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 MAXN = 1000044;
int tp, ans1, ans2, i, n, st[MAXN];
char s[MAXN];
int main() {
  scanf("%s", s);
  n = strlen(s);
  tp = 0;
  ans1 = 0, ans2 = 1;
  st[0] = -1;
  for (i = 0; i < n; ++i)
    if (tp && s[st[tp]] == '(' && s[i] == ')') {
      if ((i - st[tp - 1]) > ans1) {
        ans1 = (i - st[tp - 1]);
        ans2 = 1;
      } else if (i - st[tp - 1] == ans1)
        ++ans2;
      --tp;
    } else
      st[++tp] = i;
  printf("%d %d\n", ans1, ans2);
  return 0;
}