A complex number is a number of the form a+bi, whereby a and b are constants, and i is a special value that is defined as the square root of -1. Of course, you never try to actually calculate what the square root of -1 is, as that gives a runtime error; in complex numbers, you always let the i remain. For instance, the complex number 3+2i cannot be simplified any further.

Multiplication of two complex numbers a+bi and c+di is defined as

(a×cb×d)+(a×d+b×c)i

Assignment

We represent a complex number as a tuple of two numeric values. Write a function product that calculates the multiplication of two complex numbers.

Example

>>> product((3, 4), (7, 2))
(13, 34)