Timmy is learning about function transformations! For a function ~g(x)=af(k(x-d))+c~, ~g(x)~ is the graph of ~f(x)~, but

1. Vertically stretched by a factor of ~a~
2. Horizontally compressed by a factor of ~\frac 1k~
3. Horizontally translated by ~d~ units right
4. Vertically translated ~c~ units up

For this problem, you can assume that ~a~, ~d~, and ~c~ are all nonnegative integers, and ~k~ is a positive integer. Additionally, the numbers will always be present (even if they are redundant, such as when ~k=1~).

Can you help Timmy with his homework?

Constraints

~0\le a,d,c\le 10^6~

~0<k\le 10^6~

Input Specification

One line with one string, a function of the form ~af(k(x-d))+c~

Output Specification

4 lines of the following form:

Vertically stretched by a factor of [a]
Horizontally compressed by a factor of 1/[k]
Horizontally translated by [d] units right
Vertically translated [c] units up

Where each square bracket ([n]) means that the number n replaces the bracket (we do not include the square brackets)

Sample Input

10f(3(x-4))+5

Sample Output

Vertically stretched by a factor of 10
Horizontally compressed by a factor of 1/3
Horizontally translated by 4 units right
Vertically translated 5 units up