Flip and Slide
Coins 1..N in a row; each is heads (1) or tails (0). A move: choose a heads coin at position i, flip it to tails, and flip EXACTLY ONE coin at a position < i (either direction). The player who cannot move loses. Determine the winner.
Input: the first line has N; the second line has the N coin states.
Output: FIRST or SECOND.
Constraints:
- 1 ≤ N ≤ 105
Sample Tests
Input 1
4 0 1 0 1
Output 1
FIRST
Input 2
3 1 0 0
Output 2
SECOND
Discussion (opens after you solve — no spoilers before)
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