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;
int main() {
  string s;
  cin >> s;
  int n = s.length();
  int best = 0;
  int best_cnt = 1;
  for (int i = 0, j; i < n; i = j) {
    for (; i < n && s[i] != '('; ++i)
      ;
    if (i == n) break;
    int sum = 1;
    for (j = i + 1; j < n; ++j) {
      if (s[j] == '(')
        ++sum;
      else
        --sum;
      if (sum < 0) break;
    }
    if (j == n && sum > 0) {
      break;
    }
    if (best < j - i) {
      best = j - i;
      best_cnt = 1;
    } else if (best == j - i) {
      ++best_cnt;
    }
  }
  reverse(s.begin(), s.end());
  for (int i = 0, j; i < n; i = j) {
    for (; i < n && s[i] != ')'; ++i)
      ;
    if (i == n) break;
    int sum = 1;
    for (j = i + 1; j < n; ++j) {
      if (s[j] == ')')
        ++sum;
      else
        --sum;
      if (sum < 0) break;
    }
    if (j == n && sum > 0) {
      break;
    }
    if (best < j - i) {
      best = j - i;
      best_cnt = 1;
    } else if (best == j - i) {
      if (j - i < n) ++best_cnt;
    }
  }
  cout << best << " " << best_cnt << endl;
  return 0;
}