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;
  stack<int> st;
  cin >> s;
  int n = s.size(), maxi = 0, c = 1;
  vector<int> rb(n);
  for (int i = 0; i < n; i++) {
    if (s[i] == '(')
      st.push(i);
    else if (!st.empty()) {
      int j = st.top();
      st.pop();
      rb[i] = i - j + 1;
      if (j > 0) rb[i] += rb[j - 1];
      if (rb[i] == maxi)
        c++;
      else if (rb[i] > maxi) {
        maxi = rb[i];
        c = 1;
      }
    }
  }
  cout << maxi << " " << c;
}