





'''simple docstring'''

def 						UpperCamelCase    (							_lowerCamelCase : list[list[int | float]]	):
    A__    =      len(_lowerCamelCase	)
    A__    =      len(matrix[0]	)
    A__    =      min(_lowerCamelCase						,	_lowerCamelCase	)

    for row in range(_lowerCamelCase	):
        # Check if diagonal element is not zero
        if matrix[row][row] != 0:
            # Eliminate all the elements below the diagonal
            for col in range(row + 1						,	_lowerCamelCase	):
                A__    =      matrix[col][row] / matrix[row][row]
                for i in range(_lowerCamelCase						,	_lowerCamelCase	):
                    matrix[col][i] -= multiplier * matrix[row][i]
        else:
            # Find a non-zero diagonal element to swap rows
            A__    =      True
            for i in range(row + 1						,	_lowerCamelCase	):
                if matrix[i][row] != 0:
                    A__,     A__    =      matrix[i], matrix[row]
                    A__    =      False
                    break
            if reduce:
                rank -= 1
                for i in range(_lowerCamelCase	):
                    A__    =      matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
            row -= 1

    return rank


if __name__ == "__main__":
  import doctest

  doctest.testmod()










'''simple docstring'''

def 						UpperCamelCase    (							_lowerCamelCase : int	):

    if not isinstance(_lowerCamelCase						,	_lowerCamelCase	):
        A__    =      F"Input value of [number={number}] must be an integer"
        raise TypeError(_lowerCamelCase	)

    if number < 1:
        A__    =      F"Input value of [number={number}] must be > 0"
        raise ValueError(_lowerCamelCase	)

    A__    =      1

    for i in range(1						,	_lowerCamelCase	):
        current_number *= 4 * i - 2
        current_number //= i + 1

    return current_number


if __name__ == "__main__":
  import doctest

  doctest.testmod()



