题目描述
Two players are playing a game on a $15\times15$ chessboard. The rules of the game are as follows:
The game starts with $\boldsymbol{\mbox{k}}$ coins located at one or more $(x,y)$ coordinates on the board (a single cell may contain more than one coin). The coordinate of the upper left cell is $(1,1)$, and the coordinate of the lower right cell is $(15,15)$.
In each move, a player must move a single coin from some cell $(x,y)$ to one of the following locations:
$(x-2,y+1)$
$(x-2,y-1)$
$(x+1,y-2)$
$(x-1,y-2)$.
Note: The coin must remain inside the confines of the board.
The players move in alternating turns. The first player who is unable to make a move loses the game.
The figure below shows all four possible moves:
Note: While the figure shows a $8\times8$ board, this game is played on a $15\times15$ board.
Given the value of $\boldsymbol{\mbox{k}}$ and the initial coordinate(s) of $\boldsymbol{\mbox{k}}$ coins, determine which player will win the game. Assume both players always move optimally.
Input Format
The first line contains an integer, $\mathbf{T}$, denoting the number of test cases.
Each test case is defined as follows over the subsequent lines:
The first line contains an integer, $\boldsymbol{\mbox{k}}$, denoting the number of coins on the board.
Each line $\boldsymbol{i}$ (where $0\leq i<k$) of the $\boldsymbol{\mbox{k}}$ subsequent lines contains $2$ space-separated integers describing the respective values of $x_i$ and $y_i$ of the coordinate where coin $k_i$ is located.
Note: Recall that a cell can have more than one coin (i.e., any cell can have $0$ to $\boldsymbol{\mbox{k}}$ coins in it at any given time).
Constraints
$1\leq T\leq1000$
$1\leq k\leq1000$
$1\leq x_i,y_i\leq15$, where $0\leq i<k$.
Output Format
On a new line for each test case, print $\textbf{First}$ if the first player is the winner; otherwise, print $\textbf{Second}$.
Sample Input
2
3
5 4
5 8
8 2
6
7 1
7 2
7 3
7 4
7 4
7 4
Sample Output
First
Second
输入格式
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输出格式
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