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:
//pakage joney_000[let_me_start]
//
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
/*
 * Author    : joney_000[let_me_start]
 * Algorithm : N/A
 * Platform  : N/A
 *
 */

/*    The Main Class                */
public class A { 
  private InputStream inputStream ;
  private OutputStream outputStream ;
  private FastReader in ;
  private PrintWriter out ;
  /*
    Overhead [Additional Temporary Strorage] but provides memory reusibility for multiple test cases.
    Size Limit : 10^5 + 4 
  */
  private final int BUFFER = 10005;
  private int    tempints[] = new int[BUFFER];
  private long   templongs[] = new long[BUFFER];
  private double tempdoubles[] = new double[BUFFER];
  private char   tempchars[] = new char[BUFFER];
  private final long mod = 1000000000+7;
  private final int  INF  = Integer.MAX_VALUE / 10;
  private final long INF_L  = Long.MAX_VALUE / 10;

  public A(){}
  public A(boolean stdIO)throws FileNotFoundException{
    // stdIO = false;
    if(stdIO){
      inputStream = System.in;
      outputStream = System.out;
    }else{
      inputStream = new FileInputStream("input.txt");
      outputStream = new FileOutputStream("output.txt");
    }
    in = new FastReader(inputStream);
    out = new PrintWriter(outputStream);

  }
  int dp[][][] = new int[31][31][51];

  void run()throws Exception{
    int tests = i();
    once();
    for(int t = 1 ; t <= tests; t++){
      int n = i(); int m = i(); int k = i();
      int ans = dp[n][m][k];
      out.write(""+ans+"\n");
    }
  }// end run

  void clear(){
  
  }
  void once(){
  	for(int i = 1; i <= 30; i++){
  		for(int j = 1; j <= 30; j++){
  			for(int k = 1; k <= 50; k++){
  				// Init
  				if(i * j == k)dp[i][j][k] = 0;
  				else dp[i][j][k] = INF;

  				for(int u = 0; u <= k; u++){
  					for(int v = 1; v < i; v++){
  						dp[i][j][k] = Math.min(dp[i][j][k], dp[v][j][u] + dp[i - v][j][k - u] + j * j);
  					}
  					for(int v = 1; v < j; v++){
  						dp[i][j][k] = Math.min(dp[i][j][k], dp[i][v][u] + dp[i][j - v][k - u] + i * i);
  					}
  				}
  			}
  		}
  	}
  }

  //****************************** Gerenal Utilities ***********************//

  void print_r(Object... o){
    out.write("\n"+Arrays.deepToString(o)+"\n");
    out.flush();
  }

  boolean isPrime(long n){
    if(n<=1)return false;
    if(n<=3)return true;
    if(n%2==0)return false;
    for(int i=2 ;i <= Math.sqrt(n); i++){
      if(n%i==0)return false;
    }
    return true;
  }
  // sieve
  int[] primes(int n){       // for(int i=1;i<=arr.length-1;i++)out.write(""+arr[i]+" ");
    boolean arr[] = new boolean[n+1];
    Arrays.fill(arr,true);
    arr[1]=false;
    for(int i=2;i<=Math.sqrt(n);i++){
      if(!arr[i])continue;
      for(int j = 2*i ;j<=n;j+=i){
        arr[j]=false;
      }
    }
    LinkedList<Integer> ll = new LinkedList<Integer>();
    for(int i=1;i<=n;i++){  
      if(arr[i])ll.add(i);
    }
    n = ll.size();
    
    int primes[] = new int[n+1];
    for(int i=1;i<=n;i++){
      primes[i]=ll.removeFirst();
    }
    return primes;
  }

  long gcd(long a , long b){
    if(b==0)return a;
    return gcd(b , a%b);
  }

  long lcm(long a , long b){
    if(a==0||b==0)return 0;
    return (a*b)/gcd(a,b);
  }

  long mulmod(long a , long b ,long mod){
    if(a==0||b==0)return 0;
    if(b==1)return a;
    long ans = mulmod(a,b/2,mod);
    ans = (ans*2)% mod;
    if(b%2==1)ans = (a + ans)% mod;
    return ans;
  }
  
  long pow(long a , long b ,long mod){
    if(b==0)return 1;
    if(b==1)return a;
    long ans = pow(a,b/2,mod);
    ans = (ans * ans);
    if(ans >= mod )ans %= mod;

    if(b%2==1)ans = (a * ans);
    if(ans >= mod )ans %= mod;

    return ans;
  }
  // 20*20   nCr Pascal Table
  long[][] ncrTable(){
    long ncr[][] = new long[21][21];
    for(int i=0 ;i<=20 ;i++){ncr[i][0]=1;ncr[i][i]=1;}
      for(int j=0;j<=20 ;j++){
        for(int i=j+1;i<= 20 ;i++){
          ncr[i][j] = ncr[i-1][j]+ncr[i-1][j-1];
        }
      }
    return ncr;
  }
  //*******************************I/O******************************//  
  int i()throws Exception{
    //return Integer.parseInt(br.readLine().trim());
    return in.nextInt();
  }
  int[] is(int n)throws Exception{
  //int arr[] = new int[n+1];
    for(int i=1 ; i <= n ;i++)tempints[i] = in.nextInt();  
      return tempints;
  }
  long l()throws Exception{
    return in.nextLong();
  }
  long[] ls(int n)throws Exception{
    for(int i=1 ; i <= n ;i++)templongs[i] = in.nextLong();  
      return templongs;
  }

  double d()throws Exception{
    return in.nextDouble();
  }
  double[] ds(int n)throws Exception{
    for(int i=1 ; i <= n ;i++)tempdoubles[i] = in.nextDouble();  
      return tempdoubles;
  }
  char c()throws Exception{
    return in.nextCharacter();
  }
  char[] cs(int n)throws Exception{
    for(int i=1 ; i <= n ;i++)tempchars[i] = in.nextCharacter();  
      return tempchars;
  }
  String s()throws Exception{
    return in.nextLine();
  }
  BigInteger bi()throws Exception{
    return in.nextBigInteger();
  }
//***********************I/O ENDS ***********************//
//*********************** 0.3%f [precision]***********************//
/* roundoff upto 2 digits 
   double roundOff = Math.round(a * 100.0) / 100.0;
                    or
   System.out.printf("%.2f", val);
          
