#include <bits/stdc++.h>
using namespace std;
long long read() {
  int f = 1;
  long long res = 0;
  char ch;
  do {
    ch = getchar();
    if (ch == '-') f = -f;
  } while (ch < '0' || ch > '9');
  do {
    res = res * 10 + ch - '0';
    ch = getchar();
  } while (ch >= '0' && ch <= '9');
  return f == 1 ? res : -res;
}
void fast_io() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
const int N = 300005;
const int mod = 1e9 + 7;
const long long INF = 1e15;
int n, m;
int A[N], B[N];
char str[N];
int head[N], to[N * 2], nxt[N * 2], tot = 1, weight[N * 2];
void addEdge(int u, int v, int w = 1) {
  tot++;
  nxt[tot] = head[u];
  to[tot] = v;
  head[u] = tot;
  weight[tot] = w;
}
void initGraph() {
  for (int i = 0; i <= n; i++) head[i] = 0;
  tot = 1;
}
int countOne(long long set) {
  int res = 0;
  while (set) {
    res++;
    set &= set - 1;
  }
  return res;
}
bool contain(long long set, int i) { return (set & (1LL << i)) > 0; }
long long myPow(long long a, long long p) {
  if (p == 0) return 1;
  long long res = myPow(a, p / 2);
  res *= res;
  res %= mod;
  if (p % 2 == 1) {
    res *= a;
    res %= mod;
  }
  return res % mod;
}
void addMode(long long &a, long long b) {
  a = (a + b) % mod;
  if (a < 0) a += mod;
}
long long mul(long long a, long long b) {
  long long res = a % mod * b % mod;
  if (res < 0) res += mod;
  return res;
}
int sum[N * 2];
int miValue = N;
int la, lb;
int ans = 0;
int cntB = 0;
void solve(int s, int e) {
  int cntOne = 0;
  for (int i = s; i <= e; i++) {
    if (sum[i] == miValue + 1) cntOne++;
  }
  if (cntOne > ans) {
    ans = cntOne;
    la = s;
    lb = e;
  }
  int cntTwo = 0;
  int start = s;
  for (int i = s + 1; i < e; i++) {
    if (sum[i] == miValue + 1) {
      if (cntTwo + cntB > ans) {
        ans = cntTwo + cntB;
        la = start + 1;
        lb = i;
      }
      start = i;
      cntTwo = 0;
    } else if (sum[i] == miValue + 2)
      cntTwo++;
  }
}
int main() {
  fast_io();
  cin >> n;
  cin >> str;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (str[i] == '(')
      cnt++;
    else
      cnt--;
    sum[i + 1] = cnt;
    miValue = min(miValue, cnt);
  }
  if (cnt != 0) {
    cout << "0" << endl;
    cout << "1 1" << endl;
    return 0;
  }
  for (int i = n + 1; i <= n * 2; i++) {
    sum[i] = sum[i - n];
  }
  for (int i = 1; i <= n; i++)
    if (sum[i] == miValue) {
      cntB++;
    }
  ans = cntB;
  la = lb = 1;
  int loc = -1;
  for (int i = 1; i <= n * 2; i++) {
    if (sum[i] == miValue) {
      if (loc != -1) {
        solve(loc + 1, i);
      }
      loc = i;
    }
  }
  cout << ans << endl;
  cout << (la > n ? la - n : la) << ' ' << (lb > n ? lb - n : lb) << endl;
  return 0;
}
