/* Problem URL: https://codeforces.com/contest/598/problem/E */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    ll dp[31][31][51];
    const ll oo = INT64_MAX >> 1;

    rep(n, 31) {
        rep(m, 31) {
            rep(k, 51) {
                if (k > n * m) {
                    dp[n][m][k] = oo;
                    continue;
                }

                if (k == 0 || k == n * m) {
                    dp[n][m][k] = 0;
                    continue;
                }
                
                dp[n][m][k] = oo;

                nrep(i, 1, n) {
                    rep(j, k + 1) {
                        rmin(dp[n][m][k], dp[i][m][j] + dp[n - i][m][k - j] + m * m);
                    }
                }

                nrep(i, 1, m) {
                    rep(j, k + 1) {
                        rmin(dp[n][m][k], dp[n][i][j] + dp[n][m - i][k - j] + n * n);
                    }
                }
            }
        }
    }

    int t;
    cin >> t;
    while (t--) {
        int n, m, k;
        cin >> n >> m >> k;

        cout << dp[n][m][k] << '\n';
    }
}