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];
bool is[1000006];
int main() {
  int i, j, len;
  while (gets(s)) {
    len = strlen(s);
    memset(is, false, sizeof(is));
    stack<int> sd;
    for (i = 0; i < len; i++) {
      if (s[i] == ')') {
        if (!sd.empty()) {
          is[i] = is[sd.top()] = true;
          sd.pop();
        }
      } else {
        sd.push(i);
      }
    }
    int maxi = 0, c = 1, now = 0;
    for (i = 0; i < len; i++) {
      if (is[i] == true) {
        now++;
      } else {
        now = 0;
      }
      if (now > maxi) {
        maxi = now;
        c = 1;
      } else if (now > 0 && now == maxi) {
        c++;
      }
    }
    printf("%d %d\n", maxi, c);
  }
  return 0;
}