Bracket Sequence（CF-223A）

Problem Description

A bracket sequence is a string, containing only characters "(", ")", "[" and "]".

A correct bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()[]", "([])" are correct (the resulting expressions are: "(1)+[1]", "([1+1]+1)"), and "](" and "[" are not. The empty string is a correct bracket sequence by definition.

A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (where |s| is the length of string s) is the string slsl + 1... sr. The empty string is a substring of any string by definition.

You are given a bracket sequence, not necessarily correct. Find its substring which is a correct bracket sequence and contains as many opening square brackets «[» as possible.

Input

The first and the only line contains the bracket sequence as a string, consisting only of characters "(", ")", "[" and "]". It is guaranteed that the string is non-empty and its length doesn't exceed 105 characters.

Output

In the first line print a single integer — the number of brackets «[» in the required bracket sequence. In the second line print the optimal sequence. If there are more than one optimal solutions print any of them.

Examples

Input

([])

Output

1
([])

Input

(((

Output

0

题意：给出一个括号序列，要求寻找这个序列的子串，要求这个子串是一个匹配的括号序列，而且其中包含 [] 的个数最多

思路：栈

利用栈对括号进行匹配，不断的入栈出栈，最后使得所有不匹配的括号位置都在栈中，然后分别对栈中不匹配的位置进行分段统计，统计序列中每一段匹配位置中 [] 的个数，最后记录个数最多的值

以 ([[]]([] 为例，将括号序列与序列长度依次压入栈中，将序列长度压入栈中是为了便于统计序列最后一段

有：

栈中元素	0	1	2	3	4	5	6	7	8(len)
对应含义	(	[	[	]	]	(	[	]	序列长度

匹配完毕后：

栈中元素	0	5	8(len)
对应含义	(	(	序列长度

每次出栈两个元素，分别统计原序列区间 [1,4]、[6,7] 匹配字段中 [] 的个数，更新最大值

Source Program

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