Score : $1100$ points

Problem Statement

You are given $N$ srings $S_i\ (1\le i \le N)$ consisting of A, B, C, D.

Consider the operation below on a string $T$ consisting of A, B, C, D.

• Repeat the following until $T$ contains none of the strings $S_i$ as a substring.- Choose an $S_i$ and one of its occurrences in $T$, remove that occurrence from $T$, and concatenate the remaining parts.
• Choose an $S_i$ and one of its occurrences in $T$, remove that occurrence from $T$, and concatenate the remaining parts.

What is a substring?

A substring of a string is its contiguous subsequence. For example, A, AB, and BC are substrings of ABC, while BA and AC are not.

We say that the string $T$ is *bad* when multiple strings can result from the operation above.

Determine whether a bad string exists.

Constraints

• $1 \leq N \leq 10^6$
• $1 \leq |S_i| \leq 2 \times 10^6$
• $|S_1|+|S_2|+\dots +|S_N| \leq 2 \times 10^6$
• $S_i \neq S_j$ if $i\neq j$.
• $S_i$ is a string consisting of A, B, C, D.

Input

Input is given from Standard Input in the following format:

$N$

$S_1$

$S_2$

$\vdots$

$S_N$

Output

If a bad string exists, print Yes.

Otherwise, print No.

3
A
B
C

No

The only string we can get from $T$ is what remains after removing all occurrences of A, B, C from $T$.

1
ABA

Yes

For example, from $T=$ ABABA, we can get two strings: AB and BA, so $T$ is a bad string.

4
CBA
ACB
AD
CAB

Yes