#673077 (C++17(gcc12)) No.1574 Swap and Repaint

• 問題: No.1574 Swap and Repaint
• ユーザー: NyaanNyaan
• 提出日時: 2021-07-04 18:52:11
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 22,536 bytes
• コンパイル時間: 6,189 ms
• コンパイル使用メモリ: 280,908 KB
• 最終ジャッジ日時: 2025-01-22 17:41:44
• ジャッジサーバーID （参考情報）: judge4 / judge2

コンパイルメッセージ

main.cpp: In function 'mmint operator*(const mmint&, const mmint&)':
main.cpp:632:44: warning: AVX vector return without AVX enabled changes the ABI [-Wpsabi]
  632 |     m256 a13 = _mm256_shuffle_epi32(A, 0xF5);
      |                                            ^
In file included from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/immintrin.h:47,
                 from main.cpp:11:
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/avx2intrin.h: In function 'mmint operator+(const mmint&, const mmint&)':
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/avx2intrin.h:119:1: error: inlining failed in call to 'always_inline' '__m256i _mm256_add_epi32(__m256i, __m256i)': target specific option mismatch
  119 | _mm256_add_epi32 (__m256i __A, __m256i __B)
      | ^~~~~~~~~~~~~~~~
main.cpp:621:28: note: called from here
  621 |     return _mm256_add_epi32(add, ret);
      |            ~~~~~~~~~~~~~~~~^~~~~~~~~~
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/avx2intrin.h:179:1: error: inlining failed in call to 'always_inline' '__m256i _mm256_and_si256(__m256i, __m256i)': target specific option mismatch
  179 | _mm256_and_si256 (__m256i __A, __m256i __B)
      | ^~~~~~~~~~~~~~~~
main.cpp:620:32: note: called from here
  620 |     m256 add = _mm256_and_si256(cmp, M2);
      |                ~~~~~~~~~~~~~~~~^~~~~~~~~
/home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.4.0/lib/gcc/12/gcc/x86_64-pc-linux-gnu/12/include/avx2intrin.h:273:1: error: inlining failed in call to 'always_inline' '__m256i _mm256_cmpgt_epi32(__m256i, __m256i)': target specific option mismatch
  273 | _mm256_cmpgt_epi32 (__m256i __A, __m256i __B)
      | ^~~~~~~~~~~~~~~~~~
main.cpp:619:34: note: called from here
  619 |     m256 cmp = _mm256_cmpgt_epi32(M0, ret);
      |                ~~~~~~~~~~~~~~~~~~^~~~~~~~~
/home/linuxbrew/.linux

ソースコード

// O(N^2)です。ゆるして

/**
 *  date : 2021-07-04 01:10:55
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// 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 <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::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; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &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 <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> 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 <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> 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 <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
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 <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...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
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 <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::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 <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& 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 <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(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(); }

//


struct Timer {
  chrono::high_resolution_clock::time_point st;

  Timer() { reset(); }

  void reset() { st = chrono::high_resolution_clock::now(); }

  chrono::milliseconds::rep elapsed() {
    auto ed = chrono::high_resolution_clock::now();
    return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
  }
};



template <uint32_t mod>
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<mod>(t);
    return (is);
  }
  
  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")

using m256 = __m256i;
struct alignas(32) mmint {
  m256 x;
  static mmint R, M0, M1, M2, N2;

  mmint() : x() {}
  inline mmint(const m256& _x) : x(_x) {}
  inline mmint(unsigned int a) : x(_mm256_set1_epi32(a)) {}
  inline mmint(unsigned int a0, unsigned int a1, unsigned int a2,
               unsigned int a3, unsigned int a4, unsigned int a5,
               unsigned int a6, unsigned int a7)
      : x(_mm256_set_epi32(a7, a6, a5, a4, a3, a2, a1, a0)) {}
  inline operator m256&() { return x; }
  inline operator const m256&() const { return x; }
  inline int& operator[](int i) { return *(reinterpret_cast<int*>(&x) + i); }
  inline const int& operator[](int i) const {
    return *(reinterpret_cast<const int*>(&x) + i);
  }

  friend ostream& operator<<(ostream& os, const mmint& m) {
    unsigned r = R[0], mod = M1[0];
    auto reduce1 = [&](const uint64_t& b) {
      unsigned res = (b + uint64_t(unsigned(b) * unsigned(-r)) * mod) >> 32;
      return res >= mod ? res - mod : res;
    };
    for (int i = 0; i < 8; i++) {
      os << reduce1(m[i]) << (i == 7 ? "" : " ");
    }
    return os;
  }

  template <typename mint>
  static void set_mod() {
    R = _mm256_set1_epi32(mint::r);
    M0 = _mm256_setzero_si256();
    M1 = _mm256_set1_epi32(mint::get_mod());
    M2 = _mm256_set1_epi32(mint::get_mod() * 2);
    N2 = _mm256_set1_epi32(mint::n2);
  }

