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 a[1000005];
int main() {
  string s;
  int p = 1, q = 1, ans = 0, ansCount = 1;
  a[0] = -1;
  cin >> s;
  for (int i = 0, sz = s.length(); i < sz; i++) {
    if (s[i] == '(') {
      a[p] = i;
      p++;
    } else {
      p--;
      if (p == 0) {
        a[0] = i;
        p = 1, q = 1;
      } else {
        int dis = i - a[p - 1];
        if (dis > ans) {
          ans = dis, ansCount = 1;
        } else if (dis == ans)
          ansCount++;
      }
    }
  }
  cout << ans << " " << ansCount;
  return 0;
}