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;
int len[1000000] = {0};
int main() {
  string s;
  stack<int> st;
  int k, maxl = 0, n = 0;
  cin >> s;
  for (int i = 0; i < s.size(); i++) {
    if ('(' == s[i]) {
      st.push(i);
    } else {
      if (!st.empty()) {
        k = st.top();
        st.pop();
        len[i] = (k > 0 ? len[k - 1] : 0) + i + 1 - k;
        if (len[i] > maxl) {
          maxl = len[i];
          n = 1;
        } else if (len[i] == maxl)
          n++;
      }
    }
  }
  if (maxl > 0)
    cout << maxl << " " << n << endl;
  else
    cout << "0 1" << endl;
  return 0;
}