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No.2282 Boxed Nim

レベル : / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 158
作問者 : みここ / テスター : cureskol 👑 箱星 👑 potato167
お気に入りにしたユーザー ProblemId : 9167 / 自分の提出
問題文最終更新日: 2023-04-29 09:55:52
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Problem Statement

There are $N$ boxes, and the $i$-th box contains $A_i$ stones. Initially, the lids of all boxes are closed.

Two players play a game using these boxes. Starting with the first player, the two players alternately perform one of the following operations.

  • Choose one box whose lid is closed and open its lid.
  • Choose one box whose lid is open and which contains at least one stone, and remove one or more stones from the box.

The player who first becomes unable to perform an operation loses, and the other player wins.

Determine which player wins the game when both players act optimally.

Input

$N$
$A_1 \ A_2 \ \cdots \ A_N$
  • All input values are integers.
  • $1 \le N \le 10^5$
  • $0 \le A_i \le 10^9$

Output

Print First if the first player wins, and Second if the second player wins.

Sample

Sample 1
Input
3
0 1 2
Output
First

Here is one example of how the game may proceed.

  1. The first player opens the $2$-nd box.
  2. The second player opens the $1$-st box.
  3. The first player takes $1$ stone out of the $2$-nd box.
  4. The second player opens the $3$-rd box.
  5. The first player takes $2$ stones out of the $3$-rd box.

After that, the second player cannot perform an operation, so the first player wins.

Sample 2
Input
2
1 1
Output
Second
Sample 3
Input
8
2 0 2 3 0 2 1 0
Output
First

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