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.

Sample Input 1

3
A
B
C

Sample Output 1

No

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

Sample Input 2

1
ABA

Sample Output 2

Yes

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

Sample Input 3

4
CBA
ACB
AD
CAB

Sample Output 3

Yes