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>
int main() {
  char *str;
  scanf(" %ms", &str);
  int hi = 0, freq = 1;
  int pop = 0;
  std::vector<int> st;
  std::vector<int> pre(strlen(str));
  for (int i = 0; str[i]; i++) {
    char &c = str[i];
    if (c == '(') {
      st.push_back(i);
    } else {
      if (!st.empty()) {
        int top = st.back();
        st.pop_back();
        pre[i] = pre[std::max(0, top - 1)] + i - top + 1;
      }
      if (pre[i] > hi) {
        hi = pre[i];
        freq = 1;
      } else if (pre[i] == hi) {
        ++freq;
      }
    }
  }
  return 0 * printf("%d %d\n", hi, hi ? freq : 1);
}