#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
long long dp[31][31][51];
long long calc(long long x, long long y, long long k) {
  if (dp[x][y][k] || !k || x * y == k) return dp[x][y][k];
  long long ans = 1e9;
  for (long long i = 1; 2 * i <= x; i++) {
    for (long long j = 0; j <= k; j++) {
      ans = min(ans, y * y + calc(i, y, j) + calc(x - i, y, k - j));
    }
  }
  for (long long i = 1; 2 * i <= y; i++) {
    for (long long j = 0; j <= k; j++) {
      ans = min(ans, x * x + calc(x, i, j) + calc(x, y - i, k - j));
    }
  }
  return dp[x][y][k] = ans;
}
void solve() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, m, k;
    cin >> n >> m >> k;
    cout << calc(n, m, k) << "\n";
  }
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long tests;
  tests = 1;
  for (long long i = 0; i < tests; i++) {
    solve();
  }
}
