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;
  cin >> s;
  int len = 0;
  stack<int> stk;
  stk.push(0);
  map<int, int> mp;
  int n = s.length();
  for (int i = 0; i < n; i++) {
    if (s[i] == '(')
      stk.push(i + 1);
    else {
      if (s[stk.top() - 1] == '(') {
        stk.pop();
        int t = i + 1;
        int x = t - stk.top();
        if (x >= len) {
          len = x;
          mp[len]++;
        }
      } else
        stk.push(i + 1);
    }
  }
  if (len == 0)
    cout << "0"
         << " "
         << "1";
  else
    cout << len << " " << mp[len] << endl;
  return 0;
}