Score : $400$ points

Problem Statement

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:

$N$

$S_1$ $T_1$

$S_2$ $T_2$

$\vdots$

$S_N$ $T_N$

Output

Print Yes if they can change their handles to fulfill all of their requests subject to the conditions; print No otherwise.

2
b m
m d

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.

3
a b
b c
c a

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.

5
aaa bbb
yyy zzz
ccc ddd
xxx yyy
bbb ccc

Yes