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>
char in[1000005];
int st[1000005];
int val[1000005];
int cst;
int maxx = 0;
int ct = 1;
int main() {
  int i;
  scanf("%s", in + 1);
  for (i = 1; in[i] != '\0'; i++) {
    if (in[i] == '(')
      st[cst++] = i;
    else if (cst > 0) {
      cst--;
      val[i] = i - st[cst] + 1 + val[st[cst] - 1];
      if (val[i] > maxx)
        maxx = val[i], ct = 1;
      else if (val[i] == maxx)
        ct++;
    }
  }
  printf("%d %d\n", maxx, ct);
}