Remove a Triangular Number

Difficulty: 1800 6000 ms 128 MB

dp games

A single pile of n stones; a move removes a triangular number of stones (1, 3, 6, 10, ...). 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
0
2
9

SECOND
SECOND
SECOND

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