結果
| 問題 | No.2524 Stripes |
| ユーザー |
 noya2
|
| 提出日時 | 2023-10-27 23:51:51 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3,346 ms / 7,000 ms |
| コード長 | 32,098 bytes |
| コンパイル時間 | 3,875 ms |
| コンパイル使用メモリ | 279,516 KB |
| 実行使用メモリ | 271,948 KB |
| 最終ジャッジ日時 | 2024-09-25 15:37:21 |
| 合計ジャッジ時間 | 31,905 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 25 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"using namespace std;#include<bits/stdc++.h>#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"namespace noya2 {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p){os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p){is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v){int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v){for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &...u){cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &...u){cout << t;if (sizeof...(u)) cout << sep;out(u...);}template<typename T>void out(const vector<vector<T>> &vv){int s = (int)vv.size();for (int i = 0; i < s; i++) out(vv[i]);}struct IoSetup {IoSetup(){cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetup_noya2;} // namespace noya2#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"namespace noya2{const int iinf = 1'000'000'007;const long long linf = 2'000'000'000'000'000'000LL;const long long mod998 = 998244353;const long long mod107 = 1000000007;const long double pi = 3.14159265358979323;const vector<int> dx = {0,1,0,-1,1,1,-1,-1};const vector<int> dy = {1,0,-1,0,1,-1,-1,1};const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";const string alp = "abcdefghijklmnopqrstuvwxyz";const string NUM = "0123456789";void yes(){ cout << "Yes\n"; }void no(){ cout << "No\n"; }void YES(){ cout << "YES\n"; }void NO(){ cout << "NO\n"; }void yn(bool t){ t ? yes() : no(); }void YN(bool t){ t ? YES() : NO(); }} // namespace noya2#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"namespace noya2{unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){if (a == 0 || b == 0) return a + b;int n = __builtin_ctzll(a); a >>= n;int m = __builtin_ctzll(b); b >>= m;while (a != b) {int mm = __builtin_ctzll(a - b);bool f = a > b;unsigned long long c = f ? a : b;b = f ? b : a;a = (c - b) >> mm;}return a << min(n, m);}template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }long long sqrt_fast(long long n) {if (n <= 0) return 0;long long x = sqrt(n);while ((x + 1) * (x + 1) <= n) x++;while (x * x > n) x--;return x;}template<typename T> T floor_div(const T n, const T d) {assert(d != 0);return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);}template<typename T> T ceil_div(const T n, const T d) {assert(d != 0);return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);}template<typename T> void uniq(vector<T> &v){sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }} // namespace noya2#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"#define rep(i,n) for (int i = 0; i < (int)(n); i++)#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)#define all(v) (v).begin(),(v).end()using ll = long long;using ld = long double;using uint = unsigned int;using ull = unsigned long long;using pii = pair<int,int>;using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;namespace noya2{/* ~ (. _________ . /) */}using namespace noya2;#line 2 "c.cpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps/fps_ntt.