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No.3586 Divide and Be Conquered

レベル : / AI推定難易度 : 2100 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 1024 MB / 標準ジャッジ問題
タグ : (解説公開後に AC するまで非表示) / 解いたユーザー数 30
作問者 : marc2825 / テスター : siganai
お気に入りにしたユーザー ProblemId : 13439 / 自分の提出
問題文最終更新日: 2026-09-01 06:51:14
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yukicoder contest 504 (順位表) の他の問題:

Problem Statement

There are $N$ piles, and pile $i$ contains $A_i$ stones.

$2$ players play a game using these piles. Starting with the first player, they alternately perform the following operation† $1$ time on the current set of piles.

  1. The player whose turn it is chooses $1$ pile containing $2$ or more stones.
  2. The opponent splits that pile into $2$ piles, each containing $1$ or more stones.
    That is, letting $x$ be the number of stones in the chosen pile, the pile is split into a pile of $a$ stones and a pile of $b$ stones, using positive integers $a,b$ such that $x=a+b$.
  3. The player whose turn it is chooses one of the $2$ split piles and removes it. The other pile remains as it is.

A player who cannot perform the operation loses.

You are given $T$ test cases. For each test case, determine which player wins, the first player or the second player, when both play optimally.


† In this problem, steps 1, 2, 3 above are collectively called "1 operation".

Constraints

  • $1 \leq T \leq 10^5$
  • $1 \leq N$
  • $1 \leq A_{i} \leq 10^{18}$
  • The sum of $N$ over all test cases is at most $2 \times 10^5$
  • $T$, $N$, $A_{i}$ are integers

Input

The input is given from standard input in the following format. Here, the $t\ (1 \leq t \leq T)$-th test case is denoted by $\mathrm{case}_t$.

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$

Each test case is given in the following format.

$N$
$A_1$ $A_2$ $\dots$ $A_N$

Here, $N$ is the number of piles in that test case, and $A_i$ is the number of stones in the $i$-th pile in that test case.

Output

Output $T$ lines. For each test case, print First on 1 line if the first player wins, and Second if the second player wins.

Sample

Sample 1
Input
4
1
1
1
2
1
4
3
2 3 7
Output
Second
First
Second
First

In the $1$st test case, there is only a pile with $1$ stone, so the first player cannot perform the operation and loses.
In the $2$nd test case, the first player chooses the pile with $2$ stones. The second player has no choice but to split it into piles of $1$ stone and $1$ stone. After that, the first player removes one of them, leaving only a pile with $1$ stone. The second player cannot perform the operation and loses.

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