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;
int dp[1000005], mx, cnt = 1;
int main() {
  cin >> s;
  for (int i = 0; i < s.size(); i++) {
    int prev = i - 2 * dp[i - 1] - 1;
    if (s[i] == ')' && s[prev] == '(' && prev >= 0)
      dp[i] = dp[prev - 1] + dp[i - 1] + 1;
    if (2 * dp[i] > mx) {
      mx = 2 * dp[i];
      cnt = 1;
    } else if (2 * dp[i] == mx && mx > 0)
      cnt++;
  }
  cout << mx << " " << cnt << "\n";
  return 0;
}