As Simple as One and Two
Contest: Technocup 2020 - Elimination Round 4
Difficulty rating: 1400
Tags: dp, greedy

You are given a non-empty string $$$s=s_1s_2\dots s_n$$$, which consists only of lowercase Latin letters. Polycarp does not like a string if it contains at least one string "one" or at least one string "two" (or both at the same time) as a substring. In other words, Polycarp does not like the string $$$s$$$ if there is an integer $$$j$$$ ($$$1 \le j \le n-2$$$), that $$$s_{j}s_{j+1}s_{j+2}=$$$"one" or $$$s_{j}s_{j+1}s_{j+2}=$$$"two".

For example:

- Polycarp does not like strings "oneee", "ontwow", "twone" and "oneonetwo" (they all have at least one substring "one" or "two"),
- Polycarp likes strings "oonnee", "twwwo" and "twnoe" (they have no substrings "one" and "two").

Polycarp wants to select a certain set of indices (positions) and remove all letters on these positions. All removals are made at the same time.

For example, if the string looks like $$$s=$$$"onetwone", then if Polycarp selects two indices $$$3$$$ and $$$6$$$, then "onetwone" will be selected and the result is "ontwne".

What is the minimum number of indices (positions) that Polycarp needs to select to make the string liked? What should these positions be?

Input format:
The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases in the input. Next, the test cases are given.

Each test case consists of one non-empty string $$$s$$$. Its length does not exceed $$$1.5\cdot10^5$$$. The string $$$s$$$ consists only of lowercase Latin letters.

It is guaranteed that the sum of lengths of all lines for all input data in the test does not exceed $$$1.5\cdot10^6$$$.

Output format:
Print an answer for each test case in the input in order of their appearance.

The first line of each answer should contain $$$r$$$ ($$$0 \le r \le |s|$$$) — the required minimum number of positions to be removed, where $$$|s|$$$ is the length of the given line. The second line of each answer should contain $$$r$$$ different integers — the indices themselves for removal in any order. Indices are numbered from left to right from $$$1$$$ to the length of the string. If $$$r=0$$$, then the second line can be skipped (or you can print empty). If there are several answers, print any of them.

Constraints:
Time limit: 3.0 s
Memory limit: 256.0 MB

Note:
In the first example, answers are:

- "onetwone",
- "testme" — Polycarp likes it, there is nothing to remove,
- "oneoneone",
- "twotwo".

In the second example, answers are:

- "onetwonetwooneooonetwooo",
- "two",
- "one",
- "twooooo",
- "ttttwo",
- "ttwwoo" — Polycarp likes it, there is nothing to remove,
- "ooone",
- "onnne" — Polycarp likes it, there is nothing to remove,
- "oneeeee",
- "oneeeeeeetwooooo".

Example input:
4
onetwone
testme
oneoneone
twotwo

Example output:
2
6 3
0

3
4 1 7 
2
1 4

Example input:
10
onetwonetwooneooonetwooo
two
one
twooooo
ttttwo
ttwwoo
ooone
onnne
oneeeee
oneeeeeeetwooooo

Example output:
6
18 11 12 1 6 21 
1
1 
1
3 
1
2 
1
6 
0

1
4 
0

1
1 
2
1 11

Editorial:
Consider each occurrence of substrings one and two. Obviously, at least one character have to be deleted in such substrings. These substrings cannot intersect in any way, except for one case: twone. Thus, the answer is necessarily no less than the value $$$c_{21}+c_{1}+c_{2}$$$, where $$$c_{21}$$$ is the number of occurrences of the string twone and $$$c_{1}$$$ is the number of occurrences of the string one (which are not part of twone) and $$$c_{2}$$$ is the number of occurrences of the string two (which are not part of twone).
Let's propose a method that does exactly $$$ c_ {21} + c_ {1} + c_ {2} $$$ removals and, thus, will be optimal.
• Delete character o in each occurrence of twone. This action will delete both substrings one and two at the same time.
• Next, delete character n in each occurrence of one. This action will delete all substrings one.
• Next, delete character w in each occurrence of two. This action will delete all substrings two.
Note that it is important to delete the middle letters in the last two paragraphs to avoid appearing a new occurrence after a line is collapsed.
The following is an example of a possible implementation of the main part of a solution: