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;
const double Pi = acos(-1.0);
const int INF = 1 << 29;
int p, t, r, m = 1;
int lb[1000005], rb[1000005];
string s;
int main(int argc, char** argv) {
  cin >> s;
  for (int i = 0; i < (int)s.size(); i++) {
    if (s.c_str()[i] == '(') {
      lb[p++] = i;
    } else {
      if (p > 0) {
        p--;
        rb[i] = t = i - lb[p] + 1 + rb[lb[p] - 1];
        if (r < t) {
          r = t;
          m = 1;
        } else if (r == t) {
          m++;
        }
      }
    }
  }
  printf("%d %d\n", r, m);
  return 0;
}