import java.util.Scanner;

public class Gauss1
{
   public static void main(String[] args)
   {
      Scanner in = new Scanner(System.in);

      double[][] A;
      double[]   b;
      double     pivot, factor;
      int        n;   // Number of variables

      int i, j, k;

      System.out.print("Number of unknows: ");
      n = in.nextInt();         // Read in problem size

      A = new double[n][n];     // Reserve space for coefficient matrix
      b = new double[n];        // Reserve space for RHS vector

      // Read in the rows, one row at a time
      for (i = 0; i < n; i++)
      {
         // Read in row i's coefficients
         for (j = 0; j < n; j++)
         {
             System.out.print("A["+i+"]["+j+"] = ");
             A[i][j] = in.nextDouble();
         }

         // Read in row i's RHS
         System.out.print("b["+i+"] = ");
         b[i] = in.nextDouble();
      }

      Print(A, b);

      /* -----------------------------
         Gaussian elimination method
         ----------------------------- */
      for (i = 0; i < n; i++)
      {  // Process row i 

         /* ---------------------
            (A) Select pivot
            --------------------- */
         pivot = A[i][i];

         /* ---------------------
            (B) Normalize row i
            --------------------- */
         for (j = 0; j < n; j++)
            A[i][j] = A[i][j]/pivot;

         b[i] = b[i]/pivot;

         // ******* Show result 
         System.out.println("After normalizing row " + (i+1) + ":");
         Print(A, b);

         /* ---------------------
            (C) Sweep using row i
            --------------------- */
         for (k = 0; k < n; k++)
         {
            if ( k != i )
            {
               factor = A[k][i];

               for (j = 0; j < n; j++)
                  A[k][j] = A[k][j] - factor*A[i][j];

               b[k] = b[k] - factor*b[i];
            }
         }

         // ******* Show result 
         System.out.println("After sweeping other rows using row " 
                                + (i+1) + ":");
         Print(A, b);
      }

      System.out.println("======================");
      System.out.println("Solution:");

      for (i = 0; i < n; i++)
         System.out.println("x" + (i+1) + " = " + b[i]);

   }


   public static void Print(double[][] A, double b[])
   {
      int i, j;

      // Print the equations
      for (i = 0; i < b.length; i++)
      {  
         // Print row i
         for (j = 0; j < b.length; j++)
         {
            if ( j != 0 )
               System.out.print(" + ");

            System.out.print(A[i][j] + " x" + (j+1));    
         }

         System.out.println(" = " + b[i]);
      }

      System.out.println();
   }
}