  static inline mmint reduce(const mmint& prod02, const mmint& prod13) {
    m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
    m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
    m256 prodlo = _mm256_unpacklo_epi64(unpalo, unpahi);
    m256 prodhi = _mm256_unpackhi_epi64(unpalo, unpahi);
    m256 hiplm1 = _mm256_add_epi32(prodhi, M1);
    m256 prodlohi = _mm256_shuffle_epi32(prodlo, 0xF5);
    m256 lmlr02 = _mm256_mul_epu32(prodlo, R);
    m256 lmlr13 = _mm256_mul_epu32(prodlohi, R);
    m256 prod02_ = _mm256_mul_epu32(lmlr02, M1);
    m256 prod13_ = _mm256_mul_epu32(lmlr13, M1);
    m256 unpalo_ = _mm256_unpacklo_epi32(prod02_, prod13_);
    m256 unpahi_ = _mm256_unpackhi_epi32(prod02_, prod13_);
    m256 prod = _mm256_unpackhi_epi64(unpalo_, unpahi_);
    return _mm256_sub_epi32(hiplm1, prod);
  }

  static inline mmint itom(const mmint& A) { return A * N2; }

  static inline mmint mtoi(const mmint& A) {
    m256 A13 = _mm256_shuffle_epi32(A, 0xF5);
    m256 lmlr02 = _mm256_mul_epu32(A, R);
    m256 lmlr13 = _mm256_mul_epu32(A13, R);
    m256 prod02_ = _mm256_mul_epu32(lmlr02, M1);
    m256 prod13_ = _mm256_mul_epu32(lmlr13, M1);
    m256 unpalo_ = _mm256_unpacklo_epi32(prod02_, prod13_);
    m256 unpahi_ = _mm256_unpackhi_epi32(prod02_, prod13_);
    m256 prod = _mm256_unpackhi_epi64(unpalo_, unpahi_);
    m256 cmp = _mm256_cmpgt_epi32(prod, M0);
    m256 dif = _mm256_and_si256(cmp, M1);
    return _mm256_sub_epi32(dif, prod);
  }

  friend inline mmint operator+(const mmint& A, const mmint& B) {
    m256 apb = _mm256_add_epi32(A, B);
    m256 ret = _mm256_sub_epi32(apb, M2);
    m256 cmp = _mm256_cmpgt_epi32(M0, ret);
    m256 add = _mm256_and_si256(cmp, M2);
    return _mm256_add_epi32(add, ret);
  }

  friend inline mmint operator-(const mmint& A, const mmint& B) {
    m256 ret = _mm256_sub_epi32(A, B);
    m256 cmp = _mm256_cmpgt_epi32(M0, ret);
    m256 add = _mm256_and_si256(cmp, M2);
    return _mm256_add_epi32(add, ret);
  }

  friend inline mmint operator*(const mmint& A, const mmint& B) {
    m256 a13 = _mm256_shuffle_epi32(A, 0xF5);
    m256 b13 = _mm256_shuffle_epi32(B, 0xF5);
    m256 prod02 = _mm256_mul_epu32(A, B);
    m256 prod13 = _mm256_mul_epu32(a13, b13);
    return reduce(prod02, prod13);
  }

  inline mmint& operator+=(const mmint& A) { return (*this) = (*this) + A; }
  inline mmint& operator-=(const mmint& A) { return (*this) = (*this) - A; }
  inline mmint& operator*=(const mmint& A) { return (*this) = (*this) * A; }

  bool operator==(const mmint& A) {
    m256 sub = _mm256_sub_epi32(x, A.x);
    return _mm256_testz_si256(sub, sub) == 1;
  }
  bool operator!=(const mmint& A) { return !((*this) == A); }
};
__attribute__((aligned(32))) mmint mmint::R;
__attribute__((aligned(32))) mmint mmint::M0, mmint::M1, mmint::M2, mmint::N2;

/**
 * @brief vectorize modint
 */


template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) : f(1, T(1)), g(1, T(1)), h(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); }

  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);
  }

  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 vm = vector<mint>;
Binomial<mint> C;

mmint F[13000];
mmint DP[13000];
mmint NX[13000];

void Nyaan::solve() {
  Timer timer;
  mmint::set_mod<mint>();
  memset(F, 0, sizeof(F));
  memset(DP, 0, sizeof(F));
  memset(NX, 0, sizeof(F));

  ini(N);
  vi a(N);
  in(a);

  // calc coeff
  vm f(N);

  // 右端以外
  f[0] = mint(1) / 2;
  reg(i, 1, N - 1) {
    f[i] = C.finv(i + 1) * (C.inv(2) + i) * (C.inv(2).pow(i));
    f[i] += f[i - 1];
  }

