P22304 [CodeChef] SPACEARR
普及
题目描述

Read problem statements in [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.

Finally, progress reached the Madoka family and she decided to play with her little sister in the sensational game Space Arrays.

The rules of the game are as follows:
Initially, a sequence $a_{1}, a_{2}, \ldots, a_{N}$ is given.
The players alternate turns.
In each turn, the current player must choose an index $i$ and increment $a_{i}$, i.e. change $a_{i}$ to $a_{i} + 1$.
Afterwards, if there is no permutation $p_{1}, p_{2}, \ldots, p_{N}$ of the integers $1$ through $N$ such that $a_{i} ≤ p_{i}$ holds for each valid $i$, the current player loses.
Otherwise, the game continues with the next turn.

Madoka is asking you to help her ― tell her if the first player (the player that plays in the first turn) or second player wins this game if both play optimally.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-separated integers $a_{1}, a_{2}, \ldots, a_{N}$.

------ Output ------
For each test case, print a single line containing the string "First" if the first player wins or "Second" if the second player wins (without quotes).

------ Constraints ------
$1 ≤ T ≤ 2 \cdot 10^{4}$
$1 ≤ N ≤ 2 \cdot 10^{5}$
The sum of $N$ over all test cases doesn't exceed $2 \cdot 10^{5}$
$1 ≤ a_{i} ≤ N$ for each valid $i$

------ Subtasks ------
Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------
4

4

1 2 3 3

4

1 1 3 3

5

1 2 2 1 5

3

2 2 3
----- Sample Output 1 ------
First

Second

Second

Second
----- explanation 1 ------
Example case 1:
- If the first player increases the fourth element, the resulting sequence is $(1,2,3,4)$. The second player loses after increasing any of the elements.
- If the first player increases the second element, the resulting sequence is $(1,3,3,3)$, and he loses because there is no valid permutation. For example if $p=(2,1,4,3)$, the second element of $a$ is greater than the second element of $p$.

输入格式

见题面

输出格式

见题面

样例输入
4 4 1 2 3 3 4 1 1 3 3 5 1 2 2 1 5 3 2 2 3
样例输出
First Second Second Second