




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						list[list[int | float]]				)  ->							Optional[int]:
    UpperCAmelCase_										=					len(__UpperCamelCase				)
    UpperCAmelCase_										=					len(matrix[0]				)
    UpperCAmelCase_										=					min(__UpperCamelCase	,					__UpperCamelCase				)

    for row in range(__UpperCamelCase				):
        # 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	,					__UpperCamelCase				):
                UpperCAmelCase_										=					matrix[col][row] / matrix[row][row]
                for i in range(__UpperCamelCase	,					__UpperCamelCase				):
                    matrix[col][i] -= multiplier * matrix[row][i]
        else:
            # Find a non-zero diagonal element to swap rows
            UpperCAmelCase_										=					True
            for i in range(row + 1	,					__UpperCamelCase				):
                if matrix[i][row] != 0:
                    UpperCAmelCase_			,							UpperCAmelCase_										=					matrix[i], matrix[row]
                    UpperCAmelCase_										=					False
                    break
            if reduce:
                rank -= 1
                for i in range(__UpperCamelCase				):
                    UpperCAmelCase_										=					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()











def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						float	,					__UpperCamelCase      :						float				)  ->							float:

    if density <= 0:
        raise ValueError('''Impossible fluid density'''				)
    if bulk_modulus <= 0:
        raise ValueError('''Impossible bulk modulus'''				)

    return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
 import doctest

 doctest.testmod()





