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 sta[1000001], head, ans[1000001];
char s[1000001];
int main() {
  int ans1 = 0, ans2 = 1;
  scanf("%s", s);
  for (int i = 0; s[i]; ++i) {
    if (s[i] == ')') {
      if (!head) continue;
      head--;
      ans[i] = i - sta[head] + 1 + ans[sta[head] - 1];
      if (ans1 == ans[i])
        ans2++;
      else if (ans1 < ans[i]) {
        ans1 = ans[i];
        ans2 = 1;
      }
    } else
      sta[head++] = i;
  }
  printf("%d %d", ans1, ans2);
  return 0;
}