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;
string a;
vector<int> v;
int x, y, mx, k = -1;
int main() {
  cin >> a;
  for (int i = 0; i < a.length(); i++) {
    if (a[i] == '(')
      v.push_back(i);
    else if (v.size() > 0) {
      if (v.size() == 1)
        x = i - k;
      else
        x = i - v[v.size() - 2];
      if (x > mx) mx = x, y = 0;
      if (x == mx) y++;
      v.pop_back();
    } else
      k = i;
  }
  cout << mx << " " << max(y, 1);
}