A |
Integer
Game |
Two players, S and T, are playing a game where they make
alternate moves. S plays first.
In this game, they start with an integer N. In each move, a player removes
one digit from the integer and passes the resulting number to the other player.
The game continues in this fashion until a player finds he/she has no digit to
remove when that player is declared as the loser.
With this restriction, it’s obvious that if the number of digits in N
is odd then S wins otherwise T wins. To make the game more
interesting, we apply one additional constraint. A player can remove a
particular digit if the sum of digits of the resulting number is a multiple of
3 or there are no digits left.
Suppose N = 1234. S has 4 possible moves. That is, he can
remove 1, 2, 3, or 4. Of these, two of
them are valid moves.
- Removal of 4 results in 123 and the sum of digits = 1 + 2 + 3 = 6; 6 is
a multiple of 3.
- Removal of 1 results in 234 and the sum of digits = 2 + 3 + 4 = 9; 9 is a
multiple of 3.
The other two moves are invalid.
If both players play perfectly, who wins?
Input
The
first line of input is an integer T(T<60) that
determines the number of test cases. Each case is a line that contains a
positive integer N. N has at most 1000 digits and does not
contain any zeros.
Output
For
each case, output the case number starting from 1. If S wins then output ‘S’ otherwise output ‘T’.
3 |
Case 1: S |