#include <bits/stdc++.h>
using namespace std;
const int maxn = 3e5 + 5;
int level[maxn * 2], num[maxn * 2], par[maxn * 2];
char s[maxn * 2];
stack<int> stk;
int main() {
  int n, cnt = 0;
  scanf("%d", &n);
  scanf("%s", s + 1);
  for (int i = 1; i <= n; i++) {
    if (stk.empty())
      stk.push(i);
    else {
      int c = stk.top();
      if (s[i] == ')' && s[c] == '(')
        stk.pop();
      else
        stk.push(i);
    }
    s[i + n] = s[i];
    cnt = cnt + ((s[i] == '(') ? (1) : (-1));
  }
  if (cnt) return 0 & printf("0\n1 1\n");
  int j = 1;
  while (!stk.empty()) {
    int c = stk.top();
    if (s[c] == ')') break;
    stk.pop();
    j = c;
  }
  for (int i = 1; i <= n * 2; i++) level[i] = -1, num[i] = 0;
  while (!stk.empty()) stk.pop();
  for (int i = j; i <= j + n - 1; i++) {
    if (stk.empty()) {
      stk.push(i);
      level[i] = 1;
      cnt++;
    } else {
      int c = stk.top();
      if (s[i] == ')' && s[c] == '(') {
        stk.pop();
        par[c] = i;
      } else {
        stk.push(i);
        level[i] = stk.size();
      }
    }
  }
  int i = j;
  while (i <= j + n - 1) {
    if (level[i] == 1) {
      int r = par[i], k = i;
      while (i < r) {
        if (level[i] == 2) num[k]++;
        i++;
      }
    }
    i++;
  }
  i = j;
  while (i <= j + n - 1) {
    if (level[i] == 2) {
      int r = par[i], k = i;
      while (i < r) {
        if (level[i] == 3) num[k]++;
        i++;
      }
    }
    i++;
  }
  int ans = 0, l, r;
  for (int i = j; i <= j + n - 1; i++) {
    if (level[i] == 1) {
      if (ans < (num[i] + 1)) {
        ans = num[i] + 1;
        l = i % n;
        r = par[i] % n;
      }
    } else if (level[i] == 2) {
      if (ans < (cnt + num[i] + 1)) {
        ans = cnt + num[i] + 1;
        l = i % n;
        r = par[i] % n;
      }
    }
  }
  if (ans < cnt) ans = cnt, l = 1, r = 1;
  if (l == 0) l = n;
  if (r == 0) r = n;
  printf("%d\n%d %d\n", ans, l, r);
}
