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 D[1000100], rs, nr, N;
bool B[1000100];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> S;
  N = S.length();
  B[0] = 1;
  for (int i = 1; i <= N; i++) B[i] = S[i - 1] == ')';
  for (int i = 2; i <= N; i++) {
    if (B[i] && !B[i - D[i - 1] - 1]) D[i] = 2 + D[i - 1] + D[i - D[i - 1] - 2];
    if (D[i] > rs)
      rs = D[i], nr = 1;
    else if (D[i] == rs)
      nr++;
  }
  if (rs == 0) return cout << 0 << ' ' << 1, 0;
  cout << rs << ' ' << nr;
}