102785: [AtCoder]ABC278 F - Shiritori

Problem Statement

You are given $N$ strings $S _ 1,S _ 2,\ldots,S _ N$. $S _ i\ (1\leq i\leq N)$ is a non-empty string of length at most $10$ consisting of lowercase English letters, and the strings are pairwise distinct.

Taro the First and Jiro the Second play a word-chain game. In this game, the two players take alternating turns, with Taro the First going first. In each player's turn, the player chooses an integer $i\ (1\leq i\leq N)$, which should satisfy the following two conditions:

• $i$ is different from any integer chosen by the two players so far since the game started;
• the current turn is the first turn of the game, or the last character of $S_j$ equals the first character of $S_i$, where $j$ is the last integer chosen.

The player who is unable to choose a conforming $i$ loses; the other player wins.

Determine which player will win if the two players play optimally.

Constraints

• $1 \leq N \leq 16$
• $N$ is an integer.
• $S _ i\ (1\leq i\leq N)$ is a non-empty string of length at most $10$ consisting of lowercase English letters.
• $S _ i\neq S _ j\ (1\leq i\lt j\leq N)$

Input

The input is given from Standard Input in the following format:

$N$
$S_1$
$S_2$
$\vdots$
$S_N$

Output

Print First if Taro the First wins when the two players play optimally; print Second if Jiro the Second wins.

Sample Input 1

6
enum
float
if
modint
takahashi
template

Sample Output 1

First

For example, the game progresses as follows. Note that the two players may not be playing optimally in this example.

• Taro the First chooses $i=3$. $S _ i=$if.
• Jiro the Second chooses $i=2$. $S _ i=$float, and the last character of if equals the first character of float.
• Taro the First chooses $i=5$. $S _ i=$takahashi, and the last character of float equals the first character of takahashi.
• Jiro the Second is unable to choose $i\neq2,3,5$ such that $S _ i$ starts with i, so he loses.

In this case, Taro the First wins.

Sample Input 2

10
catch
chokudai
class
continue
copy
exec
havoc
intrinsic
static
yucatec

Sample Output 2

Second

Sample Input 3

16
mnofcmzsdx
lgeowlxuqm
ouimgdjxlo
jhwttcycwl
jbcuioqbsj
mdjfikdwix
jhvdpuxfil
peekycgxco
sbvxszools
xuuqebcrzp
jsciwvdqzl
obblxzjhco
ptobhnpfpo
muizaqtpgx
jtgjnbtzcl
sivwidaszs

Sample Output 3

First

输入

输入通过标准输入以以下格式给出：

$N$
$S_1$
$S_2$
$\vdots$
$S_N$

输出

如果小太郎在两个玩家发挥最佳水平时获胜，则打印 First；如果次郎获胜，则打印 Second。

样例输入 1

6
enum
float
if
modint
takahashi
template

样例输出 1

First

例如，游戏进行如下所示。 请注意，这两个玩家在此示例中可能没有发挥最佳水平。

• 小太郎选择 $i=3$。$S _ i=$if。
• 次郎选择 $i=2$。$S _ i=$float，并且 if 的最后一个字符等于 float 的第一个字符。
• 小太郎选择 $i=5$。$S _ i=$takahashi，并且 float 的最后一个字符等于 takahashi 的第一个字符。
• 次郎无法选择 $i\neq2,3,5$，使得 $S _ i$ 以 i 开头，所以他输掉了比赛。

在这种情况下，小太郎获胜。

样例输入 2

10
catch
chokudai
class
continue
copy
exec
havoc
intrinsic
static
yucatec

样例输出 2

Second

样例输入 3

16
mnofcmzsdx
lgeowlxuqm
ouimgdjxlo
jhwttcycwl
jbcuioqbsj
mdjfikdwix
jhvdpuxfil
peekycgxco
sbvxszools
xuuqebcrzp
jsciwvdqzl
obblxzjhco
ptobhnpfpo
muizaqtpgx
jtgjnbtzcl
sivwidaszs

样例输出 3

First