Unique Nicknames

AtCoder

IDabc247_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ people numbered Person $1$, Person $2$, $\dots$, and Person $N$. Person $i$ has a family name $s_i$ and a given name $t_i$. Consider giving a nickname to each of the $N$ people. Person $i$'s nickname $a_i$ should satisfy all the conditions below. * $a_i$ coincides with Person $i$'s family name or given name. In other words, $a_i = s_i$ and/or $a_i = t_i$ holds. * $a_i$ does not coincide with the family name and the given name of any other person. In other words, for all integer $j$ such that $1 \leq j \leq N$ and $i \neq j$, it holds that $a_i \neq s_j$ and $a_i \neq t_j$. Is it possible to give nicknames to all the $N$ people? If it is possible, print `Yes`; otherwise, print `No`. ## Constraints * $2 \leq N \leq 100$ * $N$ is an integer. * $s_i$ and $t_i$ are strings of lengths between $1$ and $10$ (inclusive) consisting of lowercase English alphabets. ## Input 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

3
tanaka taro
tanaka jiro
suzuki hanako

Output #1

Yes

The following assignment satisfies the conditions of nicknames described in the Problem Statement: $a_1 =$ `taro`, $a_2 =$ `jiro`, $a_3 =$ `hanako`. ($a_3$ may be `suzuki`, too.)  
However, note that we cannot let $a_1 =$ `tanaka`, which violates the second condition of nicknames, since Person $2$'s family name $s_2$ is `tanaka` too.

Input #2

3
aaa bbb
xxx aaa
bbb yyy

Output #2

No

There is no way to give nicknames satisfying the conditions in the Problem Statement.

Input #3

2
tanaka taro
tanaka taro

Output #3

No

There may be a pair of people with the same family name and the same given name.

Input #4

3
takahashi chokudai
aoki kensho
snu ke

Output #4

Yes

We can let $a_1 =$ `chokudai`, $a_2 =$ `kensho`, and $a_3 =$ `ke`.

API Response (JSON)

{
  "problem": {
    "name": "Unique Nicknames",
    "description": {
      "content": "There are $N$ people numbered Person $1$, Person $2$, $\\dots$, and Person $N$. Person $i$ has a family name $s_i$ and a given name $t_i$. Consider giving a nickname to each of the $N$ people. Person $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc247_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people numbered Person $1$, Person $2$, $\\dots$, and Person $N$. Person $i$ has a family name $s_i$ and a given name $t_i$.\nConsider giving a nickname to each of the $N$ people. Person $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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