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"namespace noya2{template<typename T>concept Field = requires (T a, T b){a + b; a - b; a / b; a * b;T(0); T(1);};template<class Info>concept Fps_Info = requires {typename Info::value_type;requires Field<typename Info::value_type>;{Info::multiply(declval<vector<typename Info::value_type>>(),declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typenameInfo::value_type>>;{Info::inv(declval<vector<typename Info::value_type>>(),declval<int>())} -> convertible_to<vector<typename Info::value_type>>;{Info::integral(declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;};template<Fps_Info Info>struct FormalPowerSeries : vector<typename Info::value_type> {using T = typename Info::value_type;using vector<T>::vector;using vector<T>::operator=;using FPS = FormalPowerSeries;FormalPowerSeries (const vector<T> &init_ = {}){ (*this) = init_; }void shrink(){ while (!(*this).empty() && (*this).back() == T(0)) (*this).pop_back(); }FPS &operator+=(const T &r){if ((*this).empty()) (*this).resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const T &r){if ((*this).empty()) (*this).resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const T &r){for (auto &x : *this) x *= r;return *this;}FPS &operator/=(const T &r){(*this) *= T(1)/r;}FPS &operator<<=(const int &d){(*this).insert((*this).begin(),d,T(0));return *this;}FPS &operator>>=(const int &d){if ((int)(*this).size() <= d) (*this).clear();else (*this).erase((*this).begin(),(*this).begin()+d);return *this;}FPS &operator+=(const FPS &r){if ((*this).size() < r.size()) (*this).resize(r.size());for (int i = 0; i < (int)(r.size()); i++) (*this)[i] += r[i];return *this;}FPS &operator-=(const FPS &r){if ((*this).size() < r.size()) (*this).resize(r.size());for (int i = 0; i < (int)(r.size()); i++) (*this)[i] -= r[i];return *this;}FPS &operator*=(const FPS &r){if ((*this).empty() || r.empty()){(*this).clear();return *this;}(*this) = Info::multiply(*this,r);return *this;}FPS operator+(const T &r) const { return FPS(*this) += r; }FPS operator-(const T &r) const { return FPS(*this) -= r; }FPS operator*(const T &r) const { return FPS(*this) *= r; }FPS operator/(const T &r) const { return FPS(*this) /= r; }FPS operator<<(const int &d) const { return FPS(*this) <<= d; }FPS operator>>(const int &d) const { return FPS(*this) >>= d; }FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator+() const { return *this; }FPS operator-() const {FPS res(*this);for (auto &x : res) x = -x;return res;}T eval(const T &x) const {T res = T(0), w = T(1);for (auto &e : *this) res += e * w, w *= x;return res;}static FPS dot(const FPS &lhs, const FPS &rhs){FPS res(min(lhs.size(),rhs.size()));for (int i = 0; i < (int)res.size(); i++) res[i] = lhs[i] * rhs[i];return res;}FPS pre(int siz) const {FPS ret((*this).begin(), (*this).begin() + min((int)this->size(), siz));if ((int)ret.size() < siz) ret.resize(siz);return ret;}FPS rev() const {FPS ret(*this);reverse(ret.begin(), ret.end());return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));T one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {FPS ret = Info::integral(*this);return ret;}FPS inv(int d = -1) const {FPS ret = Info::inv(*this,d);return ret;}FPS exp(int d = -1) const {const int n = (*this).size();if (d == -1) d = n;FPS f = {T(1)+(*this)[0],(*this)[1]}, res = {1,(n > 1 ? (*this)[1] : 0)};for (int sz = 2; sz < d; sz <<= 1){f.insert(f.end(),(*this).begin()+min(n,sz),(*this).begin()+min(n,sz*2));if ((int)f.size() < sz*2) f.resize(sz*2);res = res * (f - res.log(2*sz));res.resize(sz*2);}res.resize(d);return res;}FPS log(int d = -1) const {assert(!