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;
const int mod = 1e9 + 7;
string s;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  vector<long long> v;
  long long x, n = 1, max = 0, k = -1;
  string s;
  cin >> s;
  for (long long i = 0; i < s.size(); i++) {
    if (s[i] == '(')
      v.push_back(i);
    else if (!v.empty()) {
      if (v.size() == 1)
        x = i - k;
      else
        x = i - v[v.size() - 2];
      if (x > max) {
        max = x;
        n = 1;
      } else if (x == max)
        n++;
      v.pop_back();
      ;
    } else
      k = i;
  }
  cout << max << " " << n << endl;
  return 0;
}