/** * date : 2021-12-20 14:31:32 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(int r) const { return {first * r, second * r}; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &... u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // template struct RBSTSegmentTree { struct Node { Node *l, *r; I index; T key, sum; E lazy; int cnt; Node(const I &i, const T &t = ti()) : l(), r(), index(i), key(t), sum(t), lazy(ei()), cnt(1) {} }; protected: using Ptr = Node *; // 呼んだあと必ず update すること! template inline Ptr my_new(Args... args) { return new Node(args...); } inline void my_del(Ptr t) { delete t; } inline int count(const Ptr t) const { return t ? t->cnt : 0; } static uint64_t rng() { static uint64_t x_ = 88172645463325252ULL; return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull; } Ptr merge(Ptr l, Ptr r) { if (!l || !r) return l ? l : r; if (int((rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) { push(l); l->r = merge(l->r, r); return update(l); } else { push(r); r->l = merge(l, r->l); return update(r); } } Ptr build(int l, int r, const vector> &dat) { if (l == r) return nullptr; if (l + 1 == r) return my_new(dat[l].first, dat[l].second); int m = (l + r) / 2; return merge(build(l, m, dat), build(m, r, dat)); }; void push(Ptr t) { if (!t) return; if (t->lazy != ei()) { if (t->l) propagate(t->l, t->lazy); if (t->r) propagate(t->r, t->lazy); t->lazy = ei(); } } Ptr update(Ptr t) { if (!t) return t; push(t); t->cnt = 1; t->sum = t->key; if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum); if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum); return t; } void propagate(Ptr t, const E &x) { if (!t) return; t->lazy = h(t->lazy, x); t->key = g(t->key, x); t->sum = g(t->sum, x); } // [k 未満, k 以上] pair split_left(Ptr t, I k) { if (!t) return {nullptr, nullptr}; push(t); if (k == t->index) { Ptr tl = t->l; t->l = nullptr; return {tl, update(t)}; } else if (k < t->index) { auto s = split_left(t->l, k); t->l = s.second; return {s.first, update(t)}; } else { auto s = split_left(t->r, k); t->r = s.first; return {update(t), s.second}; } } // [k 未満, k, k 超過] array split_by_index(Ptr t, I k) { if (!t) return {{nullptr, nullptr, nullptr}}; push(t); if (k == t->index) { Ptr tl = t->l, tr = t->r; t->l = t->r = nullptr; return {{tl, update(t), tr}}; } else if (k < t->index) { auto s = split_by_index(t->l, k); t->l = s[2]; return {{s[0], s[1], update(t)}}; } else { auto s = split_by_index(t->r, k); t->r = s[0]; return {{update(t), s[1], s[2]}}; } } // t を根とする木の上で最小の index は? (t が空の場合は failed) I _min_index(Ptr t, const I &failed) { if (t == nullptr) return failed; while (t->l) t = t->l; return t->index; } // t を根とする木の上で最大の index は? (t が空の場合は failed) I _max_index(Ptr t, const I &failed) { if (t == nullptr) return failed; while (t->r) t = t->r; return t->index; } // t を根とする木のうち、[0, i の区間 fold が true になる最大の i は何か? // exclusive かつ (空 または[0,右]が真の場合) の場合は failed(inf) // inclusive かつ (空 または[0,0] が偽の場合) の場合は failed template I _max_right(Ptr t, C check, const I &failed, bool exclusive) { if (t == nullptr) return failed; push(t); Ptr now = t; T prod_now = ti(); while (true) { if (now->l != nullptr) { push(now->l); auto pl = f(prod_now, now->l->sum); if (check(pl)) { prod_now = pl; } else { now = now->l; continue; } } auto pl = f(prod_now, now->key); if (!check(pl)) { return exclusive ? now->index : _max_index(t->l, failed); } prod_now = pl; if (now->r == nullptr) { return exclusive ? failed : now->index; } push(now->r); now = now->r; } } // t を根とする木のうち、i, inf) の区間 fold が true になる最小の i は何か? // inclusive かつ (空 または 存在しない) 場合は failed // exlucisve かつ (空 または [左, inf) が真) の場合は