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;
const int N = 1e6 + 30;
int a[N], used[N];
int main() {
  string s;
  cin >> s;
  stack<int> st;
  int n = s.size();
  fill(a, a + n + 10, -1);
  int f = 0;
  for (int i = 0; i < n; i++) {
    if (s[i] == '(') {
      st.push(i);
      continue;
    }
    if (st.empty()) continue;
    a[st.top()] = i;
    f = 1;
    st.pop();
  }
  if (!f) {
    cout << "0 1";
    return 0;
  }
  int mx_len = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] == -1) continue;
    if (used[i]) continue;
    int len = 0;
    int j = i;
    while (a[j] < n && j < n) {
      used[j] = 1;
      if (a[j] == -1) break;
      len += a[j] - j + 1;
      j = a[j] + 1;
    }
    mx_len = max(mx_len, len);
  }
  cout << mx_len << " ";
  fill(used, used + n + 10, 0);
  int t = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] == -1) continue;
    if (used[i]) continue;
    int len = 0;
    int j = i;
    while (a[j] < n && j < n) {
      used[j] = 1;
      if (a[j] == -1) break;
      len += a[j] - j + 1;
      j = a[j] + 1;
    }
    if (len == mx_len) t++;
  }
  cout << t;
}