結果
問題 | No.2513 Power Eraser |
ユーザー |
![]() |
提出日時 | 2023-10-22 18:02:48 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,041 ms / 6,000 ms |
コード長 | 41,824 bytes |
コンパイル時間 | 3,824 ms |
コンパイル使用メモリ | 246,176 KB |
最終ジャッジ日時 | 2025-02-17 13:02:42 |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 39 |
ソースコード
#include <bits/stdc++.h>#ifdef LOCAL#include <debug.hpp>#else#define debug(...) void(0)#endif#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endif#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}// Fast modular multiplication by barrett reduction// Reference: https://en.wikipedia.org/wiki/Barrett_reduction// NOTE: reconsider after Ice Lakestruct barrett {unsigned int _m;unsigned long long im;// @param m `1 <= m < 2^31`explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}// @return munsigned int umod() const { return _m; }// @param a `0 <= a < m`// @param b `0 <= b < m`// @return `a * b % m`unsigned int mul(unsigned int a, unsigned int b) const {// [1] m = 1// a = b = im = 0, so okay// [2] m >= 2// im = ceil(2^64 / m)// -> im * m = 2^64 + r (0 <= r < m)// let z = a*b = c*m + d (0 <= c, d < m)// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2// ((ab * im) >> 64) == c or c + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};// @param n `0 <= n`// @param m `1 <= m`// @return `(x ** n) % m`constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}// Reference:// M. Forisek and J. Jancina,// Fast Primality Testing for Integers That Fit into a Machine Word// @param n `0 <= n`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;long long d = n - 1;while (d % 2 == 0) d /= 2;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {long long t = d;long long 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 = is_prime_constexpr(n);// @param b `1 <= b`// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/gconstexpr 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};// Contracts:// [1] s - m0 * a = 0 (mod b)// [2] t - m1 * a = 0 (mod b)// [3] s * |m1| + t * |m0| <= blong long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b// [3]:// (s - t * u) * |m1| + t * |m0 - m1 * u|// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)// = s * |m1| + t * |m0| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (m0 < 0) m0 += b / s;return {s, m0};}// Compile time primitive root// @param m must be prime// @return primitive root (and minimum in now)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; (long long)(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 = primitive_root_constexpr(m);// @param n `n < 2^32`// @param m `1 <= m < 2^32`// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}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;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());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 {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = internal::inv_gcd(_v, m);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;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}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;}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 = internal::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;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcoder#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param n `0 <= n`// @return minimum non-negative `x` s.t. `n <= 2**x`int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}// @param n `1 <= n`// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`constexpr int bsf_constexpr(unsigned int n) {int x = 0;while (!