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 = 1000011;
stack<int> st;
char s[N];
int n, dp[N], cnt[N];
int main() {
  scanf("%s", s + 1), n = strlen(s + 1);
  for (register int i = 1; i <= n; ++i)
    if (s[i] == '(')
      st.push(i);
    else if (st.size()) {
      dp[i] = i - st.top() + 1 + dp[st.top() - 1], ++cnt[dp[i]], st.pop();
    }
  cnt[0] = 1;
  for (register int i = n; ~i; --i)
    if (cnt[i]) {
      printf("%d %d", i, cnt[i]);
      return 0;
    }
  return 0;
}