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 main() {
  string s;
  vector<int> ind;
  cin >> s;
  stack<char> ltor, rtol;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == '(')
      ltor.push('(');
    else {
      if (ltor.empty())
        ind.push_back(i);
      else
        ltor.pop();
    }
  }
  for (int i = s.size() - 1; i >= 0; i--) {
    if (s[i] == ')')
      rtol.push(')');
    else {
      if (rtol.empty())
        ind.push_back(i);
      else
        rtol.pop();
    }
  }
  if (rtol.empty() && ltor.empty())
    cout << s.size() << " " << 1 << endl;
  else if (ind.size() == s.size())
    cout << 0 << " " << 1 << endl;
  else {
    sort(ind.begin(), ind.end());
    int maxl = ind[0], cnt = 1;
    for (int i = 1; i <= ind.size(); i++) {
      if (i < ind.size()) {
        int newl = ind[i] - ind[i - 1] - 1;
        if (newl == maxl)
          cnt++;
        else if (newl > maxl) {
          maxl = newl;
          cnt = 1;
        }
      } else {
        int newl = s.size() - ind[i - 1] - 1;
        if (newl == maxl)
          cnt++;
        else if (newl > maxl) {
          maxl = newl;
          cnt = 1;
        }
      }
    }
    cout << maxl << " " << cnt << endl;
  }
}