#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>

void** create_matrix(long long rows, long long cols, long long element_size);
void delete_matrix(void** matrix, long long rows);
int read_matrix(long double** matrix, long long equations);
void print_matrix(long double** matrix, long long equations);
bool gauss_jordan(long double** matrix, long long equations);
bool make1(long double** matrix, long long equations, int row);
void divide_row(long double** matrix, long long equations, long long row, long double divisor);
void make0(long double** matrix, long long equations, long long row, long long reference_row);

int main()
{
	long long equations = 0;

	if ( scanf("%lld\n", &equations) != 1 )
		return feof(stdin) ? 0 : 1;

	if ( equations <= 0 )
		return printf("invalid data\n");

	long double** matrix = (long double**)create_matrix(equations, equations + 1, sizeof(long double));
	if ( matrix == NULL )
		return 3;

	if ( read_matrix(matrix, equations) != 0 )
		return 4;

	print_matrix(matrix, equations);

	gauss_jordan(matrix, equations);

	delete_matrix( (void**)matrix, equations );

	return 0;
}

void** create_matrix(long long rows, long long cols, long long element_size)
{
	void** matrix = calloc(rows, sizeof(void*));
	if ( matrix == NULL )
		return NULL;

	for (long long row_index = 0; row_index < rows; ++row_index )
		if ( ( matrix[row_index] = calloc(cols, element_size) ) == NULL )
			return NULL;

	return matrix;
}

void delete_matrix(void** matrix, long long rows)
{
	for (long long row_index = 0; row_index < rows; ++row_index )
		free( matrix[row_index] );

	free(matrix);
}

int read_matrix(long double** matrix, long long equations)
{
	for (long long row_index = 0; row_index < equations; ++row_index )
		for (long long col_index = 0; col_index < equations + 1; ++col_index )
			if ( scanf("%Lg%*[ \n]", &matrix[row_index][col_index]) != 1 )
				return 4;

	return 0;
}

void print_matrix(long double** matrix, long long equations)
{
	for (long long row_index = 0; row_index < equations; ++row_index )
	{
		for (long long col_index = 0; col_index < equations; ++col_index )
			printf(" %5.2Lf", matrix[row_index][col_index]);

		printf(" | %5.2Lf\n", matrix[row_index][equations]);
	}
	putchar('\n');
}

bool gauss_jordan(long double** matrix, long long equations)
{
	for ( long long active_row = 0; active_row < equations; ++active_row )
	{
		if ( ! make1(matrix, equations, active_row) )
			return false;

		print_matrix(matrix, equations);

		for ( int other_row = 0; other_row < equations; ++other_row )
			if ( active_row != other_row )
				make0(matrix, equations, other_row, active_row);

		print_matrix(matrix, equations);
	}
	return true;
}

bool make1(long double** matrix, long long equations, int row)
{
	if ( matrix[row][row] == 0.0 )
		return false;

	printf("f%d /= %5.2Lf:\n", row + 1, matrix[row][row]);
	divide_row(matrix, equations, row, matrix[row][row]);
	return true;
}

void divide_row(long double** matrix, long long equations, long long row, long double divisor)
{
	for( int column = 0; column < equations + 1; ++column )
		matrix[row][column] /= divisor;
}

void make0(long double** matrix, long long equations, long long row, long long reference_row)
{
	long double inverse = - matrix[row][reference_row];
	printf("f%lld += %5.2Lf f%lld:\n", row + 1, inverse, reference_row + 1);
	for ( int col = 0; col < equations + 1; ++col )
		matrix[row][col] += inverse * matrix[reference_row][col];
}