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.

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.

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.

Sample Input 1

3
tanaka taro
tanaka jiro
suzuki hanako

Sample 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.

Sample Input 2

3
aaa bbb
xxx aaa
bbb yyy

Sample Output 2

No

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

Sample Input 3

2
tanaka taro
tanaka taro

Sample Output 3

No

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

Sample Input 4

3
takahashi chokudai
aoki kensho
snu ke

Sample Output 4

Yes

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

见题面 Input 部分

见题面 Output 部分