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;
stack<int> s;
int dp[1000001];
int main() {
  string str;
  cin >> str;
  int size = 0, num = 1, sum = 0, csize = 0;
  for (int i = 0; i < str.size(); i++) {
    if (str[i] == '(')
      s.push(i);
    else if (not s.empty()) {
      int j = s.top();
      int csize = (i - j) + 1;
      s.pop();
      dp[i] = csize + ((j) ? dp[j - 1] : 0);
      if (dp[i] == size)
        num++;
      else if (dp[i] > size)
        size = dp[i], num = 1;
    }
  }
  cout << size << ' ' << num << endl;
  return 0;
}