#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
template <class T>
void scan(T a) {
  cin >> a;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &);
template <class T, size_t size>
void scan(array<T, size> &);
template <class T, class L>
void scan(pair<T, L> &);
template <class T, size_t size>
void scan(T (&)[size]);
template <class T>
void scan(vector<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(deque<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T, size_t size>
void scan(array<T, size> &a) {
  for (auto &i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size>
void scan(T (&a)[size]) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(T &a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &...tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T, class S>
inline bool chmax(T &a, S b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class S>
inline bool chmin(T &a, S b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T> &x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T> &);
template <class T, size_t size>
void print(const array<T, size> &);
template <class T, class L>
void print(const pair<T, L> &p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L> &p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T>
void print(set<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T>
void print(multiset<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T &a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
template <class T>
vector<T> divisor(T x) {
  vector<T> ans;
  for (T i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
template <typename T>
void zip(vector<T> &x) {
  vector<T> y = x;
  sort(begin(y), end(y));
  for (int i = 0; i < x.size(); ++i) {
    x[i] = distance((y).begin(), lower_bound(begin(y), end(y), (x[i])));
  }
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
long long rndll(long long n) {
  return uniform_int_distribution<long long>(0, n - 1)(rng);
}
template <typename T>
void shuffle(vector<T> &v) {
  for (long long i = v.size() - 1; i >= 1; --i) {
    swap(v[i], v[rnd(i)]);
  }
}
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};
template <class... T>
void err(const T &...) {}
template <typename T>
struct edge {
  int from, to;
  T cost;
  int id;
  edge(int to, T cost) : from(-1), to(to), cost(cost) {}
  edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
  edge(int from, int to, T cost, int id)
      : from(from), to(to), cost(cost), id(id) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
struct Graph : vector<vector<int>> {
  using vector<vector<int>>::vector;
  Graph(int n, int m) : vector(n) { read(m); }
  inline void add(int a, int b, bool directed = false) {
    (*this)[a].emplace_back(b);
    if (!directed) (*this)[b].emplace_back(a);
  }
  void read(int n = -1, int offset = 1, bool directed = false) {
    if (n == -1) n = this->size() - 1;
    int a, b;
    while (n--) {
      cin >> a >> b;
      Graph::add(a - offset, b - offset, directed);
    }
  }
};
template <typename T>
struct WeightedGraph : vector<Edges<T>> {
  using vector<Edges<T>>::vector;
  inline void add(int a, int b, T c, bool directed = false) {
    (*this)[a].emplace_back(b, c);
    if (!directed) (*this)[b].emplace_back(a, c);
  }
  void read(int n = -1, int offset = 1) {
    if (n == -1) n = this->size() - 1;
    int a, b;
    T c;
    while (n--) {
      cin >> a >> b >> c;
      WeightedGraph::add(a - offset, b - offset, c);
    }
  }
};
struct Setup_io {
  Setup_io() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(15);
  }
} setup_io;
template <typename Monoid>
struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;
  int sz;
  vector<Monoid> seg;
  const F f;
  const Monoid M1;
  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n) sz <<= 1;
    seg.assign(2 * sz, M1);
  }
  void set(int k, const Monoid &x) { seg[k + sz] = x; }
  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }
  Monoid operator[](const int &k) const { return seg[k + sz]; }
  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }
  template <typename C>
  int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }
  template <typename C>
  int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
  void print(int n) {
    for (int i = 0; i < n; i++) {
      cerr << seg[i + sz] << " ";
    }
    cerr << '\n';
  }
};
constexpr int N = 500010;
SegmentTree<int> seg(
    N, [](int x, int y) { return min(x, y); }, INT_MAX);
struct SuffixArray {
  vector<int> SA;
  const string s;
  SuffixArray(const string &str) : s(str) {
    SA.resize(s.size());
    iota(begin(SA), end(SA), 0);
    sort(begin(SA), end(SA),
         [&](int a, int b) { return s[a] == s[b] ? a > b : s[a] < s[b]; });
    vector<int> classes(s.size()), c(s.begin(), s.end()), cnt(s.size());
    for (int len = 1; len < s.size(); len <<= 1) {
      for (int i = 0; i < s.size(); i++) {
        if (i > 0 && c[SA[i - 1]] == c[SA[i]] && SA[i - 1] + len < s.size() &&
            c[SA[i - 1] + len / 2] == c[SA[i] + len / 2]) {
          classes[SA[i]] = classes[SA[i - 1]];
        } else {
          classes[SA[i]] = i;
        }
      }
      iota(begin(cnt), end(cnt), 0);
      copy(begin(SA), end(SA), begin(c));
      for (int i = 0; i < s.size(); i++) {
        int s1 = c[i] - len;
        if (s1 >= 0) SA[cnt[classes[s1]]++] = s1;
      }
      classes.swap(c);
    }
  }
  int operator[](int k) const { return SA[k]; }
  size_t size() const { return s.size(); }
  bool lt_substr(const string &t, int si = 0, int ti = 0) {
    int sn = (int)s.size(), tn = (int)t.size();
    while (si < sn && ti < tn) {
      if (s[si] < t[ti]) return true;
      if (s[si] > t[ti]) return false;
      ++si, ++ti;
    }
    return si >= sn && ti < tn;
  }
  int lower_bound(const string &t) {
    int low = -1, high = (int)SA.size();
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (lt_substr(t, SA[mid]))
        low = mid;
      else
        high = mid;
    }
    return high;
  }
  pair<int, int> lower_upper_bound(string &t) {
    int idx = lower_bound(t);
    int low = idx - 1, high = (int)SA.size();
    t.back()++;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (lt_substr(t, SA[mid]))
        low = mid;
      else
        high = mid;
    }
    t.back()--;
    return {idx, high};
  }
  void output() {
    for (int i = 0; i < size(); i++) {
      cout << i << ": " << s.substr(SA[i]) << '\n';
    }
  }
};
struct LongestCommonPrefixArray {
  const SuffixArray &SA;
  vector<int> LCP, rank;
  LongestCommonPrefixArray(const SuffixArray &SA) : SA(SA), LCP(SA.size()) {
    rank.resize(SA.size());
    for (int i = 0; i < SA.size(); i++) {
      rank[SA[i]] = i;
    }
    for (int i = 0, h = 0; i < SA.size(); i++) {
      if (rank[i] + 1 < SA.size()) {
        for (int j = SA[rank[i] + 1];
             max(i, j) + h < SA.size() && SA.s[i + h] == SA.s[j + h]; ++h)
          ;
        LCP[rank[i] + 1] = h;
        if (h > 0) --h;
      }
    }
  }
  int operator[](int k) const { return LCP[k]; }
  size_t size() const { return LCP.size(); }
  void output() {
    for (int i = 0; i < size(); i++) {
      cout << i << ": " << LCP[i] << " " << SA.s.substr(SA[i]) << '\n';
    }
  }
};
int main() {
  int n;
  IN(n);
  string s;
  IN(s);
  vector<vector<int>> v(N * 2);
  int now = 0;
  for (long long i = 0; i < n + 1; ++i) {
    seg.set(i, now);
    v[now + N].emplace_back(i);
    if (i == n) break;
    if (s[i] == '(')
      now++;
    else
      now--;
  }
  seg.set(n + 1, -INT_MAX);
  seg.build();
  SuffixArray sa(s);
  LongestCommonPrefixArray lcp(sa);
  long long ans = 0;
  now = 0;
  for (long long i = 0; i < n; ++i) {
    int j = sa.SA[i];
    int d = lcp[i];
    int r = seg.find_first(j, [&](int x) { return x < seg[j]; });
    if (j + d >= r) continue;
    ans +=
        distance((v[seg[j] + N]).begin(),
                 upper_bound(begin(v[seg[j] + N]), end(v[seg[j] + N]), (r))) -
        distance(
            (v[seg[j] + N]).begin(),
            upper_bound(begin(v[seg[j] + N]), end(v[seg[j] + N]), (j + d)));
  }
  cout << ans << '\n';
}

