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;
map<int, int> c;
int main() {
  string s;
  cin >> s;
  int w = 0, cnt = 1, mx = 0;
  c[0] = -1;
  for (int i = 0; i < s.size(); i++) {
    w += (s[i] == '(' ? 1 : -1);
    if (w < 0) {
      c.clear();
      w = 0;
      c[0] = i;
      continue;
    }
    if (c.count(w) && s[i] == ')') {
      int l = i - c[w];
      if (l > mx) {
        mx = l;
        cnt = 1;
      } else if (mx == l) {
        cnt++;
      }
    } else if (s[i] == '(')
      c[w] = i;
  }
  cout << mx << " " << cnt;
}