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.

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.

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.

Sample Input 1

2
b m
m d

Sample 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.

Sample Input 2

3
a b
b c
c a

Sample 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.

Sample Input 3

5
aaa bbb
yyy zzz
ccc ddd
xxx yyy
bbb ccc

Sample Output 3

Yes

见题面 Input 部分

见题面 Output 部分