题目描述
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.
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.
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.
- $S _ i\neq S _ j$\ $(1\leq i\lt j\leq N)$
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
输入格式
见题面 Input 部分
输出格式
见题面 Output 部分