CodeForces - 5C Longest Regular Bracket Sequence

This is yet another problem dealing with regular bracket sequences.

We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not.

You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10⁶.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Example

Input

)((())))(()())

Output

6 2

Input

))(

Output

0 1

#include<iostream>
#include<string.h>
#include<cstdio>
#include<stack>

using namespace std;

char s[1000005];
int dp[1000005];
stack<int> st;

int main()
{
    scanf("%s",s);
    int ans=0,maxx=0,i,l=strlen(s);
    for(i=0;i<l;++i)
    {
        if(s[i]=='(')
            st.push(i);
            else
            {
                if(!st.empty())
                {
                    int t=st.top();
                    st.pop();
                    dp[i]=dp[t-1]+i-t+1;
                    if(dp[i]>maxx)
                    {
                        maxx=dp[i];
                        ans=1;
                    }
                    else if(dp[i]==maxx) 
                        ans++;
                }
            }
    }
    if(!maxx) 
        ans=1;
    printf("%d %d\n",maxx,ans);
    
    return 0;
}