import java.util.ArrayList;

/**
   A magic square is an n x n matrix which, if filled with numbers,
   the sum of the elements in each row, each column,
   and the two diagonal is the same value.
*/
public class Square
{
   /**
      Construct a Square object.
      @param input the list of numbers
   */
   public Square(ArrayList input)
   {
      size = (int) Math.sqrt(input.size());
      square = new int[size][size];

      for (int i = 0; i < size ; i++)
         for (int j = 0; j < size ; j++)
            square[i][j] = input.get(i * size + j);
   }

   /**
      Display the contents of the square.
      @param the ith row
      @param the jth column
      @return a string represenation of the square
   */
   public String toString(int i, int j)
   {
      String s = "   " + square[i][j];
      return s.substring(s.length() - 3, s.length());
   }

   /**
      Search for a number in the square.
      @param n the number to search for
      @return if the number is found, false otherwise
   */
   public boolean found(int n)
   {
      for (int i = 0; i < size ; i++)
      {
         for (int j = 0; j < size ; j++)
         {
            if (square[i][j] == n)
               return true;
         }
      }
      return false;
   }

   /**
      Add the numbers in the square.
      @param i the row/column to add
      @param row determines if a row or column should be added
      @return sum the sum of the row/column
   */
   public int add(int i, boolean row)
   {
      int sum = 0;

      for (int j = 0; j < size; j++)
      {
         if (row)
            sum = sum + square[i][j];
         else
            sum = sum + square[j][i];
      }
      return sum;
   }

   /**
      Find the sum of the diagonal.
      @param mainDiagonal determine if it is the main diagonal
      @return sum the sum of the diagonal
   */
   public int diagonalSum(boolean mainDiagonal)
   {
      int sum = 0;
      for (int i = 0; i < size; i++)
      {
         int j;
         if (mainDiagonal)
            j = i;
         else
            j = size - 1 - i;
         sum = sum + square[i][j];
      }
      return sum;
   }

   /**
      Determine if the square is a magic square.
      @return true if square is a magic square, false otherwise
   */
   public boolean isMagic()
   {
      for (int n = 1; n <= size * size; n++)
      {
         if (!found(n))
            return false;
      }

      int sum = diagonalSum(true);

      if (sum != diagonalSum(false))
         return false;
      for (int i = 0; i < size; i++)
      {
         if (sum != add(i, true))
            return false;
         if (sum != add(i, false))
            return false;
      }
      return true;
   }

   private int[][] square;
   private int size;