/** * author: otera * created: 07.12.2021 00:22:09 **/ #include #include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; #define repa(i, n) for(int i = 0; i < n; ++ i) #define repb(i, a, b) for(int i = a; i < b; ++ i) #define repc(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__) #define rep1a(i, n) for(int i = 0; i <= n; ++ i) #define rep1b(i, a, b) for(int i = a; i <= b; ++ i) #define rep1c(i, a, b, c) for(int i = a; i <= b; i += c) #define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__) #define per(i,n) for(int i=n-1;i>=0;i--) #define per1(i,n) for(int i=n;i>=1;i--) typedef pair P; typedef pair LP; #define pb push_back #define eb emplace_back #define fr first #define sc second #define all(c) c.begin(),c.end() #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define si(c) (int)(c).size() inline ll popcnt(ull a){ return __builtin_popcountll(a); } #define tpow(n) (1LL<<(n)) #define unless(A) if(!(A)) ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vectorname(__VA_ARGS__) #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; template void scan(T& a){ cin >> a; } template void scan(vector& a){ for(auto&& i : a) scan(i); } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ cout << ' '; } template void print(const T& a){ cout << a; } template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } } int out(){ cout << '\n'; return 0; } template int out(const T& t){ print(t); cout << '\n'; return 0; } template int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0,a1,a2,a3,a4,x,...) x #define debug_1(x1) cout<<#x1<<": "< st; vc p(n); vc num(n); int now = 0; vvc g(n); atcoder::dsu uf(n); vc

mp(n); rep(i, n) { if(s[i] == '(') { st.push({i, now}); num[i] = now; ++ now; } else { assert(si(st) >= 1); auto [v, id] = st.top(); st.pop(); p[v] = i, p[i] = v; num[i] = id; mp[id] = {v, i}; if(st.size()) { g[st.top().sc].pb(id); g[id].pb(st.top().sc); uf.merge(st.top().sc, id); } } } vc dep(n, -1); vvc par(N, vc(n, -1)); auto dfs = [&](auto &&self, int v, int pa, int d) -> void { par[0][v] = pa; dep[v] = d; for(int nv: g[v]) { if(nv == pa) continue; self(self, nv, v, d + 1); } }; rep(i, n) { if(dep[i] == -1) dfs(dfs, i, -1, 0); } for(int i = 1; i < N; ++ i) { rep(j, n) { par[i][j] = (par[i - 1][j] == -1 ? -1 : par[i - 1][par[i - 1][j]]); } } auto lca = [&](int x, int y) -> int { if(dep[x] > dep[y]) swap(x, y); rep(i, N) { if((dep[y] - dep[x]) & (1<