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 int32_t Accepted = 0;
template <typename T>
void in(T& x) {
  static char ch;
  static bool neg;
  for (ch = neg = 0; ch < '0' || '9' < ch; neg |= ch == '-', ch = getchar())
    ;
  for (x = 0; '0' <= ch && ch <= '9'; (x *= 10) += ch - '0', ch = getchar())
    ;
  x = neg ? -x : x;
}
template <typename T, typename... Types>
void in(T& x, Types&... oth) {
  static char ch;
  static bool neg;
  for (ch = neg = 0; ch < '0' || '9' < ch; neg |= ch == '-', ch = getchar())
    ;
  for (x = 0; '0' <= ch && ch <= '9'; (x *= 10) += ch - '0', ch = getchar())
    ;
  x = neg ? -x : x;
  in(oth...);
}
template <typename T>
T _pow_mod(T a, T b, T mod) {
  T base = a, res = 1;
  while (b) {
    if (b & 1) res = (res * base) % mod;
    base = (base * base) % mod;
    b >>= 1;
  }
  return res;
}
template <typename T>
T _pow(T a, T b) {
  T base = a, res = 1;
  while (b) {
    if (b & 1) res = (res * base);
    base = (base * base);
    b >>= 1;
  }
  return res;
}
template <typename T>
void out(T x) {
  char s[65];
  int32_t cnt = 0;
  if (x > 0)
    while (x > 0) s[cnt++] = (x - (x / 10 * 10)) + '0', x /= 10;
  else if (x < 0) {
    while (x < 0) s[cnt++] = (x / 10 * 10) - x + '0', x /= 10;
    s[cnt++] = '-';
  }
  if (cnt == 0)
    putchar('0');
  else
    for (int32_t i = cnt - 1; ~i; i--) putchar(s[i]);
}
template <typename T>
void print(T x) {
  out(x);
  putchar('\n');
}
template <typename T, typename... types>
void print(T x, types... oth) {
  out(x);
  putchar(' ');
  print(oth...);
}
const int32_t MAXN = 1e6 + 5;
char s[MAXN];
stack<int> a;
int pos[MAXN];
int32_t main() {
  while (~scanf("%s", s)) {
    while (!a.empty()) a.pop();
    memset(pos, 0, sizeof pos);
    int len = strlen(s);
    for (int i = 0; i < len; i++) {
      if (s[i] == '(') {
        a.push(i);
      } else {
        if (!a.empty()) {
          pos[a.top()] = 1;
          pos[i] = 1;
          a.pop();
        }
      }
    }
    int ans = 0;
    int tmp = 0;
    for (int i = 0; i < len; i++) {
      if (pos[i] == 1)
        tmp++;
      else
        tmp = 0;
      ans = max(ans, tmp);
    }
    tmp = 0;
    int cnt = 0;
    for (int i = 0; i < len; i++) {
      if (pos[i] == 1)
        tmp++;
      else
        tmp = 0;
      if (ans == tmp) cnt++;
    }
    if (ans == 0) cnt = 1;
    print(ans, cnt);
  }
  return Accepted;
}