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 dp[1234567];
char s[1234567];
int main() {
  gets(s);
  int n = strlen(s);
  vector<int> st;
  memset(dp, 0, sizeof(dp));
  for (int i = 0; i < n; i++) {
    if (s[i] == '(') {
      st.push_back(i);
    } else {
      if (st.empty()) {
      } else {
        int he = st[st.size() - 1];
        st.pop_back();
        if (!he)
          dp[i] = i + 1;
        else
          dp[i] = dp[he - 1] + i - he + 1;
      }
    }
  }
  int ans = 0, cnt = 1;
  for (int i = 0; i < n; i++) {
    if (dp[i] == ans) {
      cnt++;
    } else if (dp[i] > ans) {
      ans = dp[i];
      cnt = 1;
    }
  }
  if (!ans) cnt = 1;
  printf("%d %d\n", ans, cnt);
  return 0;
}