*/
/*
  print upto 2 digits after decimal
  val = ((long)(val * 100.0))/100.0;
  
*/    

    private void closeResources(){
     out.flush();
     out.close();
     return;
    }
    public static void main(String[] args) throws java.lang.Exception{
    //let_me_start Shinch Returns 


    /*  
        // Old Reader Writer
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out=new BufferedWriter(new OutputStreamWriter(System.out));
    BufferedReader br=new BufferedReader(new FileReader("input.txt"));
        BufferedWriter out=new BufferedWriter(new FileWriter("output.txt"));
    */   
        A driver = new A(true);
        
        driver.run();

        driver.closeResources();
        return ;

      }  

    }

    class FastReader{

      private boolean finished = false;

      private InputStream stream;
      private byte[] buf = new byte[4 * 1024];
      private int curChar;
      private int numChars;
      private SpaceCharFilter filter;

      public FastReader(InputStream stream){
        this.stream = stream;
      }

      public int read(){
        if (numChars == -1){
          throw new InputMismatchException ();
        }
        if (curChar >= numChars){
          curChar = 0;
          try{
            numChars = stream.read (buf);
          } catch (IOException e){
            throw new InputMismatchException ();
          }
          if (numChars <= 0){
            return -1;
          }
        }
        return buf[curChar++];
      }

      public int peek(){
        if (numChars == -1){
          return -1;
        }
        if (curChar >= numChars){
          curChar = 0;
          try{
            numChars = stream.read (buf);
          } catch (IOException e){
            return -1;
          }
          if (numChars <= 0){
            return -1;
          }
        }
        return buf[curChar];
      }

      public int nextInt(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        int sgn = 1;
        if (c == '-'){
          sgn = -1;
          c = read ();
        }
        int res = 0;
        do{
          if(c==','){
            c = read();
          }
          if (c < '0' || c > '9'){
            throw new InputMismatchException ();
          }
          res *= 10;
          res += c - '0';
          c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
      }

      public long nextLong(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        int sgn = 1;
        if (c == '-'){
          sgn = -1;
          c = read ();
        }
        long res = 0;
        do{
          if (c < '0' || c > '9'){
            throw new InputMismatchException ();
          }
          res *= 10;
          res += c - '0';
          c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
      }

      public String nextString(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        StringBuilder res = new StringBuilder ();
        do{
          res.appendCodePoint (c);
          c = read ();
        } while (!isSpaceChar (c));
        return res.toString ();
      }

      public boolean isSpaceChar(int c){
        if (filter != null){
          return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
      }

      public static boolean isWhitespace(int c){
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
      }

      private String readLine0(){
        StringBuilder buf = new StringBuilder ();
        int c = read ();
        while (c != '\n' && c != -1){
          if (c != '\r'){
            buf.appendCodePoint (c);
          }
          c = read ();
        }
        return buf.toString ();
      }

      public String nextLine(){
        String s = readLine0 ();
        while (s.trim ().length () == 0)
          s = readLine0 ();
        return s;
      }

      public String nextLine(boolean ignoreEmptyLines){
        if (ignoreEmptyLines){
          return nextLine ();
        }else{
          return readLine0 ();
        }
      }

      public BigInteger nextBigInteger(){
        try{
          return new BigInteger (nextString ());
        } catch (NumberFormatException e){
          throw new InputMismatchException ();
        }
      }

      public char nextCharacter(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        return (char) c;
      }

      public double nextDouble(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        int sgn = 1;
        if (c == '-'){
          sgn = -1;
          c = read ();
        }
        double res = 0;
        while (!isSpaceChar (c) && c != '.'){
          if (c == 'e' || c == 'E'){
            return res * Math.pow (10, nextInt ());
          }
          if (c < '0' || c > '9'){
            throw new InputMismatchException ();
          }
          res *= 10;
          res += c - '0';
          c = read ();
        }
        if (c == '.'){
          c = read ();
          double m = 1;
          while (!isSpaceChar (c)){
            if (c == 'e' || c == 'E'){
              return res * Math.pow (10, nextInt ());
            }
            if (c < '0' || c > '9'){
              throw new InputMismatchException ();
            }
            m /= 10;
            res += (c - '0') * m;
            c = read ();
          }
        }
        return res * sgn;
      }

      public boolean isExhausted(){
        int value;
        while (isSpaceChar (value = peek ()) && value != -1)
          read ();
        return value == -1;
      }

      public String next(){
        return nextString ();
      }

      public SpaceCharFilter getFilter(){
        return filter;
      }

      public void setFilter(SpaceCharFilter filter){
        this.filter = filter;
      }

      public interface SpaceCharFilter{
        public boolean isSpaceChar(int ch);
      }
    }
    /******************** Pair class ***********************/

  class Pair implements Comparable<Pair>{
     public int a;
     public int b;
     public Pair(){
      this.a = 0;
      this.b = 0;
    }
    public Pair(int a,int b){
      this.a = a;
      this.b = b;
    }
    public int compareTo(Pair p){
      if(this.b==p.b){
       return this.a-p.a;  
     }
     return (this.b - p.b); 
   }
   public String toString(){
    return "a="+this.a+" b="+this.b;
  }

}