P16432 [HackerRank] Chessboard game again 1
普及
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

见题面

输出格式

见题面

样例输入
2 3 5 4 5 8 8 2 6 7 1 7 2 7 3 7 4 7 4 7 4
样例输出
First Second