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;
string s;
long long n, ans;
long long sum[1000011], cnt[1000011];
stack<long long> ops;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> s;
  n = s.length();
  for (long long i = 0; i < n; i++) {
    if (s[i] == '(')
      ops.push(i);
    else {
      if (ops.empty()) continue;
      long long idx = ops.top();
      ops.pop();
      long long len = i - idx + 1;
      if (idx > 0) sum[i] = sum[idx - 1];
      sum[i] += len;
      ans = max(ans, sum[i]);
      cnt[sum[i]]++;
    }
  }
  cnt[0] = 1;
  cout << ans << " " << cnt[ans] << endl;
  return 0;
}