#include <bits/stdc++.h>
using namespace std;
template <typename T1, typename T2>
string print_iterable(T1 begin_iter, T2 end_iter, int counter) {
  bool done_something = false;
  stringstream res;
  res << "[";
  for (; begin_iter != end_iter and counter; ++begin_iter) {
    done_something = true;
    counter--;
    res << *begin_iter << ", ";
  }
  string str = res.str();
  if (done_something) {
    str.pop_back();
    str.pop_back();
  }
  str += "]";
  return str;
}
vector<int> SortIndex(int size, std::function<bool(int, int)> compare) {
  vector<int> ord(size);
  for (int i = 0; i < size; i++) ord[i] = i;
  sort(ord.begin(), ord.end(), compare);
  return ord;
}
template <typename T>
bool MinPlace(T& a, const T& b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
bool MaxPlace(T& a, const T& b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename S, typename T>
ostream& operator<<(ostream& out, const pair<S, T>& p) {
  out << "{" << p.first << ", " << p.second << "}";
  return out;
}
template <typename T>
ostream& operator<<(ostream& out, const vector<T>& v) {
  out << "[";
  for (int i = 0; i < (int)v.size(); i++) {
    out << v[i];
    if (i != (int)v.size() - 1) out << ", ";
  }
  out << "]";
  return out;
}
template <class TH>
void _dbg(const char* name, TH val) {
  clog << name << ": " << val << endl;
}
template <class TH, class... TA>
void _dbg(const char* names, TH curr_val, TA... vals) {
  while (*names != ',') clog << *names++;
  clog << ": " << curr_val << ", ";
  _dbg(names + 1, vals...);
}
const int MAXN = 301000;
int N;
int d[MAXN];
string S;
int x;
int d2[MAXN];
int compute(int a, int b) {
  for (int i = 0; i < a; i++) d2[i] = d[i];
  for (int i = b; i < N; i++) d2[i] = d[i];
  int diff = 0;
  if (S[a] == S[b])
    diff = 0;
  else if (S[a] == ')')
    diff = 2;
  else
    diff = -2;
  for (int i = a; i < b; i++) d2[i] = d[i] + diff;
  int mm = 1e9;
  int cnt = 0;
  for (int i = 0; i < N; i++) {
    if (d2[i] == mm) cnt++;
    if (d2[i] < mm) mm = d2[i], cnt = 1;
  }
  return cnt;
}
pair<int, pair<int, int>> solve1() {
  int a = N;
  int b = -1;
  for (int i = 0; i < N; i++) {
    if (S[i] == ')') a = i;
    if (d[i] == x) break;
  }
  for (int i = N - 1; i >= 0; i--) {
    if (d[i] == x) break;
    if (S[i] == '(') b = i;
  }
  if (a > b) return {compute(0, 0), {0, 0}};
  return {compute(a, b), {a, b}};
}
pair<int, pair<int, int>> solve2() {
  int a = N;
  int b = -1;
  for (int i = 0; i < N; i++) {
    if (S[i] == ')') a = i;
    if (d[i] == x or d[i] == x + 1) break;
  }
  for (int i = N - 1; i >= 0; i--) {
    if (d[i] == x or d[i] == x + 1) break;
    if (S[i] == '(') b = i;
  }
  if (a > b) return {compute(0, 0), {0, 0}};
  return {compute(a, b), {a, b}};
}
pair<int, pair<int, int>> solve0() {
  int nomove = compute(0, 0);
  int res = nomove;
  pair<int, int> best = {0, 0};
  for (int i = 0; i < N; i++) {
    if (d[i] == x or d[i] == x + 1) continue;
    int a = N;
    int b = -1;
    for (int j = i; j < N; j++) {
      if (S[j] == '(') {
        a = j;
        break;
      }
      if (d[j] == x or d[j] == x + 1) break;
    }
    int last_i = i + 1;
    for (int j = i; j < N; j++) {
      last_i = j;
      if (d[j] == x or d[j] == x + 1) break;
    }
    for (int j = last_i; j >= a; j--) {
      if (S[j] == ')') {
        b = j;
        break;
      }
    }
    i = last_i;
    if (a > b) continue;
    int ris = nomove;
    for (int j = a; j < b; j++)
      if (d[j] == x + 2) ris++;
    if (ris > res) {
      res = ris;
      best = {a, b};
    }
  }
  return {res, best};
}
pair<int, pair<int, int>> solvem1() {
  int res = 0;
  pair<int, int> best = {0, 0};
  for (int i = 0; i < N; i++) {
    if (d[i] == x) continue;
    int a = N;
    int b = -1;
    for (int j = i; j < N; j++) {
      if (S[j] == '(') {
        a = j;
        break;
      }
      if (d[j] == x) break;
    }
    int last_i = i + 1;
    for (int j = i; j < N; j++) {
      last_i = j;
      if (d[j] == x) break;
    }
    for (int j = last_i; j >= a; j--) {
      if (S[j] == ')') {
        b = j;
        break;
      }
    }
    i = last_i;
    if (a > b) continue;
    int ris = 0;
    for (int j = a; j < b; j++)
      if (d[j] == x + 1) ris++;
    if (ris > res) {
      res = ris;
      best = {a, b};
    }
  }
  return {res, best};
}
pair<int, pair<int, int>> solve_slow() {
  pair<int, int> best;
  int res = 0;
  for (int a = 0; a < N; a++) {
    for (int b = a; b < N; b++) {
      if (res < compute(a, b)) {
        res = compute(a, b);
        best = {a, b};
      }
    }
  }
  return {res, best};
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> N;
  cin >> S;
  for (int i = 0; i < N; i++) {
    if (i > 0) d[i] = d[i - 1];
    if (S[i] == '(')
      d[i]++;
    else
      d[i]--;
  }
  if (d[N - 1] != 0) {
    cout << 0 << "\n";
    cout << 1 << " " << 1 << "\n";
    return 0;
  }
  for (int i = 0; i < N; i++) x = min(x, d[i]);
  vector<pair<int, pair<int, int>>> res(4);
  res[0] = solve1();
  res[1] = solve2();
  res[2] = solve0();
  res[3] = solvem1();
  sort(res.begin(), res.end());
  cout << res.back().first << "\n";
  cout << res.back().second.first + 1 << " " << res.back().second.second + 1
       << "\n";
}
