#include using namespace std; typedef long long ll; #define F first #define S second #define pii pair #define eb emplace_back #define all(v) v.begin(), v.end() #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep3(i, l, n) for (int i = l; i < (n); ++i) #define sz(v) (int)v.size() #define endl '\n' const int inf = 1000000007; const ll INF = 1e18; int mod = 998244353; // int mod = 1000000007; #define abs(x) (x >= 0 ? x : -(x)) #define lb(v, x) (int)(lower_bound(all(v), x) - v.begin()) #define ub(v, x) (int)(upper_bound(all(v), x) - v.begin()) template inline bool chmin(T1 &a, T2 b) { if (a > b) { a = b; return 1; } return 0; } template inline bool chmax(T1 &a, T2 b) { if (a < b) { a = b; return 1; } return 0; } ll gcd(ll a, ll b) { if (b == 0) return a; return gcd(b, a % b); } ll lcm(ll a, ll b) { return a / gcd(a, b) * b; } template T pow_(T a, U b) { return b ? pow_(a * a, b / 2) * (b % 2 ? a : 1) : 1; } ll modpow(ll a, ll b, ll _mod) { return b ? modpow(a * a % _mod, b / 2, _mod) * (b % 2 ? a : 1) % _mod : 1; } template ostream& operator << (ostream& os, const pair& p) { os << p.F << " " << p.S; return os; } template ostream& operator << (ostream& os, const vector& vec) { rep(i, sz(vec)) { if (i) os << " "; os << vec[i]; } return os; } template inline istream& operator >> (istream& is, vector& v) { rep(j, sz(v)) is >> v[j]; return is; } template inline void add(T &a, T2 b) { a += b; if (a >= mod) a -= mod; } void solve(); int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cout << fixed << setprecision(10); int T; T = 1; while (T--) solve(); } // https://atcoder.jp/contests/abc167/tasks/abc167_f void solve() { int n; cin >> n; vector s(n); string w; cin >> w; string u; rep(i, n) { u += w[i]; s[i] = u; } using t = tuple; vector v; // 最下点と, 始点終点の高さの変化 auto calc = [&](string s) { int now = 0, mi = 0; rep(j, sz(s)) { if (s[j] == ')') { now--; chmin(mi, now); } else { now++; } } return pii(mi, now); }; rep(i, n) { int now = 0, mi = 0; pii tmp = calc(s[i]); if (tmp.S >= 0) v.eb(tmp.F, tmp.S, i); } auto comp = [&](t a, t b) { // debuged, 最下点だけ int mi1 = get<0>(a), now1 = get<1>(a); int mi2 = get<0>(b), now2 = get<1>(b); return mi1 > mi2; // 最下点が大きい順 }; auto out = [&](vector v) { rep(i, n) { int mi, now, j; tie(mi, now, j) = v[i]; cout << mi << " " << now << " " << j << endl; } }; sort(all(v), comp); reverse(all(v)); // 後ろから pop していく string ans; for (int i = sz(v) - 1; i >= 0; --i) { ans += s[get<2>(v[i])]; } v.clear(); rep(i, n) { int now = 0, mi = 0; pii tmp = calc(s[i]); if (tmp.S < 0) v.eb(tmp.F, tmp.S, i); } auto calc2 = [&](string s) { int now = 0, mi = 0; for (int j = sz(s) - 1; j >= 0; --j) { if (s[j] == '(') { // debuged now--; chmin(mi, now); } else { now++; } } return pii(mi, now); }; rep(i, sz(v)) { // debuged, removed t pii tmp = calc2(s[get<2>(v[i])]); // cout << tmp << endl; v[i] = make_tuple(tmp.F, tmp.S, get<2>(v[i])); } sort(all(v), comp); // debuged, removed, reverse for (int i = sz(v) - 1; i >= 0; --i) ans += s[get<2>(v[i])]; { int now = 0, cnt = 0; rep(i, sz(ans)) { if (ans[i] == ')') { if (now >= 1) { now--; cnt++; } } else { now++; } } cout << cnt * 2 << endl; } }