  // 右端
  {
    mint buf = 1;
    for (int i = 0; i < N; i++) {
      f.back() += buf;
      buf *= C.inv(2) * C.inv(i + 1);
    }
  }

  mmint* dp = DP + 1;
  mmint* nx = NX + 1;

  for (int i = 0; i < N; i++) F[i / 8][i % 8] = f[i].a;
  for (int i = 0; i < N; i++) dp[i / 8][i % 8] = mint(a[i]).a;

  mint coe = mint(2).pow(1LL * 2 * (N - 1)) * C.fac(N - 1);

  m256 MOD = _mm256_set1_epi32(998244353);
  mmint th1, th2, zero = _mm256_setzero_si256();
  th1[1] = th1[3] = th1[5] = th1[7] = mmint::M1[0];
  th2[1] = th2[3] = th2[5] = th2[7] = mmint::M2[0];

  auto normalize = [&MOD](const mmint& data) -> m256 {
    m256 flag = _mm256_cmpgt_epi32(data, MOD);
    m256 dif = _mm256_and_si256(flag, MOD);
    return _mm256_sub_epi32(data, dif);
  };

#define INIT_X(x)                          \
  m256 prod02##x = _mm256_setzero_si256(); \
  m256 prod13##x = _mm256_setzero_si256()

#define ADD(x)                                        \
  m256 f02##x = normalize(F[j + x]);                  \
  m256 f13##x = _mm256_shuffle_epi32(f02##x, 0xF5);   \
  m256 dp02##x = normalize(dp[j + x]);                \
  m256 dp13##x = _mm256_shuffle_epi32(dp02##x, 0xF5); \
  m256 fd02##x = _mm256_mul_epi32(f02##x, dp02##x);   \
  m256 fd13##x = _mm256_mul_epi32(f13##x, dp13##x);   \
  prod02##x = _mm256_add_epi64(prod02##x, fd02##x);   \
  prod13##x = _mm256_add_epi64(prod13##x, fd13##x)

#define COMP(x)                                        \
  m256 cmp02##x = _mm256_cmpgt_epi64(zero, prod02##x); \
  m256 cmp13##x = _mm256_cmpgt_epi64(zero, prod13##x); \
  m256 dif02##x = _mm256_and_si256(cmp02##x, th2);     \
  m256 dif13##x = _mm256_and_si256(cmp13##x, th2);     \
  prod02##x = _mm256_sub_epi64(prod02##x, dif02##x);   \
  prod13##x = _mm256_sub_epi64(prod13##x, dif13##x)

#define REDUCE(x)                                    \
  for (int _ = 0; _ < 2; _++) {                      \
    m256 cmp02 = _mm256_cmpgt_epi64(prod02##x, th1); \
    m256 cmp13 = _mm256_cmpgt_epi64(prod13##x, th1); \
    m256 dif02 = _mm256_and_si256(cmp02, th1);       \
    m256 dif13 = _mm256_and_si256(cmp13, th1);       \
    prod02##x = _mm256_sub_epi64(prod02##x, dif02);  \
    prod13##x = _mm256_sub_epi64(prod13##x, dif13);  \
  }                                                  \
  buf += mmint::reduce(prod02##x, prod13##x)

  auto done = [&]() {
    INIT_X(0);
    INIT_X(1);
    INIT_X(2);
    INIT_X(3);
    for (int i = 0; i < N / 8 + 32; i += 32) {
      for (int j = i; j < i + 32; j += 4) {
        ADD(0);
        ADD(1);
        ADD(2);
        ADD(3);
      }
      COMP(0);
      COMP(1);
      COMP(2);
      COMP(3);
    }
    mmint buf{0};
    REDUCE(0);
    REDUCE(1);
    REDUCE(2);
    REDUCE(3);
    buf = mmint::mtoi(buf);
    mint res = 0;
    rep(i, 8) res += buf[i];
    out(res * coe);
  };

  done();

  mint Nm2 = N - 2;
  mint Nm3 = N - 3;

  rep(_, N) {
    mint* dp0 = reinterpret_cast<mint*>(dp);
    mint* nx0 = reinterpret_cast<mint*>(nx);

    mmint NM3{Nm3.a};
    for (int i = 0; i < N / 8 + 3; i++) {
      __m256i p1 = _mm256_loadu_si256((__m256i*)(dp0 + i * 8 - 1));
      __m256i p2 = _mm256_loadu_si256((__m256i*)(dp0 + i * 8 + 1));
      nx[i] = dp[i] * NM3 + p1 + p2;
    }
    nx0[0] = dp0[1] + dp0[0] * Nm2;
    nx0[N - 1] = dp0[N - 2] + dp0[N - 1] * Nm2;
    swap(dp, nx);

    trc(dp);
    done();
  }

  cerr << timer.elapsed() << "\n";
}