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 arr[1000000];
int main() {
  string s;
  cin >> s;
  stack<int> st;
  int p = s.length();
  int cnt = 0, mx = 0, anx = 0;
  for (int x = 0; x < p; x++) {
    if (s[x] == '(') {
      st.push(x);
    } else {
      if (!st.empty()) {
        int top = st.top();
        st.pop();
        arr[x] = arr[top - 1] + x - top + 1;
        if (arr[x] > mx) {
          mx = arr[x];
          anx = 1;
        } else if (arr[x] == mx) {
          anx++;
        }
      }
    }
  }
  if (mx != 0)
    cout << mx << " " << anx;
  else
    cout << 0 << " " << 1;
}