Minlexes

题意翻译

给定一只由小写字母组成的字符串 $s$，可以先删除任意个 两相邻相同字符，再把剩下的部分拼接起来。 对于 $s$ 的每个后缀，求进行上述操作后得到的字典序最小的字符串。 $1\le |s|\le 10^5$。

题目描述

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. After that Lesha removes all characters on indexes contained in these pairs and the algorithm is over. Lesha is interested in the lexicographically smallest strings he can obtain by applying the algorithm to the suffixes of the given string.

输入输出格式

输入格式

The only line contains the string $ s $ ( $ 1 \le |s| \le 10^5 $ ) — the initial string consisting of lowercase English letters only.

输出格式

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.

输入输出样例

输入样例 #1

abcdd

输出样例 #1

3 abc
2 bc
1 c
0 
1 d

输入样例 #2

abbcdddeaaffdfouurtytwoo

输出样例 #2

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

说明

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"