#include <bits/stdc++.h>
using namespace std;
template <class T>
bool mini(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool maxi(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
int get(vector<int> &a, int l, int r) {
  if (l > r) return 0;
  return a[r] - (l > 0 ? a[l - 1] : 0);
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.precision(10);
  cout << fixed;
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> a(n);
  for (int i = 0; i < (int)(n); i++)
    a[i] = (i > 0 ? a[i - 1] : 0) + (s[i] == '(' ? 1 : -1);
  if (a.back() != 0) return cout << 0 << "\n" << 1 << ' ' << 1 << "\n", 0;
  int shift = min_element((a).begin(), (a).end()) - a.begin();
  int val = a[shift];
  rotate(a.begin(), a.begin() + ++shift, a.end());
  for (int i = (int)(n)-1; i >= 0; --i) a[i] -= val;
  s = "";
  s += '(';
  for (int i = 1; i <= (int)(n - 1); i++) s += a[i] < a[i - 1] ? ')' : '(';
  vector<vector<int> > cnt(3, vector<int>(n));
  for (int i = 0; i < (int)(n); i++)
    for (int j = 0; j < (int)(3); j++)
      cnt[j][i] += (a[i] == j) + (i > 0 ? cnt[j][i - 1] : 0);
  int pos1 = 0, pos2 = 0;
  int ans = count((a).begin(), (a).end(), 0), l = 0, r = 0;
  for (int i = 0; i < (int)(n - 1); i++) {
    if (a[i] < 1)
      pos1 = i + 1;
    else if (s[i + 1] == ')') {
      while (pos1 <= i && s[pos1] == ')') pos1++;
      if (pos1 <= i && maxi(ans, get(cnt[1], pos1, i))) l = pos1, r = i + 1;
    }
    if (a[i] < 2)
      pos2 = i + 1;
    else if (s[i + 1] == ')') {
      while (pos2 <= i && s[pos2] == ')') pos2++;
      if (pos2 <= i &&
          maxi(ans, get(cnt[2], pos2, i) + get(cnt[0], 0, pos2 - 1) +
                        get(cnt[0], i + 1, n - 1)))
        l = pos2, r = i + 1;
    }
  }
  cout << ans << "\n";
  cout << (l + shift) % n + 1 << ' ' << (r + shift) % n + 1 << "\n";
}
