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 str[1000005];
int a[1000005], s[1000005];
int main() {
  int i = 0, j = 0, max = 0, maxnum = 0;
  scanf("%s", str);
  memset(a, 0, sizeof(a));
  for (i = 0; str[i] != '\0'; i++) {
    if (str[i] == '(')
      s[j++] = i;
    else if (str[i] == ')' && j != 0) {
      int temp = s[--j];
      a[i] = a[temp - 1] + i - temp + 1;
      if (a[i] > max) {
        maxnum = 1;
        max = a[i];
      } else if (a[i] == max)
        maxnum++;
    }
  }
  if (max == 0)
    printf("0 1\n");
  else
    printf("%d %d\n", max, maxnum);
  return 0;
}