/** * date : 2022-12-23 00:39:02 */ #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; 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; } template P &operator*=(const S &r) { first *= r, second *= r; 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; } template P operator*(const S &r) const { return P(*this) *= 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; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } template using minpq = priority_queue, greater>; } // 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; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } 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 #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (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(); } // namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = u64(chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count()) * 10150724397891781847ULL; _x ^= _x << 7; return _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % (r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % (r - l); } // choose n numbers from [l, r) without overlapping vector randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector ret; for (auto& x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } template void randshf(vector& v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; // template struct SegmentTree { int N; int size; vector seg; const F f; const T I; SegmentTree(F _f, const T &I_) : N(0), size(0), f(_f), I(I_) {} SegmentTree(int _N, F _f, const T &I_) : f(_f), I(I_) { init(_N); } SegmentTree(const vector &v, F _f, T I_) : f(_f), I(I_) { init(v.size()); for (int i = 0; i < (int)v.size(); i++) { seg[i + size] = v[i]; } build(); } void init(int _N) { N = _N; size = 1; while (size < N) size <<= 1; seg.assign(2 * size, I); } void set(int k, T x) { seg[k + size] = x; } void build() { for (int k = size - 1; k > 0; k--) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } void update(int k, T x) { k += size; seg[k] = x; while (k >>= 1) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } void add(int k, T x) { k += size; seg[k] += x; while (k >>= 1) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } // query to [a, b) T query(int a, int b) { T L = I, R = I; for (a += size, b += size; a < b; a >>= 1, b >>= 1) { if (a & 1) L = f(L, seg[a++]); if (b & 1) R = f(seg[--b], R); } return f(L, R); } T &operator[](const int &k) { return seg[k + size]; } // check(a[l] * ... * a[r-1]) が true となる最大の r // (右端まですべて true なら N を返す) template int max_right(int l, C check) { assert(0 <= l && l <= N); assert(check(I) == true); if (l == N) return N; l += size; T sm = I; do { while (l % 2 == 0) l >>= 1; if (!check(f(sm, seg[l]))) { while (l < size) { l = (2 * l); if (check(f(sm, seg[l]))) { sm = f(sm, seg[l]); l++; } } return l - size; } sm = f(sm, seg[l]); l++; } while ((l & -l) != l); return N; } // check(a[l] * ... * a[r-1]) が true となる最小の l // (左端まで true なら 0 を返す) template int min_left(int r, C check) { assert(0 <= r && r <= N); assert(check(I) == true); if (r == 0) return 0; r += size; T sm = I; do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!check(f(seg[r], sm))) { while (r < size) { r = (2 * r + 1); if (check(f(seg[r], sm))) { sm = f(seg[r], sm); r--; } } return r + 1 - size; } sm = f(seg[r], sm); } while ((r & -r) != r); return 0; } }; // template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { return pow(mod - 2); } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; template struct Binomial { vector f, g, h; Binomial(int MAX = 0) { assert(T::get_mod() != 0 && "Binomial()"); f.resize(1, T{1}); g.resize(1, T{1}); h.resize(1, T{1}); while (MAX >= (int)f.size()) extend(); } void extend() { int n = f.size(); int m = n * 2; f.resize(m); g.resize(m); h.resize(m); for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i); g[m - 1] = f[m - 1].inverse(); h[m - 1] = g[m - 1] * f[m - 2]; for (int i = m - 2; i >= n; i--) { g[i] = g[i + 1] * T(i + 1); h[i] = g[i] * f[i - 1]; } } T fac(int i) { if (i < 0) return T(0); while (i >= (int)f.size()) extend(); return f[i]; } T finv(int i) { if (i < 0) return T(0); while (i >= (int)g.size()) extend(); return g[i]; } T inv(int i) { if (i < 0) return -inv(-i); while (i >= (int)h.size()) extend(); return h[i]; } T C(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } inline T operator()(int n, int r) { return C(n, r); } template T multinomial(const vector& r) { static_assert(is_integral::value == true); int n = 0; for (auto& x : r) { if (x < 0) return T(0); n += x; } T res = fac(n); for (auto& x : r) res *= finv(x); return res; } template T operator()(const vector& r) { return multinomial(r); } T C_naive(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r); } // [x^r] 1 / (1-x)^n T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; // using namespace Nyaan; using mint = LazyMontgomeryModInt<998244353>; // using mint = LazyMontgomeryModInt<1000000007>; using vm = vector; using vvm = vector; Binomial C; using namespace Nyaan; mint dp[5050][5050]; mint calc(ll N, vl A) { SegmentTree seg( A, [](ll a, ll b) { return a | b; }, 0LL); vi r(N + 1); rep(i, N) { int j = N; if (A[i] == 0) { j = i + 1; } else if (i + 1 != N) { j = seg.max_right(i + 1, [&](ll x) { return (x & A[i]) < A[i]; }); } r[i] = j; } r[N] = N; trc(r); /* rep(i, N + 1) rep(j, N + 1) dp[i][j] = 0; dp[0][0] = 1; rep(i, N + 1) reg(j, i, N + 1) { if (i) dp[i][j] += dp[i - 1][j]; if (j and j <= r[i]) dp[i][j] += dp[i][j - 1]; } rep(i,N+1){ rep(j,N+1)cerr< dq; rep(i, N + 1) dq.push_back(0); dq[0] = 1; rep(i, N) { rep(j, r[i] - i) dq[j + 1] += dq[j]; dq.pop_front(); } return dq[0]; } mint naive(int N, vl A) { set ans; auto dfs = [&](auto rc, int i, int j, vi v) -> void { if (i == N) { ans.insert(v); return; } j = max(j, i + 1); for (int k = j; k <= N; k++) { vi w{v}; reg(l, i, k) w[l] |= A[i]; rc(rc, i + 1, k, w); } }; dfs(dfs, 0, 0, vi(N, 0)); // trc(ans); return sz(ans); } void test() { rep(t, 100) { int N = rng(3, 12); vl A(N); each(x, A) x = rng(0, 7); auto ansc = calc(N, A); auto ansn = naive(N, A); if (ansc != ansn) { trc(N, A, ansc, ansn); exit(1); } } cerr << "OK" << endl; } void q() { inl(N); vl A(N); in(A); out(calc(N, A)); } void Nyaan::solve() { // test(); int t = 1; // in(t); while (t--) q(); }