### Prompt

Please create a solution in Cpp to the following problem:

Alex was programming while Valentina (his toddler daughter) got there and started asking many questions about the round brackets (or parenthesis) in the code. He explained her a bit and when she got it he gave her a task in order to finish his code on time.

For the purpose of this problem we consider only strings consisting of opening and closing round brackets, that is characters '(' and ')'.

The sequence of brackets is called correct if: 

  1. it's empty; 
  2. it's a correct sequence of brackets, enclosed in a pair of opening and closing brackets; 
  3. it's a concatenation of two correct sequences of brackets. 



For example, the sequences "()()" and "((()))(())" are correct, while ")(()", "(((((" and "())" are not.

Alex took a piece of paper, wrote a string s consisting of brackets and asked Valentina to count the number of distinct non-empty substrings of s that are correct sequences of brackets. In other words, her task is to count the number of non-empty correct sequences of brackets that occur in a string s as a substring (don't mix up with subsequences).

When Valentina finished the task, Alex noticed he doesn't know the answer. Help him don't loose face in front of Valentina and solve the problem!

Input

The first line of the input contains an integer n (1 ≤ n ≤ 500 000) — the length of the string s.

The second line contains a string s of length n consisting of only '(' and ')'.

Output

Print the number of distinct non-empty correct sequences that occur in s as substring.

Examples

Input

10
()()()()()


Output

5


Input

7
)(())()


Output

3

Note

In the first sample, there are 5 distinct substrings we should count: "()", "()()", "()()()", "()()()()" and "()()()()()".

In the second sample, there are 3 distinct substrings we should count: "()", "(())" and "(())()".

