Description

To distinguish between genuine and fake educational websites, you need to write a program to judge website domain names.

In this problem, a website domain name must satisfy the following requirements:

• It is a string composed of uppercase and lowercase letters, digits, and ..

• No two . are adjacent, and the string does not start or end with a ..

• There is at least one ..

Additionally, in this problem, an educational website domain name must satisfy the following requirements:

• It is a valid website domain name.

• Let the domain name be in the format $T_1.T_2.\ \dots\ .T_{m-1}.T_m$, where $m$ is a positive integer with $m\geq 3$, and $T_i$ represents the $i$-th maximal contiguous segment consisting only of letters and digits.

• In the above condition, $T_{m-1}$ must be equivalent to $\texttt{edu}$, and $T_m$ must be equivalent to $\texttt{cn}$ (in this problem, two strings are equivalent if they are equal when case is ignored for letters).

You are given a string $S$ of length $n$, guaranteed to conform to the website domain name format described above.

Let $S_i$ denote the substring of $S$ from the first character to the $i$-th character. For all positive integers $i$ satisfying $1\leq i\leq n$, you need to determine whether $S_i$ is an educational website domain name, i.e., whether it satisfies the educational website domain name format. Output all such positive integers $i$ in ascending order.

You do not need to verify whether the given domain name actually exists.

Input Format

A single line containing the string $S$, guaranteed to conform to the website domain name format described in the problem.

Output Format

A single line containing all positive integers $i$ that satisfy the conditions, listed in ascending order.

h5.zxx.edu.CN

13

FeOI.Round3.5.on.1u0gu.0r9

A.Edu.Cn1.Edu.Cn2

8 16

Hint

Sample Explanation #1

$S_{13}=\texttt{h5.zxx.edu.CN}$. For $S_{13}$, $m=4$, $T_1=\texttt{h5}$, $T_2=\texttt{zxx}$, $T_3=\texttt{edu}$, $T_4=\texttt{CN}$.

Here, $T_3$ is equivalent to $\texttt{edu}$, and $T_4$ is equivalent to $\texttt{cn}$, so $S_{13}$ is an educational website domain name.

Sample Explanation #2

None of the $S_i$ substrings are educational website domain names.

Constraints

This problem uses bundled tests.

For all test data: $3\leq n\leq 10^6$.

• Subtask 1 (20 points): $n\leq 6$.

• Subtask 2 (40 points): $n\leq 1000$.

• Subtask 3 (40 points): No additional constraints.

By Deepseek V3.