(*this).empty() && (*this)[0] == T(1));if (d == -1) d = (*this).size();return (this->diff() * this->inv(d)).pre(d - 1).integral();}};} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"namespace noya2 {template<typename mint>struct binomial {binomial(int len = 300000){ extend(len); }static mint fact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _fact[n];}static mint ifact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _ifact[n];}static mint inv(int n){return ifact(n) * fact(n-1);}static mint C(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(r) * ifact(n-r);}static mint P(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(n-r);}inline mint operator()(int n, int r) { return C(n, r); }template<class... Cnts> static mint M(const Cnts&... cnts){return multinomial(0,1,cnts...);}private:static mint multinomial(const int& sum, const mint& div_prod){if (sum < 0) return 0;return fact(sum) * div_prod;}template<class... Tail> static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){if (n1 < 0) return 0;return multinomial(sum+n1,div_prod*ifact(n1),tail...);}static vector<mint> _fact, _ifact;static void extend(int len = -1){if (_fact.empty()){_fact = _ifact = {1,1};}int siz = _fact.size();if (len == -1) len = siz * 2;len = min<int>(len, mint::mod()-1);if (len < siz) return ;_fact.resize(len+1), _ifact.resize(len+1);for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;_ifact[len] = _fact[len].inv();for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;}};template<typename T>std::vector<T>binomial<T>::_fact = vector<T>(2,T(1));template<typename T>std::vector<T>binomial<T>::_ifact = vector<T>(2,T(1));} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/fps/ntt.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"namespace noya2 {constexpr ll safe_mod(ll x, ll m) {x %= m;if (x < 0) x += m;return x;}constexpr ll pow_mod_constexpr(ll x, ll n, int m) {if (m == 1) return 0;uint _m = (uint)(m);ull r = 1;ull y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;ll d = n - 1;while (d % 2 == 0) d /= 2;constexpr ll bases[3] = {2, 7, 61};for (ll a : bases) {ll t = d;ll y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u;auto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (ll)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);} // namespace noya2#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"namespace noya2{struct barrett {uint _m;ull im;explicit barrett(uint m) : _m(m), im((ull)(-1) / m + 1) {}uint umod() const { return _m; }uint mul(uint a, uint b) const {ull z = a;z *= b;ull x = ull((__uint128_t(z) * im) >> 64);uint v = (uint)(z - x * _m);if (_m <= v) v += _m;return v;}};template <int m>struct static_modint {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}constexpr static_modint() : _v(0) {}template<signed_integral T>constexpr static_modint(T v){ll x = (ll)(v % (ll)(umod()));if (x < 0) x += umod();_v = (uint)(x);}template<unsigned_integral T>constexpr static_modint(T v){_v = (uint)(v % umod());}constexpr unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}constexpr mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}constexpr mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}constexpr mint& operator*=(const mint& rhs) {ull z = _v;z *= rhs._v;_v = (uint)(z % umod());return *this;}constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return mint() - *this; }constexpr mint pow(ll n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend constexpr mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend constexpr mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend constexpr mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend constexpr mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend constexpr bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = is_prime_flag<m>;};template <int id> struct dynamic_modint {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template<signed_integral T>dynamic_modint(T v){ll x = (ll)(v % (ll)(mod()));if (x < 0) x += mod();_v = (uint)(x);}template<unsigned_integral T>dynamic_modint(T v){_v = (uint)(v % mod());}uint val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = noya2::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;template<typename T>concept Modint = requires (T &a){T::mod();a.inv();a.val();a.pow(declval<int>());};} // namespace