CodeForces 3D Least Cost Bracket Sequence

题意：给你一串序列，有左括号右括号和问号，现在需要你把问号变成括号，求最小代价把这个序列变成合法的，如果没有则输出-1

思路：直接暴力扫一遍，先将问号的都变成右括号，如果当前这个括号的位置<0的话，那么就把y-x最大的返回回去变成左括号就行了

#include<bits/stdc++.h>
using namespace std;

priority_queue<pair<long long,int> >Q;
string s;
int main()
{
    cin>>s;
    if(s.size()%2==1)return puts("-1"),0;
    int now=0;
    long long ans=0;
    for(int i=0;i<s.size();i++)
    {
        if(s[i]=='(')
            now++;
        else if(s[i]==')')
            now--;
        else
        {
            int x,y;scanf("%d%d",&x,&y);
            now--;s[i]=')';ans+=y;
            Q.push(make_pair(y-x,i));
        }
        if(now<0)
        {
            if(Q.size()==0)break;
            pair<int,int> a = Q.top();Q.pop();
            ans-=a.first;s[a.second]='(';
            now+=2;
        }
    }
    if(now!=0)return puts("-1"),0;
    cout<<ans<<endl;
    cout<<s<<endl;
}

Description

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.

Input

The first line contains a non-empty pattern of even length, consisting of characters "(", ")" and "?". Its length doesn't exceed 5·10⁴. 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 ≤ 10⁶), where a_i is the cost of replacing the i-th character "?" with an opening bracket, and b_i

Output

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.

Sample Input

Input

(??) 1 2 2 8

Output

4 ()()