(n & (1 << x))) x++;return x;}// @param n `1 <= n`// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {template <class mint,int g = internal::primitive_root<mint::mod()>,internal::is_static_modint_t<mint>* = nullptr>struct fft_info {static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;fft_info() {root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);iroot[rank2] = root[rank2].inv();for (int i = rank2 - 1; i >= 0; i--) {root[i] = root[i + 1] * root[i + 1];iroot[i] = iroot[i + 1] * iroot[i + 1];}{mint prod = 1, iprod = 1;for (int i = 0; i <= rank2 - 2; i++) {rate2[i] = root[i + 2] * prod;irate2[i] = iroot[i + 2] * iprod;prod *= iroot[i + 2];iprod *= root[i + 2];}}{mint prod = 1, iprod = 1;for (int i = 0; i <= rank2 - 3; i++) {rate3[i] = root[i + 3] * prod;irate3[i] = iroot[i + 3] * iprod;prod *= iroot[i + 3];iprod *= root[i + 3];}}}};template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {int n = int(a.size());int h = internal::ceil_pow2(n);static const fft_info<mint> info;int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (len < h) {if (h - len == 1) {int p = 1 << (h - len - 1);mint rot = 1;for (int s = 0; s < (1 << len); s++) {int offset = s << (h - len);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * rot;a[i + offset] = l + r;a[i + offset + p] = l - r;}if (s + 1 != (1 << len))rot *= info.rate2[bsf(~(unsigned int)(s))];}len++;} else {// 4-baseint p = 1 << (h - len - 2);mint rot = 1, imag = info.root[2];for (int s = 0; s < (1 << len); s++) {mint rot2 = rot * rot;mint rot3 = rot2 * rot;int offset = s << (h - len);for (int i = 0; i < p; i++) {auto mod2 = 1ULL * mint::mod() * mint::mod();auto a0 = 1ULL * a[i + offset].val();auto a1 = 1ULL * a[i + offset + p].val() * rot.val();auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();auto a1na3imag =1ULL * mint(a1 + mod2 - a3).val() * imag.val();auto na2 = mod2 - a2;a[i + offset] = a0 + a2 + a1 + a3;a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));a[i + offset + 2 * p] = a0 + na2 + a1na3imag;a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);}if (s + 1 != (1 << len))rot *= info.rate3[bsf(~(unsigned int)(s))];}len += 2;}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {int n = int(a.size());int h = internal::ceil_pow2(n);static const fft_info<mint> info;int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformedwhile (len) {if (len == 1) {int p = 1 << (h - len);mint irot = 1;for (int s = 0; s < (1 << (len - 1)); s++) {int offset = s << (h - len + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *irot.val();;}if (s + 1 != (1 << (len - 1)))irot *= info.irate2[bsf(~(unsigned int)(s))];}len--;} else {// 4-baseint p = 1 << (h - len);mint irot = 1, iimag = info.iroot[2];for (int s = 0; s < (1 << (len - 2)); s++) {mint irot2 = irot * irot;mint irot3 = irot2 * irot;int offset = s << (h - len + 2);for (int i = 0; i < p; i++) {auto a0 = 1ULL * a[i + offset + 0 * p].val();auto a1 = 1ULL * a[i + offset + 1 * p].val();auto a2 = 1ULL * a[i + offset + 2 * p].val();auto a3 = 1ULL * a[i + offset + 3 * p].val();auto a2na3iimag =1ULL *mint((mint::mod() + a2 - a3) * iimag.val()).val();a[i + offset] = a0 + a1 + a2 + a3;a[i + offset + 1 * p] =(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();a[i + offset + 2 * p] =(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *irot2.val();a[i + offset + 3 * p] =(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *irot3.val();}if (s + 1 != (1 << (len - 2)))irot *= info.irate3[bsf(~(unsigned int)(s))];}len -= 2;}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution_naive(const std::vector<mint>& a,const std::vector<mint>& b) {int n = int(a.size()), m = int(b.size());std::vector<mint> ans(n + m - 1);if (n < m) {for (int j = 0; j < m; j++) {for (int i = 0; i < n; i++) {ans[i + j] += a[i] * b[j];}}} else {for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}}return ans;}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}} // namespace internaltemplate <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) return convolution_naive(a, b);return internal::convolution_fft(a, b);}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(const std::vector<mint>& a,const std::vector<mint>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) return convolution_naive(a, b);return internal::convolution_fft(a, b);}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;// B = 2^63, -B <= x, r(real value) < B// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)// r = c1[i] (mod MOD1)// focus on MOD1// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)// r = x,// x - M' + (0 or 2B),// x - 2M' + (0, 2B or 4B),// x - 3M' + (0, 2B, 4B or 6B) (without mod!)// (r - x) = 0, (0)// - M' + (0 or 2B), (1)// -2M' + (0 or 2B or 4B), (2)// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)// we checked that// ((1) mod MOD1) mod 5 = 2// ((2) mod MOD1) mod 5 = 3// ((3) mod MOD1) mod 5 = 4long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}} // namespace atcodertemplate <typename T> struct FormalPowerSeries : std::vector<T> {private:using std::vector<T>::vector;using FPS = FormalPowerSeries;void shrink() {while (this->size() and this->back() == T(0)) this->pop_back();}FPS pre(size_t sz) const { return FPS(this->begin(), this->begin() + std::min(this->size(), sz)); }FPS rev() const {FPS ret(*this);std::reverse(ret.begin(), ret.end());return ret;}FPS operator>>(size_t sz) const {if (this->size() <= sz) return {};return FPS(this->begin() + sz, this->end());}FPS operator<<(size_t sz) const {if (this->empty()) return {};FPS ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}public:FPS& operator+=(const FPS& r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < int(r.size()); i++) (*this)[i] += r[i];shrink();return *this;}FPS& operator+=(const T& v) {if (this->empty()) this->resize(1);(*this)[0] += v;shrink();return *this;}FPS& operator-=(const FPS& r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < int(r.size()); i++) (*this)[i] -= r[i];shrink();return *this;}FPS& operator-=(const T& v) {if (this->empty()) this->resize(1);(*this)[0] -= v;shrink();return *this;}FPS& operator*=(const FPS& r) {auto res = atcoder::convolution(*this, r);return *this = {res.begin(), res.end()};}FPS& operator*=(const T& v) {for (auto& x : (*this)) x *= v;shrink();return *this;}FPS& operator/=(const FPS& r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS& operator%=(const FPS& r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS& r) const { return FPS(*this) += r; }FPS operator+(const T& v) const { return FPS(*this) += v; }FPS operator-(const FPS& r) const { return FPS(*this) -= r; }FPS operator-(const T& v) const { return FPS(*this) -= v; }FPS operator*(const FPS& r) const { return FPS(*this) *= r; }FPS operator*(const T& v) const { return FPS(*this) *= v; }FPS operator/(const FPS& r) const { return FPS(*this) /= r; }FPS operator%(const FPS& r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret = *this;for (auto& v : ret) v = -v;return ret;}FPS differential() const {const int n = (int)this->size();FPS ret(std::max(0, n - 1));for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = T(0);if (n > 0) ret[1] = T(1);auto mod = T::mod();for (int i = 2; i <= n; i++) ret[i] = -ret[mod % i] * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}FPS inv(int deg = -1) const {assert((*this)[0] != T(0));const int n = (int)this->size();if (deg == -1) deg = n;FPS ret{(*this)[0].inv()};ret.reserve(deg);for (int d = 1; d < deg; d <<= 1) {FPS f(d << 1), g(d << 