Shiritori

AtCoder

IDabc278_f

Time2000ms

Memory256MB

Difficulty—

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: $N$ $S_1$ $S_2$ $\vdots$ $S_N$ [samples]

Samples

Input #1

6
enum
float
if
modint
takahashi
template

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.

Input #2

10
catch
chokudai
class
continue
copy
exec
havoc
intrinsic
static
yucatec

Output #2

Second

Input #3

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

Output #3

First

API Response (JSON)

{
  "problem": {
    "name": "Shiritori",
    "description": {
      "content": "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 distin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc278_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 distin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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