code forces 990C

时间：2018-06-11 13:20:53 阅读：172 评论：0 收藏：0 [点我收藏+]

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

A regular 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 regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You are given $n$

If $s_{i} + s_{j}$

Input

The first line contains one integer $n (1 \leq n \leq 3 \cdot 10^{5})$

Output

In the single line print a single integer — the number of pairs $i, j (1 \leq i, j \leq n)$

Examples

input

Copy

3
)
()
(

output

Copy

input

Copy

2
()
()

output

Copy

Note

In the first example, suitable pairs are $(3, 1)$

In the second example, any pair is suitable, namely $(1, 1), (1, 2), (2, 1), (2, 2)$

题意，寻找合法的括号匹配对数（1,3）和（3,1）不同

题解：感谢llw大佬讲题，思路是将每一组括号转化成对应的值来匹配，计算可匹配的值，相加即可得到答案

#include<bits/stdc++.h>
using namespace std;
const int maxn = 3e5+5;
typedef long long ll;
ll n,mx=0;
char str[maxn];
map<ll,ll> mp;
int main(){
    ios::sync_with_stdio(false);
    cin>>n;
    while(n--){
        cin>>str;
        ll flag=0,k=0,len=strlen(str);
        for(int i=0;i<len;i++){
              if(str[i]==‘(‘) k++;
              else k--;
              //k=0的情况是这组数据符合要求
              //k>0的情况是左大于右
              //k<0的情况是右大于左
              if(k<0) flag=min(flag,k);
        }
        if(flag<0&&k>flag) continue;  //不合法的序列不用管,譬如())(
        else{
            //cout<<k<<" "<<flag<<endl;
            mp[k]++;
            mx=max(k,mx);
        }
    }
    ll ans=0;
    for(int i=0;i<=mx;i++){
        ans+=mp[i]*mp[-i];
    }
    cout<<ans<<endl;
    return 0;
}

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

You are given $n$ bracket sequences $s_{1}, s_{2}, \dots, s_{n}$ . Calculate the number of pairs $i, j (1 \leq i, j \leq n)$ such that the bracket sequence $s_{i} + s_{j}$ is a regular bracket sequence. Operation $+$ means concatenation i.e. "()(" + ")()" = "()()()".

If $s_{i} + s_{j}$ and $s_{j} + s_{i}$ are regular bracket sequences and $i \neq j$ , then both pairs $(i, j)$ and $(j, i)$ must be counted in the answer. Also, if $s_{i} + s_{i}$ is a regular bracket sequence, the pair $(i, i)$ must be counted in the answer.

Input

The first line contains one integer $n (1 \leq n \leq 3 \cdot 10^{5})$ — the number of bracket sequences. The following $n$ lines contain bracket sequences — non-empty strings consisting only of characters "(" and ")". The sum of lengths of all bracket sequences does not exceed $3 \cdot 10^{5}$ .

Output

In the single line print a single integer — the number of pairs $i, j (1 \leq i, j \leq n)$ such that the bracket sequence $s_{i} + s_{j}$ is a regular bracket sequence.

Examples
input
Copy
3
)
()
(
output
Copy
2
input
Copy
2
()
()
output
Copy
4

Note

In the first example, suitable pairs are $(3, 1)$ and $(2, 2)$ .

In the second example, any pair is suitable, namely $(1, 1), (1, 2), (2, 1), (2, 2)$ .

code forces 990C

原文：https://www.cnblogs.com/buerdepepeqi/p/9166339.html

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