noya2#line 5 "/Users/noya2/Desktop/Noya2_library/fps/ntt.hpp"namespace noya2{template<Modint mint>struct NTT {static constexpr uint mod = mint::mod();static constexpr uint pr = primitive_root_constexpr(mod);static constexpr int level = countr_zero(mod-1);mint wp[level+1], wm[level+1];void set_ws(){mint r = mint(pr).pow((mod-1) >> level);wp[level] = r, wm[level] = r.inv();for (int i = level-1; i >= 0; i--){wp[i] = wp[i+1] * wp[i+1];wm[i] = wm[i+1] * wm[i+1];}}NTT () { set_ws(); }void fft2(vector<mint> &a, int k, int l = -1){if (k <= 0 || a.empty()) return ;if (l == -1) l = 0;for (int t = 1, v = 1<<(k-1), wi = k; v > 0; t <<= 1, v >>= 1, wi -= 1){mint ww = 1;int pl = 1<<wi;for (int j = 0; j < v; j++, ww *= wm[wi]){int j0 = l+j, j1 = j0+v;for (int i = 0; i < t; i++, j0 += pl, j1 += pl){mint a1 = a[j1];a[j1] = (a[j0] - a1) * ww;a[j0] += a1;}}}}void ifft2(vector<mint> &a, int k, int l = -1){if (k <= 0 || a.empty()) return ;if (l == -1) l = 0;for (int v = 1, t = 1<<(k-1), wi = 1; t > 0; v <<= 1, t >>= 1, wi += 1){mint ww = 1;int pl = 1<<wi;for (int j = 0; j < v; j++, ww *= wp[wi]){int j0 = l+j, j1 = j0+v;for (int i = 0; i < t; i++, j0 += pl, j1 += pl){mint a1 = a[j1] * ww;a[j1] = a[j0] - a1;a[j0] += a1;}}}}void fft4(vector<mint> &a, int k, int l = -1){if (k <= 0 || a.empty()) return ;if (l == -1) l = 0;if (k == 1){mint a1 = a[l+1];a[l+1] = a[l] - a1;a[l] += a1;return ;}if (k & 1){int v = 1 << (k - 1);mint ww = 1;for (int i = 0; i < v; i++, ww *= wm[k]){mint aiv = a[l+i+v];a[l+i+v] = (a[l+i] - aiv) * ww;a[l+i] = a[l+i] + aiv;}}mint im = wm[2];for (int t = 1 << (k & 1), v = 1 << (k - 2 - (k & 1)), wi = k - (k & 1); v > 0; t <<= 2, v >>= 2, wi -= 2){mint ww = 1, xx = 1;int pl = 1 << wi;for (int j = 0; j < v; j++, ww *= wm[wi], xx = ww * ww){int j0 = l+j, j1 = j0 + v, j2 = j1 + v, j3 = j2 + v;for (int i = 0; i < t; i++, j0 += pl, j1 += pl, j2 += pl, j3 += pl){mint a0 = a[j0], a1 = a[j1], a2 = a[j2], a3 = a[j3];mint a0p2 = a0 + a2, a0m2 = (a0 - a2) * ww;mint a1p3 = a1 + a3, a1m3 = (a1 - a3) * im * ww;a[j0] = a0p2 + a1p3, a[j2] = (a0p2 - a1p3) * xx;a[j1] = a0m2 + a1m3, a[j3] = (a0m2 - a1m3) * xx;}}}}void ifft4(vector<mint> &a, int k, int l = -1){if (k <= 0 || a.empty()) return ;if (l == -1) l = 0;if (k == 1){mint a1 = a[l+1];a[l+1] = a[l] - a1;a[l+0] += a1;return ;}mint im = wp[2];for (int v = 1, t = 1 << (k - 2), wi = 2; t > 0; v <<= 2, t >>= 2, wi += 2){mint ww = 1, xx = 1;int pl = 1 << wi;for (int j = 0; j < v; j++, ww *= wp[wi], xx = ww * ww){int j0 = l+j, j1 = j0 + v, j2 = j1 + v, j3 = j2 + v;for (int i = 0; i < t; i++, j0 += pl, j1 += pl, j2 += pl, j3 += pl){mint a0 = a[j0], a1 = a[j1] * ww, a2 = a[j2] * xx, a3 = a[j3] * ww * xx;mint a0p2 = a0 + a2, a0m2 = a0 - a2;mint a1p3 = a1 + a3, a1m3 = (a1 - a3) * im;a[j0] = a0p2 + a1p3, a[j2] = a0p2 - a1p3;a[j1] = a0m2 + a1m3, a[j3] = a0m2 - a1m3;}}}if (k & 1){int v = 1 << (k - 1);mint ww = 1;for (int i = 0; i < v; i++, ww *= wp[k]){mint aiv = a[l+i+v] * ww;a[l+i+v] = a[l+i] - aiv;a[l+i] += aiv;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;fft4(a, 63-countl_zero(a.size()));}void intt(vector<mint> &a, bool stop = false) {if ((int)a.size() <= 1) return;ifft4(a, 63-countl_zero(a.size()));if (stop) return ;mint iv = mint(a.size()).inv();for (auto &x : a) x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40){vector<mint> s(l);for (int i = 0; i < (int)a.size(); i++) for (int j = 0; j < (int)b.size(); j++) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;set_ws();vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];}else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inv();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}};} // namespace noya2#line 6 "/Users/noya2/Desktop/Noya2_library/fps/fps_ntt.hpp"namespace noya2{template<typename T>struct fps_ntt{using