Least Cost Bracket Sequence

题意翻译

给一个序列，序列里面会有左括号、问号、右括号。对于一个‘？’而言，可以将其替换为一个‘（’，也可以替换成一个‘）’，但是都有相应的代价。问：如何替换使得代价最小。前提是替换之后的序列中，括号是匹配的。如果不能替换为一个括号匹配的序列则输出-1。 ------------ ### 输入 第一行是序列，序列长度不超过 $5\times 10^4$，下面$m$（$m$是？的数量）行有每行 $2$ 个数据，第一个是 '（'的代价，第2个是 '）' 的代价。 ### 输出： 第一行输出最小代价，第二行输出替换后的序列。不行输出 $-1$。

题目描述

This is yet another problem on regular bracket sequences. A bracket sequence is called regular, if by inserting "+" and "1" into it we get a correct mathematical expression. For example, sequences "(())()", "()" and "(()(()))" are regular, while ")(", "(()" and "(()))(" are not. You have a pattern of a bracket sequence that consists of characters "(", ")" and "?". You have to replace each character "?" with a bracket so, that you get a regular bracket sequence. For each character "?" the cost of its replacement with "(" and ")" is given. Among all the possible variants your should choose the cheapest.

输入输出格式

输入格式

The first line contains a non-empty pattern of even length, consisting of characters "(", ")" and "?". Its length doesn't exceed $ 5·10^{4} $ . Then there follow $ m $ lines, where $ m $ is the number of characters "?" in the pattern. Each line contains two integer numbers $ a_{i} $ and $ b_{i} $ ( $ 1<=a_{i},b_{i}<=10^{6} $ ), where $ a_{i} $ is the cost of replacing the $ i $ -th character "?" with an opening bracket, and $ b_{i} $ — with a closing one.

输出格式

Print the cost of the optimal regular bracket sequence in the first line, and the required sequence in the second. Print -1, if there is no answer. If the answer is not unique, print any of them.

输入输出样例

输入样例 #1

(??)
1 2
2 8

输出样例 #1

4
()()