Remove One or Cut to a Third

Difficulty: 1800 6000 ms 128 MB

dp games

A single pile of n stones; a move removes 1 stone, or removes exactly two-thirds (so a pile of size divisible by 3 may drop to a third). The player unable to move loses. For each query n, print the winner.

Input: the first line has Q; each of the next Q lines has a pile size n.

Output: one line per query.

Constraints:

• 1 ≤ Q ≤ 10⁴
• 0 ≤ n ≤ 10⁴

Sample Tests

3
1
3
9

FIRST
FIRST
SECOND

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