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
template <class T>
void scan(T a) {
  cin >> a;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &);
template <class T, size_t size>
void scan(array<T, size> &);
template <class T, class L>
void scan(pair<T, L> &);
template <class T, size_t size>
void scan(T (&)[size]);
template <class T>
void scan(vector<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(deque<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T, size_t size>
void scan(array<T, size> &a) {
  for (auto &i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size>
void scan(T (&a)[size]) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(T &a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &...tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T, class S>
inline bool chmax(T &a, S b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class S>
inline bool chmin(T &a, S b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T> &x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T> &);
template <class T, size_t size>
void print(const array<T, size> &);
template <class T, class L>
void print(const pair<T, L> &p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L> &p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T>
void print(set<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T>
void print(multiset<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T &a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
template <class T>
vector<T> divisor(T x) {
  vector<T> ans;
  for (T i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
template <typename T>
void zip(vector<T> &x) {
  vector<T> y = x;
  sort(begin(y), end(y));
  for (int i = 0; i < x.size(); ++i) {
    x[i] = distance((y).begin(), lower_bound(begin(y), end(y), (x[i])));
  }
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
long long rndll(long long n) {
  return uniform_int_distribution<long long>(0, n - 1)(rng);
}
template <typename T>
void shuffle(vector<T> &v) {
  for (long long i = v.size() - 1; i >= 1; --i) {
    swap(v[i], v[rnd(i)]);
  }
}
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};
template <class... T>
void err(const T &...) {}
template <typename T>
struct edge {
  int from, to;
  T cost;
  int id;
  edge(int to, T cost) : from(-1), to(to), cost(cost) {}
  edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
  edge(int from, int to, T cost, int id)
      : from(from), to(to), cost(cost), id(id) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
struct Graph : vector<vector<int>> {
  using vector<vector<int>>::vector;
  Graph(int n, int m) : vector(n) { read(m); }
  inline void add(int a, int b, bool directed = false) {
    (*this)[a].emplace_back(b);
    if (!directed) (*this)[b].emplace_back(a);
  }
  void read(int n = -1, int offset = 1, bool directed = false) {
    if (n == -1) n = this->size() - 1;
    int a, b;
    while (n--) {
      cin >> a >> b;
      Graph::add(a - offset, b - offset, directed);
    }
  }
};
template <typename T>
struct WeightedGraph : vector<Edges<T>> {
  using vector<Edges<T>>::vector;
  inline void add(int a, int b, T c, bool directed = false) {
    (*this)[a].emplace_back(b, c);
    if (!directed) (*this)[b].emplace_back(a, c);
  }
  void read(int n = -1, int offset = 1) {
    if (n == -1) n = this->size() - 1;
    int a, b;
    T c;
    while (n--) {
      cin >> a >> b >> c;
      WeightedGraph::add(a - offset, b - offset, c);
    }
  }
};
struct Setup_io {
  Setup_io() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(15);
  }
} setup_io;
template <typename Monoid>
struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;
  int sz;
  vector<Monoid> seg;
  const F f;
  const Monoid M1;
  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n) sz <<= 1;
    seg.assign(2 * sz, M1);
  }
  void set(int k, const Monoid &x) { seg[k + sz] = x; }
  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }
  Monoid operator[](const int &k) const { return seg[k + sz]; }
  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }
