#pragma region Macros #include using namespace std; // input output utils namespace siro53_io { // https://maspypy.github.io/library/other/io_old.hpp struct has_val_impl { template static auto check(T &&x) -> decltype(x.val(), std::true_type{}); template static auto check(...) -> std::false_type; }; template class has_val : public decltype(has_val_impl::check(std::declval())) { }; // debug template ::value, int> = 0> void dump(const T t) { cerr << t; } template ::value, int> = 0> void dump(const T t) { cerr << t; } template ::value>::type * = nullptr> void dump(const T &t) { cerr << t.val(); } void dump(__int128_t n) { if(n == 0) { cerr << '0'; return; } else if(n < 0) { cerr << '-'; n = -n; } string s; while(n > 0) { s += (char)('0' + n % 10); n /= 10; } reverse(s.begin(), s.end()); cerr << s; } void dump(const string &s) { cerr << s; } void dump(const char *s) { int n = (int)strlen(s); for(int i = 0; i < n; i++) cerr << s[i]; } template void dump(const pair &p) { cerr << '('; dump(p.first); cerr << ','; dump(p.second); cerr << ')'; } template void dump(const vector &v) { cerr << '{'; for(int i = 0; i < (int)v.size(); i++) { dump(v[i]); if(i < (int)v.size() - 1) cerr << ','; } cerr << '}'; } template void dump(const set &s) { cerr << '{'; for(auto it = s.begin(); it != s.end(); it++) { dump(*it); if(next(it) != s.end()) cerr << ','; } cerr << '}'; } template void dump(const map &mp) { cerr << '{'; for(auto it = mp.begin(); it != mp.end(); it++) { dump(*it); if(next(it) != mp.end()) cerr << ','; } cerr << '}'; } template void dump(const unordered_map &mp) { cerr << '{'; for(auto it = mp.begin(); it != mp.end(); it++) { dump(*it); if(next(it) != mp.end()) cerr << ','; } cerr << '}'; } template void dump(const deque &v) { cerr << '{'; for(int i = 0; i < (int)v.size(); i++) { dump(v[i]); if(i < (int)v.size() - 1) cerr << ','; } cerr << '}'; } template void dump(queue q) { cerr << '{'; while(!q.empty()) { dump(q.front()); if((int)q.size() > 1) cerr << ','; q.pop(); } cerr << '}'; } void debug_print() { cerr << endl; } template void debug_print(const Head &h, const Tail &...t) { dump(h); if(sizeof...(Tail)) dump(' '); debug_print(t...); } // print template ::value, int> = 0> void print_single(const T t) { cout << t; } template ::value, int> = 0> void print_single(const T t) { cout << t; } template ::value>::type * = nullptr> void print_single(const T t) { cout << t.val(); } void print_single(__int128_t n) { if(n == 0) { cout << '0'; return; } else if(n < 0) { cout << '-'; n = -n; } string s; while(n > 0) { s += (char)('0' + n % 10); n /= 10; } reverse(s.begin(), s.end()); cout << s; } void print_single(const string &s) { cout << s; } void print_single(const char *s) { int n = (int)strlen(s); for(int i = 0; i < n; i++) cout << s[i]; } template void print_single(const pair &p) { print_single(p.first); cout << ' '; print_single(p.second); } template void print_single(const vector &v) { for(int i = 0; i < (int)v.size(); i++) { print_single(v[i]); if(i < (int)v.size() - 1) cout << ' '; } } template void print_single(const set &s) { for(auto it = s.begin(); it != s.end(); it++) { print_single(*it); if(next(it) != s.end()) cout << ' '; } } template void print_single(const deque &v) { for(int i = 0; i < (int)v.size(); i++) { print_single(v[i]); if(i < (int)v.size() - 1) cout << ' '; } } template void print_single(queue q) { while(!q.empty()) { print_single(q.front()); if((int)q.size() > 1) cout << ' '; q.pop(); } } void print() { cout << '\n'; } template void print(const Head &h, const Tail &...t) { print_single(h); if(sizeof...