Problem: You have a rectangular chocolate bar consisting of n × m single squares. You want to eat exactly k squares, so you may need to break the chocolate bar. 

In one move you can break any single rectangular piece of chocolate in two rectangular pieces. You can break only by lines between squares: horizontally or vertically. The cost of breaking is equal to square of the break length.

For example, if you have a chocolate bar consisting of 2 × 3 unit squares then you can break it horizontally and get two 1 × 3 pieces (the cost of such breaking is 32 = 9), or you can break it vertically in two ways and get two pieces: 2 × 1 and 2 × 2 (the cost of such breaking is 22 = 4).

For several given values n, m and k find the minimum total cost of breaking. You can eat exactly k squares of chocolate if after all operations of breaking there is a set of rectangular pieces of chocolate with the total size equal to k squares. The remaining n·m - k squares are not necessarily form a single rectangular piece.

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 40910) — the number of values n, m and k to process.

Each of the next t lines contains three integers n, m and k (1 ≤ n, m ≤ 30, 1 ≤ k ≤ min(n·m, 50)) — the dimensions of the chocolate bar and the number of squares you want to eat respectively.

Output

For each n, m and k print the minimum total cost needed to break the chocolate bar, in order to make it possible to eat exactly k squares.

Examples

Input

4
2 2 1
2 2 3
2 2 2
2 2 4


Output

5
5
4
0

Note

In the first query of the sample one needs to perform two breaks:

  * to split 2 × 2 bar into two pieces of 2 × 1 (cost is 22 = 4), 
  * to split the resulting 2 × 1 into two 1 × 1 pieces (cost is 12 = 1). 



In the second query of the sample one wants to eat 3 unit squares. One can use exactly the same strategy as in the first query of the sample.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Ruins He
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskE solver = new TaskE();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskE {
    private long[][][] dp;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int T = in.nextInt();
      dp = new long[51][31][31];
      for (long[][] a : dp) for (long[] b : a) Arrays.fill(b, -1);
      for (int cas = 1; cas <= T; cas++) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        out.println(dfs(k, n, m));
      }
    }

    private long dfs(int k, int n, int m) {
      if (n > m) return dfs(k, m, n);
      if (dp[k][n][m] != -1) return dp[k][n][m];
      if (n * m == k || k == 0) return dp[k][n][m] = 0;
      if (n * m < k) return dp[k][n][m] = Long.MAX_VALUE;
      long res = Long.MAX_VALUE;

      long lhs, rhs;
      for (int nk = 0; nk <= k; nk++) {
        for (int i = 1; i < n; i++) {
          lhs = dfs(nk, i, m);
          rhs = dfs(k - nk, n - i, m);
          if (lhs != Long.MAX_VALUE && rhs != Long.MAX_VALUE)
            res = Math.min(res, lhs + rhs + m * m);
        }
        for (int i = 1; i < m; i++) {
          lhs = dfs(nk, n, i);
          rhs = dfs(k - nk, n, m - i);
          if (lhs != Long.MAX_VALUE && rhs != Long.MAX_VALUE)
            res = Math.min(res, lhs + rhs + n * n);
        }
      }

      return dp[k][n][m] = res;
    }

  }

  static class InputReader {
    public final BufferedReader reader;
    public StringTokenizer tokenizer = null;

    public InputReader(Reader reader) {
      this.reader = new BufferedReader(reader, 32767);
    }

    public InputReader(InputStream inputStream) {
      this(new InputStreamReader(inputStream));
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

  }

  static class OutputWriter {
    private final PrintWriter writer;

    private OutputWriter(Writer writer, boolean autoFlush) {
      this.writer = new PrintWriter(new BufferedWriter(writer, 32767), autoFlush);
    }

    public OutputWriter(Writer writer) {
      this(writer, true);
    }

    public OutputWriter(OutputStream outputStream) {
      this(new OutputStreamWriter(outputStream), false);
    }

    public OutputWriter println(long value) {
      writer.println(value);
      return this;
    }

    public void close() {
      writer.close();
    }

  }
}