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 = 1e6 + 50;
char st[maxn];
int main() {
  while (~scanf("%s", st)) {
    int n = strlen(st);
    int op = -1, ed = n, cnt = 0, len = 0, h = 0;
    for (int i = 0; i < n; ++i) {
      if (st[i] == '(')
        ++cnt;
      else if (st[i] == ')')
        --cnt;
      if (cnt == 0) {
        int le = i - op;
        if (le > len) {
          len = le;
          h = 1;
        } else if (le == len) {
          h++;
        }
      } else if (cnt < 0) {
        op = i;
        cnt = 0;
      }
    }
    int tl = 0, tc = 0;
    cnt = 0;
    for (int i = n - 1; i > 0; --i) {
      if (st[i] == ')')
        ++cnt;
      else if (st[i] == '(')
        --cnt;
      if (cnt == 0) {
        int le = ed - i;
        if (le > tl) {
          tl = le;
          tc = 1;
        } else if (le == tl) {
          tc++;
        }
      } else if (cnt < 0) {
        ed = i;
        cnt = 0;
        if (len < tl) {
          len = tl;
          h = tc;
        } else if (len == tl) {
          h += tc;
        }
        tc = 0;
      }
    }
    if (len == 0 && h == 0) h = 1;
    printf("%d %d\n", len, h);
  }
  return 0;
}