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;
void solve() {
  string s;
  cin >> s;
  int n = s.size();
  int dp[n];
  stack<int> st;
  int mx = 0;
  for (int i = 0; i < n; i++) {
    if (s[i] == '(') {
      dp[i] = 0;
      st.push(i);
    } else {
      if (st.empty()) {
        dp[i] = 0;
      } else {
        int k = st.top();
        dp[i] = i - k + 1 + dp[max(k - 1, 0)];
        st.pop();
      }
    }
    mx = max(dp[i], mx);
  }
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (dp[i] == mx) cnt++;
  }
  if (mx != 0) {
    cout << mx << " " << cnt << endl;
  } else
    cout << 0 << " " << 1 << endl;
}
int main() {
  solve();
  return 0;
}