failed template I _min_left(Ptr t, C check, const I &failed, bool inclusive) { if (t == nullptr) return failed; push(t); Ptr now = t; T prod_now = ti(); while (true) { if (now->r != nullptr) { push(now->r); auto pr = f(now->r->sum, prod_now); if (check(pr)) { prod_now = pr; } else { now = now->r; continue; } } auto pr = f(now->key, prod_now); if (!check(pr)) { return inclusive ? _min_index(now->r, failed) : now->index; } prod_now = pr; if (now->l == nullptr) { return inclusive ? now->index : failed; } push(now->l); now = now->l; } } void inner_dump(Ptr t) { push(t); if (t->l) inner_dump(t->l); cerr << "## i = " << t->index << ", "; cerr << "\tkey = " << t->key << ", "; cerr << "\tsum = " << t->sum << ", "; cerr << "\tchild = "; cerr << "( " << (t->l ? to_string(t->l->index) : "nil"); cerr << ", "; cerr << (t->r ? to_string(t->r->index) : "nil"); cerr << " )" << endl; if (t->r) inner_dump(t->r); } public: Ptr root; RBSTSegmentTree() : root(nullptr) {} RBSTSegmentTree(const vector xs, const vector &is = {}) { if (!is.empty()) assert(xs.size() == is.size()); int n = xs.size(); vector> dat(n); for (int i = 0; i < n; i++) dat[i] = {is.empty() ? i : is[i], xs[i]}; root = build(0, n, dat); } // 1 点 値の書き換え void set_val(I i, T x) { auto s = split_by_index(root, i); if (s[1] == nullptr) { s[1] = my_new(i, x); } else { s[1]->key = x; } root = merge(merge(s[0], update(s[1])), s[2]); } // 1 点取得 T get_val(I i) { auto s = split_by_index(root, i); T res = s[1] ? s[1]->key : ti(); root = merge(merge(s[0], s[1]), s[2]); return res; } // 頂点の削除 void erase(I i) { auto s = split_by_index(root, i); if (s[1]) my_del(s[1]); root = merge(s[0], s[2]); } // 範囲作用 void apply(I l, I r, const E &e) { auto [x, aux] = split_left(root, l); auto [y, z] = split_left(aux, r); propagate(y, e); root = merge(merge(x, y), z); } // 範囲取得 T fold(I l, I r) { auto [x, aux] = split_left(root, l); auto [y, z] = split_left(aux, r); T res = y ? y->sum : ti(); root = merge(merge(x, y), z); return res; } // n 未満の i のうち、[i, n) の区間 fold が true になる最小の i は何か? // (存在しない場合は failed を返す) template I min_left(I n, C check, I failed) { assert(check(ti()) == true); auto [x, y] = split_left(root, n); I res = _min_left(x, check, failed, true); root = merge(x, y); return res; } // n 未満の i のうち、(i, n) の区間 fold が true になる最小の i は何か? // (空だったり (左端, n) が 真の場合は minus_infty を返す) template I min_left_exclusive(I n, C check, I minus_infty) { assert(check(ti()) == true); auto [x, y] = split_left(root, n); I res = _min_left(x, check, minus_infty, false); root = merge(x, y); return res; } // n 以上の i のうち、[n, i) の区間 fold が true になる最大の i は何か? // (空だったり [n, 右端] が true の場合は infty を返す) template I max_right(I n, C check, I infty) { assert(check(ti()) == true); auto [x, y] = split_left(root, n); I res = _max_right(y, check, infty, true); root = merge(x, y); return res; } // n 以上の i のうち、[n, i] の区間 fold が true になる最大の i は何か? // (存在しない場合は failed を返す) template I max_right_inclusive(I n, C check, I failed) { assert(check(ti()) == true); auto [x, y] = split_left(root, n); I res = _max_right(y, check, failed, false); root = merge(x, y); return res; } void dump() { inner_dump(root); } }; // using namespace Nyaan; int f(int a, int b) { return max(a, b); } int g(int a, int b) { return a + b; } int ti() { return -inf; } int ei() { return 0; } using Seg = RBSTSegmentTree; void Nyaan::solve() { inl(N); int pre = 0; Seg seg; rep(i, N) { inl(A); A ^= pre; int mx = seg.fold(A, infLL); int sc = max(0, mx + 1); seg.apply(0, A, 1); seg.apply(A, infLL, -1); seg.set_val(A, sc); ll ans = seg.min_left_exclusive( infLL, [](int x) { return x < 0; }, -infLL); out(ans); pre = ans; } }