#include <bits/stdc++.h>
using namespace std;
int n;
string s, t;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> t;
  int ph = 0;
  pair<int, int> mh = {0, 0};
  for (int i = 0; i < n; i++) {
    if (t[i] == '(')
      ph++;
    else
      ph--;
    mh = min(mh, make_pair(ph, i + 1));
  }
  if (ph != 0) {
    cout << "0\n1 1\n";
    return 0;
  }
  string s;
  for (int i = mh.second; i < n; i++) {
    s.push_back(t[i]);
  }
  for (int i = 0; i < mh.second; i++) {
    s.push_back(t[i]);
  }
  int shift = mh.second;
  int h = 0, cnt = 0, one = 0, two = 0, piv = 0, piv2 = -1;
  pair<int, pair<int, int>> opt = {-1, {-1, -1}};
  pair<int, pair<int, int>> opt2 = {-1, {-1, -1}};
  for (int i = 0; i < n; i++) {
    if (s[i] == '(')
      h++;
    else
      h--;
    if (h == 0) {
      cnt++;
      opt = max(opt, make_pair(one, make_pair(piv, i)));
      one = 0;
      piv = i + 1;
      piv2 = -1;
    } else if (h == 1) {
      one++;
      if (piv2 != -1) opt2 = max(opt2, make_pair(two, make_pair(piv2, i)));
      two = 0;
      piv2 = i + 1;
    } else if (h == 2)
      two++;
  }
  if (opt.first <= cnt + max(0, opt2.first)) {
    if (opt2.first == -1) {
      cout << cnt << "\n1 1\n";
      return 0;
    }
    cout << cnt + opt2.first << '\n';
    cout << (opt2.second.first + shift) % n + 1 << ' ';
    cout << (opt2.second.second + shift) % n + 1 << '\n';
    return 0;
  }
  cout << opt.first << '\n'
       << (opt.second.first + shift) % n + 1 << ' '
       << (opt.second.second + shift) % n + 1 << '\n';
  return 0;
}
