#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vb = vector<bool>;
using vc = vector<char>;
using vvc = vector<vc>;
using vvi = vector<vi>;
using vvb = vector<vb>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vull = vector<ull>;
constexpr int INF = 2000000000;
constexpr ll INFl = 2000000000ll;
constexpr ll INFll = 2000000000000000000ll;
constexpr ll mod = 1e9 + 7;
struct num {
  num(ll val = 0) : v{val} {
    if (v >= mod) v %= mod;
  };
  ll v;
  operator ll() { return v; };
  num operator+(const num& o) const { return {v + o.v}; };
  num operator-(const num& o) const { return {v - o.v + mod}; };
  num operator*(const num& o) const { return {v * o.v}; };
  num operator+=(const num& o) {
    v = num{v + o.v};
    return *this;
  };
  num operator-=(const num& o) {
    v = num{v - o.v + mod};
    return *this;
  };
  num operator*=(const num& o) {
    v = num{v * o.v};
    return *this;
  };
  num operator!() const {
    num R = 1;
    for (__typeof(v + 1) i = (2); i <= (v + 1); ++i) R *= num{i};
    return R;
  }
  num operator^(ll b) const {
    num R{1}, a{v};
    while (b > 0) {
      if (b & 1) R *= a;
      a *= a, b /= 2;
    }
    return R;
  }
  num operator/(const num& o) const { return (*this) * (o ^ (mod - 2)); }
};
template <typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> x) {
  os << '(' << x.first << ' ' << x.second << ')';
  return os;
}
template <typename T1, typename T2>
istream& operator>>(istream& is, pair<T1, T2>& x) {
  is >> x.first >> x.second;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, vector<T>& x) {
  for (T& i : x) os << i << ' ';
  return os;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& x) {
  for (T& i : x) is >> i;
  return is;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(const pair<T1, T2>& A, const pair<T1, T2>& B) {
  return {A.first + B.first, A.second + B.second};
}
template <typename T1, typename T2>
pair<T1, T2> operator-(const pair<T1, T2>& A, const pair<T1, T2>& B) {
  return {A.first - B.first, A.second - B.second};
}
template <typename T1, typename T2>
pair<T1, T2> operator-(const pair<T1, T2>& A) {
  return {-A.first, -A.second};
}
template <typename T1, typename T2>
bool maxe(T1& A, const T2& B) {
  if (B > A) {
    A = B;
    return 1;
  }
  return 0;
}
template <typename T1, typename T2>
bool mine(T1& A, const T2& B) {
  if (B < A) {
    A = B;
    return 1;
  }
  return 0;
}
int n;
vi T;
bool in() {
  cin >> n;
  T.resize(n);
  for (__typeof(n - 1) i = (0); i <= (n - 1); ++i) {
    char x;
    cin >> x;
    if (x == '(')
      T[i] = 1;
    else if (x == ')')
      T[i] = -1;
    else
      return false;
  }
  return true;
}
int minPos() {
  pii R{INF, 0};
  int S = 0;
  for (__typeof(n - 1) i = (0); i <= (n - 1); ++i) {
    S += T[i];
    mine(R, pii{S, i});
  }
  return R.second;
}
void zrotatuj(int x) {
  vi T2;
  T2.reserve(n);
  for (__typeof(n - 1) i = (x + 1); i <= (n - 1); ++i) T2.emplace_back(T[i]);
  for (__typeof(x) i = (0); i <= (x); ++i) T2.emplace_back(T[i]);
  T = T2;
}
int ile0() {
  int S = 0;
  int R = 0;
  for (__typeof(n - 1) i = (0); i <= (n - 1); ++i) {
    S += T[i];
    R += (S == 0);
  }
  return R;
}
bool czyTyleSamo() {
  int S = 0;
  for (auto x : T) S += x;
  return S == 0;
}
ll solve() {
  if (!czyTyleSamo()) {
    cout << 0 << '\n';
    cout << "1 1" << '\n';
    return -INF;
  }
  int x = minPos();
  zrotatuj(x);
  ;
  ;
  int ile = ile0();
  pair<int, pii> R{0, pii{0, 0}};
  {
    int j = 0;
    int S = 0;
    int r = 0;
    for (__typeof(n - 1) i = (0); i <= (n - 1); ++i) {
      S += T[i];
      if (S < 1) {
        j = i + 1;
        r = 0;
      }
      if (S == 1) ++r;
      maxe(R, pair<int, pii>(r, pii(j, i + 1)));
    }
  };
  ;
  {
    int j = 0;
    int S = 0;
    int r = 0;
    for (__typeof(n - 1) i = (0); i <= (n - 1); ++i) {
      S += T[i];
      if (S < 2) {
        j = i + 1;
        r = 0;
      } else if (S == 2)
        ++r;
      maxe(R, pair<int, pii>(r + ile, pii{j, i + 1}));
    }
  };
  int a = (R.second.first + x + 1) % n;
  int b = (R.second.second + x + 1) % n;
  cout << R.first << '\n';
  cout << a + 1 << ' ' << b + 1 << '\n';
  return -INF;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int noOfTests = 1;
  while (noOfTests-- > 0) {
    if (!in()) {
      cout << "popsute_wejscie\n";
      continue;
    }
    ll result = solve();
    if (result == ll(-'t'))
      cout << "TAK\n";
    else if (result == ll(-'n'))
      cout << "NIE\n";
    else if (result == ll(-'e'))
      cout << "Popsute\n";
    else if (result != -INF)
      cout << result << '\n';
  }
  return 0;
}
