#include <bits/stdc++.h>
using namespace std;
long long int pwr(long long int base, long long int p, long long int mod) {
  long long int ans = 1;
  while (p) {
    if (p & 1) ans = (ans * base) % mod;
    base = (base * base) % mod;
    p /= 2;
  }
  return ans;
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int dp[32][32][53];
int coco(int n, int m, int k) {
  if (n * m < k) return 1 << 25;
  if (dp[n][m][k] != -1) return dp[n][m][k];
  if (n * m == k) return 0;
  if (k == 0) return 0;
  dp[n][m][k] = 1 << 25;
  for (int i = 0; i <= k; i++) {
    for (int j = 1; j < n; j++) {
      dp[n][m][k] =
          min(dp[n][m][k], coco(n - j, m, i) + coco(j, m, k - i) + (m * m));
      dp[n][m][k] =
          min(dp[n][m][k], coco(n - j, m, k - i) + coco(j, m, i) + (m * m));
    }
    for (int j = 1; j < m; j++) {
      dp[n][m][k] =
          min(dp[n][m][k], coco(n, m - j, i) + coco(n, j, k - i) + (n * n));
      dp[n][m][k] =
          min(dp[n][m][k], coco(n, m - j, k - i) + coco(n, j, i) + (n * n));
    }
  }
  return dp[n][m][k];
}
int main() {
  int t;
  scanf("%d", &t);
  for (int i = 0; i <= 30; i++) {
    for (int j = 0; j <= 30; j++) {
      for (int k = 0; k <= 50; k++) {
        dp[i][j][k] = -1;
      }
    }
  }
  while (t--) {
    int n, m, k;
    scanf("%d", &n);
    scanf("%d", &m);
    scanf("%d", &k);
    printf("%d\n", coco(n, m, k));
  }
  return 0;
}