(Tail)) print_single(' '); print(t...); } // input template ::value, int> = 0> void input_single(T &t) { cin >> t; } template ::value, int> = 0> void input_single(T &t) { cin >> t; } template ::value>::type * = nullptr> void input_single(T &t) { cin >> t; } void input_single(__int128_t &n) { string s; cin >> s; if(s == "0") { n = 0; return; } bool is_minus = false; if(s[0] == '-') { s = s.substr(1); is_minus = true; } n = 0; for(int i = 0; i < (int)s.size(); i++) n = n * 10 + (int)(s[i] - '0'); if(is_minus) n = -n; } void input_single(string &s) { cin >> s; } template void input_single(pair &p) { input_single(p.first); input_single(p.second); } template void input_single(vector &v) { for(auto &e : v) input_single(e); } void input() {} template void input(Head &h, Tail &...t) { input_single(h); input(t...); } }; // namespace siro53_io #ifdef DEBUG #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debug_print(__VA_ARGS__) #else #define debug(...) (void(0)) #endif // io setup struct Setup { Setup() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __Setup; using namespace siro53_io; // types using ll = long long; using i128 = __int128_t; // input macros #define INT(...) \ int __VA_ARGS__; \ input(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ input(__VA_ARGS__) #define STRING(...) \ string __VA_ARGS__; \ input(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ input(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ input(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ input(__VA_ARGS__) #define UINT(...) \ unsigned int __VA_ARGS__; \ input(__VA_ARGS__) #define ULL(...) \ unsigned long long __VA_ARGS__; \ input(__VA_ARGS__) #define VEC(name, type, len) \ vector name(len); \ input(name); #define VEC2(name, type, len1, len2) \ vector name(len1, vector(len2)); \ input(name); // other macros // https://trap.jp/post/1224/ #define OVERLOAD3(_1, _2, _3, name, ...) name #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define REP1(i, n) for(int i = 0; i < int(n); i++) #define REP2(i, a, b) for(int i = (a); i < int(b); i++) #define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__) #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(RALL(v)) #define UNIQUE(v) \ sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()), v.shrink_to_fit() #define REV(v) reverse(ALL(v)) #define SZ(v) ((int)(v).size()) #define MIN(v) (*min_element(ALL(v))) #define MAX(v) (*max_element(ALL(v))) // util const const int INF = 1 << 30; const ll LLINF = 1LL << 60; constexpr int MOD = 1000000007; constexpr int MOD2 = 998244353; const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; // util functions void Case(int i) { cout << "Case #" << i << ": "; } int popcnt(int x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } template inline bool chmax(T &a, T b) { return (a < b ? a = b, true : false); } template inline bool chmin(T &a, T b) { return (a > b ? a = b, true : false); } template auto make_vector_impl(vector& sizes, const T &e) { if constexpr(dim == 1) { return vector(sizes[0], e); } else { int n = sizes[dim - 1]; sizes.pop_back(); return vector(n, make_vector_impl(sizes, e)); } } template auto make_vector(const int (&sizes)[dim], const T &e = T()) { vector s(dim); for(int i = 0; i < dim; i++) s[i] = sizes[dim - i - 1]; return make_vector_impl(s, e); } #pragma endregion Macros int main() { INT(N); STRING(S); VEC(A, ll, N*2); auto dp = make_vector({N*2+1, N*2+1}, LLINF); dp[0][0] = 0; REP(i, N*2) { REP(j, N*2+1) { if(dp[i][j] == LLINF) continue; if(S[i] == '(') { if(j + 1 <= N*2) chmin(dp[i+1][j+1], dp[i][j]); if(j - 1 >= 0) chmin(dp[i+1][j-1], dp[i][j] + A[i]); } else { if(j + 1 <= N*2) chmin(dp[i+1][j+1], dp[i][j] + A[i]); if(j - 1 >= 0) chmin(dp[i+1][j-1], dp[i][j]); } } } print(dp[N*2][0]); }