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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  stack<long long> st;
  st.push(-1);
  long long max_len = 0, count = 0;
  for (long long i = 0; i < (s.size()); i++) {
    if (s[i] == '(') {
      st.push(i);
    } else {
      st.pop();
      if (!st.empty()) {
        if (i - st.top() == max_len)
          count++;
        else if (i - st.top() > max_len) {
          max_len = i - st.top();
          count = 1;
        }
      } else {
        st.push(i);
      }
    }
  }
  if (max_len > 0)
    cout << max_len << " " << count << "\n";
  else
    cout << "0 1"
         << "\n";
  return 0;
}