1);std::copy(this->begin(), this->begin() + std::min(n, d << 1), f.begin());std::copy(ret.begin(), ret.end(), g.begin());atcoder::internal::butterfly(f);atcoder::internal::butterfly(g);for (int i = 0; i < (d << 1); i++) f[i] *= g[i];atcoder::internal::butterfly_inv(f);std::fill(f.begin(), f.begin() + d, T(0));atcoder::internal::butterfly(f);for (int i = 0; i < (d << 1); i++) f[i] *= g[i];atcoder::internal::butterfly_inv(f);T iz = T(d << 1).inv();iz *= -iz;for (int i = d; i < std::min(d << 1, deg); i++) ret.push_back(f[i] * iz);}return ret.pre(deg);}FPS log(int deg = -1) const {assert((*this)[0] == T(1));if (deg == -1) deg = (int)this->size();return (differential() * inv(deg)).pre(deg - 1).integral();}FPS sqrt(const std::function<T(T)>& get_sqrt, int deg = -1) const {const int n = this->size();if (deg == -1) deg = n;if (this->empty()) return FPS(deg, 0);if ((*this)[0] == T(0)) {for (int i = 1; i < n; i++) {if ((*this)[i] != T(0)) {if (i & 1) return {};if (deg - i / 2 <= 0) break;auto ret = (*this >> i).sqrt(get_sqrt, deg - i / 2);if (ret.empty()) return {};ret = ret << (i / 2);if ((int)ret.size() < deg) ret.resize(deg, T(0));return ret;}}return FPS(deg, T(0));}auto sqrtf0 = T(get_sqrt((*this)[0]));if (sqrtf0 * sqrtf0 != (*this)[0]) return {};FPS ret{sqrtf0};T inv2 = T(2).inv();for (int i = 1; i < deg; i <<= 1) ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;return ret.pre(deg);}/*** @brief Exp of Formal Power Series** @see https://arxiv.org/pdf/1301.5804.pdf*/FPS exp(int deg = -1) const {assert(this->empty() or (*this)[0] == T(0));if (this->size() <= 1) return {T(1)};if (deg == -1) deg = (int)this->size();FPS inv;inv.reserve(deg + 1);inv.push_back(T(0));inv.push_back(T(1));auto inplace_integral = [&](FPS& F) -> void {const int n = (int)F.size();auto mod = T::mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back(-inv[mod % i] * (mod / i));}F.insert(F.begin(), T(0));for (int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_differential = [](FPS& F) -> void {if (F.empty()) return;F.erase(F.begin());for (size_t i = 0; i < F.size(); i++) F[i] *= T(i + 1);};FPS f{1, (*this)[1]}, g{T(1)}, g_fft{T(1), T(1)};for (int m = 2; m < deg; m <<= 1) {const T iz1 = T(m).inv(), iz2 = T(m << 1).inv();auto f_fft = f;f_fft.resize(m << 1);atcoder::internal::butterfly(f_fft);{// Step 2.a'FPS _g(m);for (int i = 0; i < m; i++) _g[i] = f_fft[i] * g_fft[i];atcoder::internal::butterfly_inv(_g);std::fill(_g.begin(), _g.begin() + (m >> 1), T(0));atcoder::internal::butterfly(_g);for (int i = 0; i < m; i++) _g[i] *= -g_fft[i] * iz1 * iz1;atcoder::internal::butterfly_inv(_g);g.insert(g.end(), _g.begin() + (m >> 1), _g.end());g_fft = g;g_fft.resize(m << 1);atcoder::internal::butterfly(g_fft);}FPS x(this->begin(), this->begin() + std::min((int)this->size(), m));{// Step 2.b'x.resize(m);inplace_differential(x);x.push_back(T(0));atcoder::internal::butterfly(x);}{// Step 2.c'for (int i = 0; i < m; i++) x[i] *= f_fft[i] * iz1;atcoder::internal::butterfly_inv(x);}{// Step 2.d' and 2.e'x -= f.differential();x.resize(m << 1);for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = T(0);atcoder::internal::butterfly(x);for (int i = 0; i < (m << 1); i++) x[i] *= g_fft[i] * iz2;atcoder::internal::butterfly_inv(x);}{// Step 2.f'x.pop_back();inplace_integral(x);for (int i = m; i < std::min((int)this->size(), m << 1); i++) x[i] += (*this)[i];std::fill(x.begin(), x.begin() + m, T(0));}{// Step 2.g' and 2.h'atcoder::internal::butterfly(x);for (int i = 0; i < (m << 1); i++) x[i] *= f_fft[i] * iz2;atcoder::internal::butterfly_inv(x);f.insert(f.end(), x.begin() + m, x.end());}}return FPS{f.begin(), f.begin() + deg};}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {auto res = FPS(deg, T(0));res[0] = T(1);return res;}for (int i = 0; i < n; i++) {if ((*this)[i] != T(0)) {if (i >= (deg + k - 1) / k) return FPS(deg, T(0));T rev = (*this)[i].inv();FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, T(0));return ret;}}return FPS(deg, T(0));}T eval(T x) const {T ret = 0, w = 1;for (const auto& v : *this) ret += w * v, w *= x;return ret;}static FPS product_of_polynomial_sequence(const std::vector<FPS>& fs) {if (fs.empty()) return {T(1)};auto comp = [](const FPS& f, const FPS& g) { return f.size() > g.size(); };std::priority_queue<FPS, std::vector<FPS>, decltype(comp)> pq{comp};for (const auto& f : fs) pq.emplace(f);while (pq.size() > 1) {auto f = pq.top();pq.pop();auto g = pq.top();pq.pop();pq.emplace(f * g);}return pq.top();}static FPS pow_sparse(const std::vector<std::pair<int, T>>& f, int64_t k, int n) {assert(k >= 0);int d = f.size(), offset = 0;while (offset < d and f[offset].second == 0) offset++;FPS res(n, 0);if (offset == d) {if (k == 0) res[0]++;return res;}if (f[offset].first > 0) {int deg = f[offset].first;if (k > (n - 1) / deg) return res;std::vector<std::pair<int, T>> g(f.begin() + offset, f.end());for (auto& p : g) p.first -= deg;auto tmp = pow_sparse(g, k, n - k * deg);for (int i = 0; i < n - k * deg; i++) res[k * deg + i] = tmp[i];return res;}std::vector<T> invs(n + 1);invs[0] = T(0);invs[1] = T(1);auto mod = T::mod();for (int i = 2; i <= n; i++) invs[i] = -invs[mod % i] * (mod / i);res[0] = f[0].second.pow(k);T coef = f[0].second.inv();for (int i = 1; i < n; i++) {for (int j = 1; j < d; j++) {if (i - f[j].first < 0) break;res[i] += f[j].second * res[i - f[j].first] * (T(k) * f[j].first - (i - f[j].first));}res[i] *= invs[i] * coef;}return res;}FPS taylor_shift(T c) const {FPS f(*this);const int n = f.size();std::vector<T> fac(n), finv(n);fac[0] = 1;for (int i = 1; i < n; i++) {fac[i] = fac[i - 1] * i;f[i] *= fac[i];}finv[n - 1] = fac[n - 1].inv();for (int i = n - 1; i > 0; i--) finv[i - 1] = finv[i] * i;std::reverse(f.begin(), f.end());FPS g(n);g[0] = T(1);for (int i = 1; i < n; i++) g[i] = g[i - 1] * c * finv[i] * fac[i - 1];f = (f * g).pre(n);std::reverse(f.begin(), f.end());for (int i = 0; i < n; i++) f[i] *= finv[i];return f;}};using namespace std;typedef long long ll;#define all(x) begin(x), end(x)constexpr int INF = (1 << 30) - 1;constexpr long long IINF = (1LL << 60) - 1;constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};template <class T> istream& operator>>(istream& is, vector<T>& v) {for (auto& x : v) is >> x;return is;}template <class T> ostream& operator<<(ostream& os, const vector<T>& v) {auto sep = "";for (const auto& x : v) os << exchange(sep, " ") << x;return os;}template <class T, class U = T> bool chmin(T& x, U&& y) { return y < x and (x = forward<U>(y), true); }template <class T, class U = T> bool chmax(T& x, U&& y) { return x < y and (x = forward<U>(y), true); }template <class T> void mkuni(vector<T>& v) {sort(begin(v), end(v));v.erase(unique(begin(v), end(v)), end(v));}template <class T> int lwb(const vector<T>& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); }using mint = atcoder::modint998244353;using FPS = FormalPowerSeries<mint>;int main() {ios::sync_with_stdio(false);cin.tie(nullptr);int N;cin >> N;vector<int> A(N);for (int& x : A) cin >> x;int k = 1;while (k < N) k <<= 1;vector<FPS> prod(k << 1, {1});for (int i = 0; i < N; i++) prod[k + i] = {-A[i], 1};for (int i = k - 1; i > 0; i--) prod[i] = prod[i << 1] * prod[i << 1 | 1];vector<FPS> f(k << 1);f[0] = {1};for (int i = 1; i < k + N; i++) {f[i] = f[i >> 1];if (~i & 1) f[i] *= prod[i | 1];f[i] %= prod[i];}mint ans = 1;for (int i = 0; i < N; i++) ans *= f[k + i][0];cout << ans.val() << '\n';return 0;}