value_type = T;static NTT<T> ntt;static vector<T> multiply(const vector<T> &a, const vector<T> &b){return ntt.multiply(a,b);}static vector<T> inv(const vector<T> &a, int d = -1){const int n = a.size();if (d == -1) d = n;vector<T> res = {a[0].inv()};for (int siz = 1; siz < d; siz <<= 1){vector<T> f(a.begin(),a.begin()+min(n,siz*2)), g(res);f.resize(siz*2), g.resize(siz*2);ntt.ntt(f), ntt.ntt(g);for (int i = 0; i < siz*2; i++) f[i] *= g[i];ntt.intt(f,true);f.erase(f.begin(),f.begin()+siz);f.resize(siz*2);ntt.ntt(f);for (int i = 0; i < siz*2; i++) f[i] *= g[i];ntt.intt(f,true);T siz2_inv = T(siz*2).inv(); siz2_inv *= -siz2_inv;for (int i = 0; i < siz; i++) f[i] *= siz2_inv;res.insert(res.end(),f.begin(),f.begin()+siz);}res.resize(d);return res;}static binomial<T> bnm;static vector<T> integral(const vector<T> &a){const int n = a.size();vector<T> res(n+1);for (int i = 1; i <= n; i++) res[i] = a[i-1] * bnm.inv(i);return res;}};template<typename T> NTT<T> fps_ntt<T>::ntt;template<typename T> using FPS_ntt = FormalPowerSeries<fps_ntt<T>>;} // namespace noya2#line 4 "c.cpp"using mint = modint998244353;using fps = FPS_ntt<mint>;using mat = array<fps,9>;fps f0 = {0}, f1 = {1}, fx = {0,1};mat mulmat(mat a, mat b){mat c{f0,f0,f0,f0,f0,f0,f0,f0,f0};rep(i,3) rep(k,3) rep(j,3) c[i*3+j] += a[i*3+k] * b[k*3+j];return c;}#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/segment_tree.hpp"namespace noya2{template <class S, S (*op)(S, S), S (*e)()> struct segtree {public:segtree() : segtree(0) {}segtree(int n) : segtree(std::vector<S>(n, e())) {}segtree(const std::vector<S>& v) : _n(int(v.size())) {log = 0;size = 1;while (size < _n) size <<= 1, log++;d = std::vector<S>(2 * size, e());for (int i = 0; i < _n; i++) d[size + i] = v[i];for (int i = size - 1; i >= 1; i--) {update(i);}}void set(int p, S x) {assert(0 <= p && p < _n);p += size;d[p] = x;for (int i = 1; i <= log; i++) update(p >> i);}S get(int p) {assert(0 <= p && p < _n);return d[p + size];}S prod(int l, int r) {assert(0 <= l && l <= r && r <= _n);S sml = e(), smr = e();l += size;r += size;while (l < r) {if (l & 1) sml = op(sml, d[l++]);if (r & 1) smr = op(d[--r], smr);l >>= 1;r >>= 1;}return op(sml, smr);}S all_prod() { return d[1]; }template <bool (*f)(S)> int max_right(int l) {return max_right(l, [](S x) { return f(x); });}template <class F> int max_right(int l, F f) {assert(0 <= l && l <= _n);assert(f(e()));if (l == _n) return _n;l += size;S sm = e();do {while (l % 2 == 0) l >>= 1;if (!f(op(sm, d[l]))) {while (l < size) {l = (2 * l);if (f(op(sm, d[l]))) {sm = op(sm, d[l]);l++;}}return l - size;}sm = op(sm, d[l]);l++;} while ((l & -l) != l);return _n;}template <bool (*f)(S)> int min_left(int r) {return min_left(r, [](S x) { return f(x); });}template <class F> int min_left(int r, F f) {assert(0 <= r && r <= _n);assert(f(e()));if (r == 0) return 0;r += size;S sm = e();do {r--;while (r > 1 && (r % 2)) r >>= 1;if (!f(op(d[r], sm))) {while (r < size) {r = (2 * r + 1);if (f(op(d[r], sm))) {sm = op(d[r], sm);r--;}}return r + 1 - size;}sm = op(d[r], sm);} while ((r & -r) != r);return 0;}private:int _n, size, log;std::vector<S> d;void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }};} // namespace noya2#line 17 "c.cpp"mat e(){return mat{f1,f0,f0,f0,f1,f0,f0,f0,f1};}void matout(mat f){rep(i,3) rep(j,3){out(i,j,":",f[i*3+j]);} out();}void solve(){int n; in(n);string s; in(s);mat r = {f1,fx,f1,f0,f1,f0,f0,f0,f1};mat b = {f1,f0,f0,fx,f1,f1,f0,f0,f1};segtree<mat,mulmat,e> seg([&]{vector<mat> a(n);rep(i,n) a[n-1-i] = (s[i] == 'R' ? r : b);return a;}());mat f = seg.all_prod();fps ans = ((f[2] + f[5]) << 1);ans.resize(n+1);rep(i,n) out(ans[i+1]);//f = mulmat(mulmat(r,b),mulmat(r,r));// matout(f);// rep(i,4) matout(seg.get(i));}int main(){int t = 1; //in(t);while (t--) { solve(); }}