Minlexes
Description
Some time ago Lesha found an entertaining string $s$ consisting of lowercase English letters. Lesha immediately developed an unique algorithm for this string and shared it with you. The algorithm is as follows.
Lesha chooses an arbitrary (possibly zero) number of pairs on positions $(i, i + 1)$ in such a way that the following conditions are satisfied:
- for each pair $(i, i + 1)$ the inequality $0 \le i < |s| - 1$ holds;
- for each pair $(i, i + 1)$ the equality $s_i = s_{i + 1}$ holds;
- there is no index that is contained in more than one pair.
Lesha is interested in the lexicographically smallest strings he can obtain by applying the algorithm to the suffixes of the given string.
The only line contains the string $s$ ($1 \le |s| \le 10^5$) — the initial string consisting of lowercase English letters only.
In $|s|$ lines print the lengths of the answers and the answers themselves, starting with the answer for the longest suffix. The output can be large, so, when some answer is longer than $10$ characters, instead print the first $5$ characters, then "...", then the last $2$ characters of the answer.
Input
The only line contains the string $s$ ($1 \le |s| \le 10^5$) — the initial string consisting of lowercase English letters only.
Output
In $|s|$ lines print the lengths of the answers and the answers themselves, starting with the answer for the longest suffix. The output can be large, so, when some answer is longer than $10$ characters, instead print the first $5$ characters, then "...", then the last $2$ characters of the answer.
Samples
abcdd
3 abc
2 bc
1 c
0
1 d
abbcdddeaaffdfouurtytwoo
18 abbcd...tw
17 bbcdd...tw
16 bcddd...tw
15 cddde...tw
14 dddea...tw
13 ddeaa...tw
12 deaad...tw
11 eaadf...tw
10 aadfortytw
9 adfortytw
8 dfortytw
9 fdfortytw
8 dfortytw
7 fortytw
6 ortytw
5 rtytw
6 urtytw
5 rtytw
4 tytw
3 ytw
2 tw
1 w
0
1 o
Note
Consider the first example.
- The longest suffix is the whole string "abcdd". Choosing one pair $(4, 5)$, Lesha obtains "abc".
- The next longest suffix is "bcdd". Choosing one pair $(3, 4)$, we obtain "bc".
- The next longest suffix is "cdd". Choosing one pair $(2, 3)$, we obtain "c".
- The next longest suffix is "dd". Choosing one pair $(1, 2)$, we obtain "" (an empty string).
- The last suffix is the string "d". No pair can be chosen, so the answer is "d".
In the second example, for the longest suffix "abbcdddeaaffdfouurtytwoo" choose three pairs $(11, 12)$, $(16, 17)$, $(23, 24)$ and we obtain "abbcdddeaadfortytw"