbuf(input_stream.rdbuf());
  cout.rdbuf(output_stream.rdbuf());
  cin.tie(nullptr), cout.tie(nullptr);
}
}  // namespace base

using base::Array;

const int kMaxN = 1.0e5 + 5;
const int64_t kBase = 1 << 20;
int n, m;
Array<int, kMaxN> a, sum_a;
Tree tree;

struct Node {
  int val, num;
};

Array<Node, kMaxN> b;

int Divide(int x, int y) { return x >= 0 ? x / y : (x - y + 1) / y; }

void Solve() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  sum_a[0] = 0;
  for (int i = 1; i <= n; i++) sum_a[i] = sum_a[i - 1] + a[i];
  int s = sum_a[n];

  if (s < 0) {
    cout << "-1\n";
    return;
  }

  if (s == 0) {
    if (std::count(a.begin() + 1, a.begin() + n + 1, 0) == n) {
      cout << "0\n";
    } else {
      cout << "-1\n";
    }

    return;
  }

  int64_t ans = 0;

  for (int i = 0; i < n; i++) {
    ans += tree.size() - tree.order_of_key((sum_a[i] + 1) * kBase);
    tree.insert(sum_a[i] * kBase + i);
  }

  tree.clear();
  std::sort(sum_a.begin(), sum_a.begin() + n);
  m = 0;

  for (int i = 0; i < n;) {
    int j = i;
    while (j < n && sum_a[i] == sum_a[j]) j++;
    b[++m] = {sum_a[i], j - i};
    i = j;
  }

  int64_t sum_q = 0;
  int num = 0;

  for (int i = 1; i <= m; i++) {
    int q = Divide(b[i].val, s);
    int r = b[i].val - q * s;
    ans += static_cast<int64_t>(b[i].num) * num * q - sum_q;
    // ans -= static_cast<int64_t>(b[i].num) *
    //        (tree.size() - tree.order_of_key((r + 1) * kBase));
    r++;
    if (r == s) r = 0, q++;
    sum_q += static_cast<int64_t>(b[i].num) * q;
    for (int j = 0; j < b[i].num; j++) tree.insert(r * kBase + (++num));

    for (int j = 1; j < i; j++) {
      int qq = Divide(b[j].val, s);

      if (r < b[j].val - qq * s) {
        ans -= static_cast<int64_t>(b[i].num) * b[j].num;
      }
    }

    b[i].val++;
  }

  tree.clear();
  cout << ans << "\n";
}

int Main() {
  base::OptimizeIO();
  int t;
  cin >> t;
  while (t--) Solve();
  return 0;
}
}  // namespace

int main() { return Main(); }