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;
long long int sqr(long long int x) { return x * x; }
inline long long int add(long long int a, long long int b) {
  long long int c = (a % 1000000007) + (b % 1000000007);
  if (c >= 1000000007) c -= 1000000007;
  return c;
}
inline long long int mul(long long int a, long long int b) {
  return ((a % 1000000007) * 1ll * (b % 1000000007)) % 1000000007;
}
inline long long int sub(long long int a, long long int b) {
  long long int c = (a % 1000000007) - (b % 1000000007);
  if (c < 0) c += 1000000007;
  return c;
}
const long long int nax = 300 * 1000 + 10;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  string s;
  cin >> s;
  stack<long long int> st;
  st.push(-1);
  long long int ans = 0, last = 1;
  for (long long int i = 0; i < s.size(); ++i) {
    if (s[i] == '(') {
      st.push(i);
    } else {
      if (st.size()) {
        st.pop();
        if (st.empty()) {
          st.push(i);
          continue;
        }
        long long int to = st.top();
        if (i - to > ans) {
          ans = i - to;
          last = 1;
        } else if (i - to == ans) {
          ++last;
        }
      }
    }
  }
  if (ans == 0)
    cout << "0 1";
  else
    cout << ans << " " << last;
  return 0;
}