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 l[1000006];
int main() {
  string s;
  cin >> s;
  int j = 0;
  int m = 0, p = 1;
  stack<int> st;
  unordered_map<int, int> mp;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == '(') {
      st.push(i);
    } else if (!st.empty()) {
      int len = i - st.top() + 1;
      if (st.top() != 0)
        l[i] = len + l[i - len];
      else
        l[i] = len;
      mp[l[i]]++;
      st.pop();
    }
  }
  int n = s.length();
  mp[0] = 1;
  cout << *max_element(l, l + n) << " " << mp[*max_element(l, l + n)];
  return 0;
}