A. Convoluted

The discrete convolution of the two vectors <A, B, C> and <X, Y, Z> is <A*X, B*X + A*Y, C*X + B*Y + A*Z>. Generally, the convolution of f and g, f*g, is

 

(with 0's understood for vector indices < 0 and ≥ the vectors's length).

We want to find the convolutions of vectors of complex numbers. Recall the multiplication of two complex numbers:

Input

The input consists of pairs of lines of complex numbers. The real and imaginary component of each number is an integer. Each line of the pair represents a vector, and both vectors have equal length. Each pair will be separated by a blank line.

No line will be more than 12 complex numbers. Assume the convoluted terms can be represented by 32-bit integers.

The imaginary part never is written with a unary minus in front; e.g., -1 + -2i. Rather, that would be written as -1-2i. Also the real and imaginary components are always written even when zero; e.g., -1+0i and 0-2i. For 0i, always precede it with a plus; e.g., -1+0i, not -1-0i.

Output

Your output should be a single line of complex numbers (space separated) that is the convolution for the imput pair. There should be a blank line between cases.

Sample Input

4+4i
2-2i

-7+3i 5-2i
11-13i -17+19i

5-4i 3+2i 7+0i
2+8i 9-13i 1-9i

Sample Output

16+0i

-38+124i 91-271i

42+32i -17-73i 36-14i