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;
char s[1000006];
int op[10000006];
int main() {
  scanf("%s", s);
  int top = 0, len = strlen(s), bt = 0;
  int max1 = 0, maxcnt = 1;
  memset(op, -1, sizeof(op));
  for (int i = 0; i < len; i++) {
    if (s[i] == '(') {
      if (op[top] == -1) op[top] = i;
      top++;
    } else {
      if (top == bt) {
        top++;
        bt++;
      } else {
        if (i - op[top - 1] + 1 > max1) {
          max1 = i - op[top - 1] + 1;
          maxcnt = 1;
        } else if (i - op[top - 1] + 1 == max1) {
          maxcnt++;
        }
        op[top] = -1;
        top--;
      }
    }
  }
  printf("%d %d", max1, maxcnt);
  return 0;
}