#include <bits/stdc++.h>
using namespace std;
template <typename T>
void __read(T& a) {
  cin >> a;
}
template <typename T, typename... Args>
void __read(T& a, Args&... args) {
  cin >> a;
  __read(args...);
}
constexpr long long M7 = 1000000007ll;
constexpr long long M9 = 1000000009ll;
constexpr long long MFFT = 998244353ll;
template <class T>
void outv(T& a) {
  for (auto& x : a) cout << x << ' ';
}
mt19937 rnd(static_cast<unsigned>(
    chrono::steady_clock::now().time_since_epoch().count()));
template <class T>
void random_shuffle(T s, T e) {
  shuffle(s, e, rnd);
};
static auto __super_speed__ = (ios_base::sync_with_stdio(0), cin.tie(0));
signed dp[30 + 1][30 + 1][51];
signed calc(signed n, signed m, signed k) {
  signed& v = dp[n][m][k];
  if (v != -1) return v;
  if (n * m == k || k == 0) return v = 0;
  v = M7;
  for (signed i = 1; i < n; ++i)
    for (signed nk = 0; nk < k; ++nk)
      v = min(v, calc(i, m, nk) + calc(n - i, m, k - nk) + m * m);
  for (signed i = 1; i < m; ++i)
    for (signed nk = 0; nk < k; ++nk)
      v = min(v, calc(n, i, nk) + calc(n, m - i, k - nk) + n * n);
  return v;
}
int32_t main() {
  memset(dp, -1, sizeof(dp));
  signed t;
  __read(t);
  while (t--) {
    signed n, m, k;
    __read(n, m, k);
    cout << calc(n, m, k) << '\n';
  }
  return 0;
}
