Picture
by Liftarn on Wikipedia, public domain
Brian and Susan are old friends, and they always dare
each other to do reckless things. Recently Brian had the
audacity to take the bottom right exit out of their annual maze
race, instead of the usual top left one. In order to trump
this, Susan needs to think big. She will build a house of cards
so big that, should it topple over, the entire country would be
buried by cards. Itâ€™s going to be huge!
The house will have a triangular shape. The illustration to
the right shows a house of height $6$, and Figure 1 shows a
schematic figure of a house of height $5$.
For aesthetic reasons, the cards used to build the tower
should feature each of the four suits (clubs, diamonds, hearts,
spades) equally often. Depending on the height of the tower,
this may or may not be possible. Given a lower bound
$h_0$ on the height of the
tower, what is the smallest possible height $h \ge h_0$ such that it is possible
to build the tower?
Input
A single integer $1 \le h_0
\le 10^{1000}$, the minimum height of the tower.
Output
An integer, the smallest $h
\ge h_0$ such that it is possible to build a tower of
height $h$.
Sample Input 1 
Sample Output 1 
2

5

Sample Input 2 
Sample Output 2 
42

45
