Change Usernames

AtCoder

IDabc285_d

Time2000ms

Memory256MB

Difficulty—

You run a web service with $N$ users. The $i$\-th user with a current handle $S_i$ wants to change it to $T_i$. Here, $S_1,\ldots$, and $S_N$ are pairwise distinct, and so are $T_1,\ldots$, and $T_N$. Determine if there is an appropriate order to change their handles to fulfill all of their requests subject to the following conditions: * you change only one user's handle at a time; * you change each user's handle only once; * when changing the handle, the new handle should not be used by other users at that point. ## Constraints * $1 \leq N \leq 10^5$ * $S_i$ and $T_i$ are strings of length between $1$ and $8$ (inclusive) consisting of lowercase English letters. * $S_i \neq T_i$ * $S_i$ are pairwise distinct. * $T_i$ are pairwise distinct. ## Input The input is given from Standard Input in the following format: $N$ $S_1$ $T_1$ $S_2$ $T_2$ $\vdots$ $S_N$ $T_N$ [samples]

Samples

Input #1

2
b m
m d

Output #1

Yes

The $1$\-st user with a current handle `b` wants to change it to `m`.  
The $2$\-nd user with a current handle `m` wants to change it to `d`.
First, you change the $2$\-nd user's handle from `m` to `d`; then you change the $1$\-st user's handle from `b` to `m`. This way, you can achieve the objective.
Note that you cannot change the $1$\-st user's handle to `m` at first, because it is used by the $2$\-nd user at that point.

Input #2

3
a b
b c
c a

Output #2

No

The $1$\-st user with a current handle `a` wants to change it to `b`.  
The $2$\-nd user with a current handle `b` wants to change it to `c`.  
The $3$\-rd user with a current handle `c` wants to change it to `a`.
We cannot change their handles subject to the conditions.

Input #3

5
aaa bbb
yyy zzz
ccc ddd
xxx yyy
bbb ccc

Output #3

Yes

API Response (JSON)

{
  "problem": {
    "name": "Change Usernames",
    "description": {
      "content": "You run a web service with $N$ users. The $i$\\-th user with a current handle $S_i$ wants to change it to $T_i$.   Here, $S_1,\\ldots$, and $S_N$ are pairwise distinct, and so are $T_1,\\ldots$, and $T_N",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc285_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You run a web service with $N$ users.\nThe $i$\\-th user with a current handle $S_i$ wants to change it to $T_i$.  \nHere, $S_1,\\ldots$, and $S_N$ are pairwise distinct, and so are $T_1,\\ldots$, and $T_N...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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