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;
long long max(long long x, long long y) { return x > y ? x : y; }
long long min(long long x, long long y) { return x < y ? x : y; }
void _(long long& a, long long b) {
  a = (a % 1000000007 + b % 1000000007) % 1000000007;
  a = (a + 1000000007) % 1000000007;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  string s;
  cin >> s;
  long long n = s.size();
  long long d[n];
  long long c[n];
  memset(d, 0, sizeof(d));
  memset(c, 0, sizeof(c));
  stack<long long> st;
  for (long long i = 0; i < n; ++i) {
    if (s[i] == '(')
      st.push(i);
    else {
      if (st.empty()) {
        d[i] = c[i] = -1;
      } else {
        d[i] = st.top();
        st.pop();
        c[i] = i - d[i] + 1;
        if (d[i] - 1 >= 0) c[i] = max(c[i], c[i] + c[d[i] - 1]);
      }
    }
  }
  long long ans = 0;
  for (long long i = 0; i < n; ++i) {
    ans = max(ans, c[i]);
  }
  long long dans = 0;
  for (long long i = 0; i < n; ++i) {
    if (c[i] == ans) dans++;
  }
  if (ans)
    cout << ans << " " << dans;
  else
    cout << ans << " 1";
}