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;
char s[1000010];
int sta[1000010], size = 0, d[1000010];
int main() {
  cin >> s;
  int len = 0, cnt = 1;
  for (int i = 0; s[i]; i++) {
    if (s[i] == '(')
      sta[++size] = i;
    else {
      if (size) {
        int x;
        d[i] = (x = sta[size--])
                   ? ((s[x - 1] == ')' && d[x - 1] != -1) ? d[x - 1] : x)
                   : 0;
        if (i - d[i] + 1 > len) {
          len = i - d[i] + 1;
          cnt = 1;
        } else if (i - d[i] + 1 == len) {
          cnt++;
        }
      } else
        d[i] = -1;
    }
  }
  printf("%d %d\n", len, cnt);
}