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>
const double PI = 3.141592653589793238460;
using namespace std;
int E[1000001], S[1000001], F[1000001];
int main() {
  string st;
  int mx = 0;
  stack<int> stk;
  cin >> st;
  for (int i = 0; i < st.size(); i++) {
    char ch = st[i];
    if (ch == '(') {
      stk.push(i);
    } else {
      if (stk.empty()) {
        S[i] = E[i] = -1;
      } else {
        int idx = stk.top();
        stk.pop();
        S[i] = E[i] = idx;
        if (idx > 0 && st[idx - 1] == ')' && S[idx - 1] >= 0) E[i] = E[idx - 1];
        int l = i - E[i] + 1;
        F[l]++;
        mx = max(mx, l);
      }
    }
  }
  F[0] = 1;
  cout << mx << " " << F[mx];
}