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 char IO_MODE = 0;
inline long long ReadInt() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
inline void WriteInt(long long x) {
  char CH[20];
  if (x < 0) putchar('-');
  x = -x;
  int Num = 0;
  if (!x) {
    putchar('0');
    return;
  }
  while (x > 0) CH[++Num] = x % 10, x /= 10;
  while (Num) putchar(CH[Num--] + 48);
}
inline void out(int x) {
  if (IO_MODE & 1)
    WriteInt(x);
  else
    printf("%i", x);
}
template <typename... Args>
inline void out(int x, Args... args) {
  out(x);
  putc(' ', stdout);
  out(args...);
}
inline void in(int &x) {
  if (IO_MODE & 2)
    x = ReadInt();
  else
    scanf("%i", &x);
}
template <typename... Args>
inline void in(int &x, Args &...args) {
  in(x);
  in(args...);
}
inline void outll(long long x) {
  if (IO_MODE & 1)
    WriteInt(x);
  else
    printf("%I64d", x);
}
template <typename... Args>
inline void outll(long long x, Args... args) {
  outll(x);
  putc(' ', stdout);
  outll(args...);
}
inline void inll(long long &x) {
  if (IO_MODE & 2)
    x = ReadInt();
  else
    scanf("%I64d", &x);
}
template <typename... Args>
inline void inll(long long &x, Args &...args) {
  inll(x);
  inll(args...);
}
int aa, bb, cc, dd, ee, ff, gg, hh, ii, jj, kk, mm, nn, oo, pp, qq, rr, ss, tt,
    uu, vv, ww, xx, yy, zz;
int tc;
string s;
int dp[1000100];
int main() {
  cin >> s;
  stack<int> st;
  int mx = 0, cnt = 0;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == '(')
      st.push(i);
    else if (!st.empty()) {
      dp[st.top()] = i - st.top() + 1;
      st.pop();
    }
  }
  for (int i = s.size(); i--;) {
    dp[i] += dp[i + dp[i]];
    if (dp[i] > mx)
      mx = dp[i], cnt = 1;
    else if (dp[i] == mx)
      cnt++;
  }
  out(mx, mx ? cnt : 1);
  putc('\n', stdout);
}