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>
char a[1000006];
int posOpen[1000006];
int dp[1000005];
int val(char x) {
  if (x == '(') {
    return 1;
  } else {
    return -1;
  }
}
int main() {
  scanf("%s", a);
  int n = strlen(a);
  int c = 0;
  int max = 0;
  int maxC = 1;
  for (int i = 0; i < n; i++) {
    if (a[i] == '(') {
      posOpen[c++] = i;
    } else {
      if (c == 0) {
        continue;
      }
      c--;
      int ans = i - posOpen[c] + 1;
      if (posOpen[c] > 0) {
        ans += dp[posOpen[c] - 1];
      }
      dp[i] = ans;
      if (dp[i] > max) {
        max = dp[i];
        maxC = 1;
      } else if (dp[i] == max) {
        maxC++;
      }
    }
  }
  printf("%d %d\n", max, maxC);
}