  template <typename C>
  int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }
  template <typename C>
  int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
  void print(int n) {
    for (int i = 0; i < n; i++) {
      cerr << seg[i + sz] << " ";
    }
    cerr << '\n';
  }
};
constexpr int N = 500010;
SegmentTree<int> seg(
    N, [](int x, int y) { return min(x, y); }, INT_MAX);
struct SuffixArray {
  vector<int> SA;
  const string s;
  SuffixArray(const string &str) : s(str) {
    SA.resize(s.size());
    iota(begin(SA), end(SA), 0);
    sort(begin(SA), end(SA),
         [&](int a, int b) { return s[a] == s[b] ? a > b : s[a] < s[b]; });
    vector<int> classes(s.size()), c(s.begin(), s.end()), cnt(s.size());
    for (int len = 1; len < s.size(); len <<= 1) {
      for (int i = 0; i < s.size(); i++) {
        if (i > 0 && c[SA[i - 1]] == c[SA[i]] && SA[i - 1] + len < s.size() &&
            c[SA[i - 1] + len / 2] == c[SA[i] + len / 2]) {
          classes[SA[i]] = classes[SA[i - 1]];
        } else {
          classes[SA[i]] = i;
        }
      }
      iota(begin(cnt), end(cnt), 0);
      copy(begin(SA), end(SA), begin(c));
      for (int i = 0; i < s.size(); i++) {
        int s1 = c[i] - len;
        if (s1 >= 0) SA[cnt[classes[s1]]++] = s1;
      }
      classes.swap(c);
    }
  }
  int operator[](int k) const { return SA[k]; }
  size_t size() const { return s.size(); }
  bool lt_substr(const string &t, int si = 0, int ti = 0) {
    int sn = (int)s.size(), tn = (int)t.size();
    while (si < sn && ti < tn) {
      if (s[si] < t[ti]) return true;
      if (s[si] > t[ti]) return false;
      ++si, ++ti;
    }
    return si >= sn && ti < tn;
  }
  int lower_bound(const string &t) {
    int low = -1, high = (int)SA.size();
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (lt_substr(t, SA[mid]))
        low = mid;
      else
        high = mid;
    }
    return high;
  }
  pair<int, int> lower_upper_bound(string &t) {
    int idx = lower_bound(t);
    int low = idx - 1, high = (int)SA.size();
    t.back()++;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (lt_substr(t, SA[mid]))
        low = mid;
      else
        high = mid;
    }
    t.back()--;
    return {idx, high};
  }
  void output() {
    for (int i = 0; i < size(); i++) {
      cout << i << ": " << s.substr(SA[i]) << '\n';
    }
  }
};
struct LongestCommonPrefixArray {
  const SuffixArray &SA;
  vector<int> LCP, rank;
  LongestCommonPrefixArray(const SuffixArray &SA) : SA(SA), LCP(SA.size()) {
    rank.resize(SA.size());
    for (int i = 0; i < SA.size(); i++) {
      rank[SA[i]] = i;
    }
    for (int i = 0, h = 0; i < SA.size(); i++) {
      if (rank[i] + 1 < SA.size()) {
        for (int j = SA[rank[i] + 1];
             max(i, j) + h < SA.size() && SA.s[i + h] == SA.s[j + h]; ++h)
          ;
        LCP[rank[i] + 1] = h;
        if (h > 0) --h;
      }
    }
  }
  int operator[](int k) const { return LCP[k]; }
  size_t size() const { return LCP.size(); }
  void output() {
    for (int i = 0; i < size(); i++) {
      cout << i << ": " << LCP[i] << " " << SA.s.substr(SA[i]) << '\n';
    }
  }
};
int main() {
  int n;
  IN(n);
  string s;
  IN(s);
  vector<vector<int>> v(N * 2);
  int now = 0;
  for (long long i = 0; i < n + 1; ++i) {
    seg.set(i, now);
    v[now + N].emplace_back(i);
    if (i == n) break;
    if (s[i] == '(')
      now++;
    else
      now--;
  }
  seg.set(n + 1, -INT_MAX);
  seg.build();
  SuffixArray sa(s);
  LongestCommonPrefixArray lcp(sa);
  long long ans = 0;
  now = 0;
  for (long long i = 0; i < n; ++i) {
    int j = sa.SA[i];
    int d = lcp[i];
    int r = seg.find_first(j, [&](int x) { return x < seg[j]; });
    if (j + d >= r) continue;
    ans +=
        distance((v[seg[j] + N]).begin(),
                 upper_bound(begin(v[seg[j] + N]), end(v[seg[j] + N]), (r))) -
        distance(
            (v[seg[j] + N]).begin(),
            upper_bound(begin(v[seg[j] + N]), end(v[seg[j] + N]), (j + d)));
  }
  cout << ans << '\n';
}

```