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.

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.