#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; const int MOD = 1000000007; // const int MOD = 998244353; template struct Segment_Tree { using F = function; int n; vector seg; const F f; const Monoid e1; // f(f(a,b),c) = f(a,f(b,c)), f(e1,a) = f(a,e1) = a Segment_Tree(const vector &v, const F &f, const Monoid &e1) : f(f), e1(e1) { int m = v.size(); n = 1; while (n < m) n <<= 1; seg.assign(2 * n, e1); copy(begin(v), end(v), seg.begin() + n); for (int i = n - 1; i > 0; i--) seg[i] = f(seg[2 * i], seg[2 * i + 1]); } Segment_Tree(int m, const Monoid &x, const F &f, const Monoid &e1) : f(f), e1(e1) { n = 1; while (n < m) n <<= 1; seg.assign(2 * n, e1); vector v(m, x); copy(begin(v), end(v), begin(seg) + n); for (int i = n - 1; i > 0; i--) seg[i] = f(seg[2 * i], seg[2 * i + 1]); } void change(int i, const Monoid &x, bool update = true) { if (update) { seg[i + n] = x; } else { seg[i + n] = f(seg[i + n], x); } i += n; while (i >>= 1) seg[i] = f(seg[2 * i], seg[2 * i + 1]); } Monoid query(int l, int r) const { Monoid L = e1, R = e1; l += n, r += n; while (l < r) { if (l & 1) L = f(L, seg[l++]); if (r & 1) R = f(seg[--r], R); l >>= 1, r >>= 1; } return f(L, R); } Monoid operator[](int i) const { return seg[n + i]; } template int find_subtree(int i, const C &check, const Monoid &x, Monoid &M, int type) const { while (i < n) { Monoid nxt = type ? f(seg[2 * i + type], M) : f(M, seg[2 * i + type]); if (check(nxt, x)) { i = 2 * i + type; } else { M = nxt; i = 2 * i + (type ^ 1); } } return i - n; } template int find_first(int l, const C &check, const Monoid &x) const { // check((区間 [l,r] での演算結果), x) を満たす最小の r Monoid L = e1; int a = l + n, b = n + n; while (a < b) { if (a & 1) { Monoid nxt = f(L, seg[a]); if (check(nxt, x)) return find_subtree(a, check, x, L, 0); L = nxt, a++; } a >>= 1, b >>= 1; } return n; } template int find_last(int r, const C &check, const Monoid &x) const { // check((区間 [l,r) での演算結果), x) を満たす最大の l Monoid R = e1; int a = n, b = r + n; while (a < b) { if ((b & 1) || a == 1) { Monoid nxt = f(seg[--b], R); if (check(nxt, x)) return find_subtree(b, check, x, R, 1); R = nxt; } a >>= 1, b >>= 1; } return -1; } }; vector solve(int N, vector a, bool flag) { vector v(N + 1, 0); rep(i, N) { if (a[i] == 1) { v[i + 1] = v[i] + 1; } else { v[i + 1] = v[i] - 1; } } auto f = [](int a, int b) { return min(a, b); }; auto c = [](int a, int b) { return a < b; }; Segment_Tree seg(v, f, inf); vector dp1(N + 1, -inf), dp2(N + 1, -inf); dp1[0] = 0; rep(i, N) { if (a[i] != 1) { chmax(dp1[i + 1], dp1[i]); chmax(dp1[i + 1], dp2[i]); } if (a[i] != -1) { int j = seg.find_first(i + 1, c, v[i + 1]); chmax(dp2[j], dp1[i] + 1); chmax(dp2[j], dp2[i]); } } // print(dp1), print(dp2); if (flag) rep(i, N + 1) chmax(dp1[i], dp2[i]); return dp1; } int main() { int N; string S; cin >> N >> S; vector a(N); rep(i, N) a[i] = (S[i] == '(' ? 1 : S[i] == ')' ? -1 : 0); vector b = a; reverse(all(b)); rep(i, N) b[i] *= -1; // print(a), print(b); auto dp1 = solve(N, a, true); auto dp2 = solve(N, b, false); int ans = -inf; rep2(i, 0, N) chmax(ans, dp1[i] + dp2[N - i]); cout << ans << '\n'; }