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() {
  long maxi = 0;
  long kol = 1;
  string s;
  cin >> s;
  long now = 0;
  long last = 0;
  long koll = 0;
  for (long i = 0; i < s.size(); i++) {
    if (s[i] == '(')
      now++;
    else
      now--;
    if (now < 0) {
      if (koll == maxi) kol++;
      if (koll > maxi) {
        maxi = koll;
        kol = 1;
      }
      last = i + 1;
      now = 0;
      koll = 0;
    } else
      koll++;
  }
  if (now == 0) {
    if (koll == maxi) kol++;
    if (koll > maxi) {
      maxi = koll;
      kol = 1;
    }
  }
  if (now > 0) {
    s.assign(s.begin() + last, s.end());
    reverse(s.begin(), s.end());
    now = 0;
    last = -1;
    koll = 0;
    for (long i = 0; i < s.size(); i++) {
      if (s[i] == ')')
        now++;
      else
        now--;
      if (now < 0) {
        if (koll == maxi) kol++;
        if (koll > maxi) {
          maxi = koll;
          kol = 1;
        }
        last = i + 1;
        now = 0;
        koll = 0;
      } else
        koll++;
    }
    if (now == 0) {
      if (koll == maxi) kol++;
      if (koll > maxi) {
        maxi = koll;
        kol = 1;
      }
    }
  }
  if (maxi == 0) kol = 1;
  cout << maxi << " " << kol;
}