Polish mathematician Wacław Sierpiński (18821969)
described the 2D geometric figure known as the
Sierpiński triangle as part of his work on set theory in
1915. The triangle, which is really an infinite collection of
points, can be constructed by the following algorithm:

The initial shape is a solid triangle.

Shrink the current shape to half its dimensions (both
height and width), and make two more copies of it (giving
three copies total).

Arrange the three copies so that each touches the two
others at their corners. Set the current shape to be the
union of these three.

Repeat from step 2.
Here is an illustration of the first few iterations:






iteration

$0$

$1$

$2$

$3$

$4$

As the iterations go to infinity, this process creates an
infinite number of connected points. However, consider the case
of a finite number of iterations. If the initial triangle has a
circumference of $3$, what
is the sum of the circumferences of all (black) triangles at a
given iteration? Write a program to find out not the exact
circumference, but the number of decimal digits required to
represent its integer portion. That is, find the number of
decimal digits required to represent the largest integer that
is at most as large as the circumference.
Input
Each test case is a line containing a nonnegative integer
$0 \leq n \leq 10\, 000$
indicating the number of iterations.
Output
For each case, display the case number followed by the
number of decimal digits required to represent the integer
portion of the circumference for the given number of
iterations. Follow the format of the sample output.
Sample Input 1 
Sample Output 1 
0
1
5
10
100

Case 1: 1
Case 2: 1
Case 3: 2
Case 4: 3
Case 5: 19
