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B - Unique Nicknames

Score : $200$ points

Problem Statement

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.

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Input

Input is given from Standard Input in the following format:

$N$

$s_1$ $t_1$

$s_2$ $t_2$

$\vdots$

$s_N$ $t_N$

Output

If it is possible to give nicknames to all the $N$ people, print Yes; otherwise, print No.

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3
tanaka taro
tanaka jiro
suzuki hanako

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.

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3
aaa bbb
xxx aaa
bbb yyy

No

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

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2
tanaka taro
tanaka taro

No

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

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3
takahashi chokudai
aoki kensho
snu ke

Yes

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