Problem: 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".

Examples

Input

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


Output

6 2


Input

))(


Output

0 1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long M = 1000000007;
const double pi = acos(-1);
const int N = 1e5 + 10;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  string s;
  cin >> s;
  stack<long long> st;
  st.push(-1);
  long long q = 0, mx = 0, c = 0;
  for (long long i = 0; i < s.size(); i++) {
    if (s[i] == '(')
      st.push(i);
    else {
      st.pop();
      if (st.empty())
        st.push(i);
      else {
        q = i - st.top();
        if (q == mx) c++;
        if (q > mx) mx = q, c = 1;
      }
    }
  }
  if (mx == 0) c = 1;
  cout << mx << " " << c;
}