結果
問題 | No.1195 数え上げを愛したい(文字列編) |
ユーザー | 👑 potato167 |
提出日時 | 2022-05-10 21:19:00 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 546 ms / 3,000 ms |
コード長 | 34,300 bytes |
コンパイル時間 | 3,408 ms |
コンパイル使用メモリ | 244,896 KB |
実行使用メモリ | 21,168 KB |
最終ジャッジ日時 | 2024-07-18 04:07:42 |
合計ジャッジ時間 | 12,060 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 535 ms
18,596 KB |
testcase_01 | AC | 536 ms
19,368 KB |
testcase_02 | AC | 546 ms
21,168 KB |
testcase_03 | AC | 69 ms
8,748 KB |
testcase_04 | AC | 67 ms
9,480 KB |
testcase_05 | AC | 72 ms
16,340 KB |
testcase_06 | AC | 2 ms
6,944 KB |
testcase_07 | AC | 2 ms
6,940 KB |
testcase_08 | AC | 87 ms
6,944 KB |
testcase_09 | AC | 528 ms
19,240 KB |
testcase_10 | AC | 288 ms
11,864 KB |
testcase_11 | AC | 462 ms
19,540 KB |
testcase_12 | AC | 436 ms
17,296 KB |
testcase_13 | AC | 367 ms
15,076 KB |
testcase_14 | AC | 240 ms
11,552 KB |
testcase_15 | AC | 272 ms
12,824 KB |
testcase_16 | AC | 239 ms
10,900 KB |
testcase_17 | AC | 91 ms
6,944 KB |
testcase_18 | AC | 443 ms
17,384 KB |
testcase_19 | AC | 438 ms
17,188 KB |
testcase_20 | AC | 382 ms
14,352 KB |
testcase_21 | AC | 483 ms
17,400 KB |
testcase_22 | AC | 350 ms
13,480 KB |
testcase_23 | AC | 2 ms
6,940 KB |
testcase_24 | AC | 2 ms
6,940 KB |
testcase_25 | AC | 2 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") #define _GLIBCXX_DEBUG using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; ll ILL=2167167167167167167; const int INF=2100000000; const ll mod=998244353; #define rep(i,a) for (ll i=0;i<a;i++) #define all(p) p.begin(),p.end() template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>; template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;} template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());} template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template<class T> void vec_out(vector<T> &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";} namespace 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` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal namespace internal { // @param m `1 <= m` // @return x mod m constexpr 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 Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned 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 + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned 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/g 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}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b 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; // |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| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (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); } // namespace internal namespace internal { #ifndef _MSC_VER template <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; #else template <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; #endif template <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 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 internal template <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()); } static_modint(bool 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()); } dynamic_modint(bool 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 internal { template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly(std::vector<mint>& a) { static constexpr int g = internal::primitive_root<mint::mod()>; int n = int(a.size()); int h = internal::ceil_pow2(n); static bool first = true; static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i] if (first) { first = false; mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1 int cnt2 = bsf(mint::mod() - 1); mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv(); for (int i = cnt2; i >= 2; i--) { // e^(2^i) == 1 es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; for (int i = 0; i <= cnt2 - 2; i++) { sum_e[i] = es[i] * now; now *= ies[i]; } } for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint now = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p] * now; a[i + offset] = l + r; a[i + offset + p] = l - r; } now *= sum_e[bsf(~(unsigned int)(s))]; } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly_inv(std::vector<mint>& a) { static constexpr int g = internal::primitive_root<mint::mod()>; int n = int(a.size()); int h = internal::ceil_pow2(n); static bool first = true; static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i] if (first) { first = false; mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1 int cnt2 = bsf(mint::mod() - 1); mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv(); for (int i = cnt2; i >= 2; i--) { // e^(2^i) == 1 es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; for (int i = 0; i <= cnt2 - 2; i++) { sum_ie[i] = ies[i] * now; now *= es[i]; } } for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint inow = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 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()) * inow.val(); } inow *= sum_ie[bsf(~(unsigned int)(s))]; } } } } // namespace internal template <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) { if (n < m) { std::swap(n, m); std::swap(a, b); } std::vector<mint> ans(n + m - 1); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; } } return ans; } 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; } 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; // 2^24 static constexpr unsigned long long MOD2 = 167772161; // 2^25 static constexpr unsigned long long MOD3 = 469762049; // 2^26 static 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 = 4 long 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 atcoder using namespace atcoder; void vec_out(std::vector<long long> &p){ cout<<p.size()<<"\n"; for(int i=0;i<(int)(p.size());i++) cout<<p[i]<<" "; cout<<"\n"; } //参考 https://nyaannyaan.github.io/library/fps/formal-power-series.hpp.html namespace po167{ long long rev(long long a,long long MOD){ long long D=1,C=MOD-2; while(C){ if(C&1) D=(D*a)%MOD; C>>=1; a=(a*a)%MOD; } return D; } template <unsigned int mod = 998244353> std::vector<long long> add_Polynomial(std::vector<long long> &p,std::vector<long long> &q){ std::vector<long long> r(std::max(p.size(),q.size())); for(int i=0;i<(int)r.size();i++){ if((int)p.size()>i) r[i]=p[i]; if((int)q.size()>i) r[i]=(r[i]+q[i])%mod; } return r; } template <unsigned int mod = 998244353> std::vector<long long> sub_Polynomial(std::vector<long long> &p,std::vector<long long> &q){ std::vector<long long> r(std::max(p.size(),q.size())); for(int i=0;i<(int)r.size();i++){ if((int)p.size()>i) r[i]=p[i]; if((int)q.size()>i) r[i]=(r[i]-q[i]); if(r[i]<0) r[i]=(r[i]%mod+mod)%mod; } return r; } template <unsigned int mod = 998244353> long long substitution_Polynomial(std::vector<long long> &p,long long x){ long long ans=0; long long D=1; for(int i=0;i<p.size();i++){ ans=(ans+(D*p[i])%mod)%mod; D=(D*x)%mod; } return ans; } template <unsigned int mod = 998244353> std::vector<long long> differential_Polynomial(std::vector<long long> &p){ int N=p.size(); std::vector<long long> r(N); for(int i=1;i<N;i++){ r[i-1]=((long long)(i)*p[i])%mod; } return r; } template <unsigned int mod = 998244353> std::vector<long long> Integral_Polynomial(std::vector<long long> &p){ int N=p.size(); std::vector<long long> r(1+N); std::vector<long long> rev(N+1,1); for(int i=0;i<N;i++){ if(i+1>1){ rev[i+1]=(mod-((mod/(i+1))*rev[mod%(i+1)])%mod)%mod; } r[i+1]=(rev[i+1]*p[i])%mod; } return r; } template <class T> std::vector<T> slice_vec(std::vector<T> &p,int S){ if(S>=(int)(p.size())) return p; std::vector<T> r(S); for(int i=0;i<S;i++) r[i]=p[i]; return r; } // return f^{-1} mod x^{L} // https://judge.yosupo.jp/submission/79004 template <unsigned int mod = 998244353> std::vector<long long> inv_FPS(int N,int L,std::vector<long long> &p){ assert((int)p.size()==N); assert(0<N); assert(p[0]%mod!=0); std::vector<long long> q={1},tmp,tmp2; long long D=p[0]; long long C=mod-2; while(C){ if(C&1){ q[0]=(q[0]*D)%mod; } C>>=1; D=(D*D)%mod; } int S=1; while(S<L){ S*=2; tmp.assign(S,0); for(int i=0;i<std::min((int)(p.size()),S);i++) tmp[i]=p[i]; tmp2=convolution<mod>(tmp,convolution<mod>(q,q)); for(int i=0;i<S;i++){ if(i*2<S) tmp[i]=(2ll*q[i]-tmp2[i]+mod)%mod; else tmp[i]=(-tmp2[i]+mod)%mod; } swap(tmp,q); } std::vector<long long> ans(S); for(int i=0;i<S;i++) ans[i]=q[i]; return ans; } // return log f(x) // https://judge.yosupo.jp/submission/79008 template <unsigned int mod = 998244353> std::vector<long long> log_FPS(int N,int L,std::vector<long long> &p){ assert(p[0]==1); auto tmp=convolution<mod>(differential_Polynomial<mod>(p),inv_FPS<mod>(N,L,p)); auto tmp3=Integral_Polynomial<mod>(tmp); return slice_vec(tmp3,L); } // return e^{f(x)} template <unsigned int mod = 998244353> std::vector<long long> exp_FPS(int N,int L,std::vector<long long> &p){ assert((int)p.size()==N); assert(0<N); assert(p[0]%mod==0); std::vector<long long> q={1},tmp,tmp2,tmp3; int S=1; while(S<L){ S*=2; tmp=slice_vec(p,S); tmp2=log_FPS<mod>(S/2,S,q); tmp3=sub_Polynomial<mod>(tmp,tmp2); tmp3[0]++; tmp=convolution<mod>(q,tmp3); for(int i=0;i<S;i++){ if(i==(int)(q.size())) q.push_back(tmp[i]); else q[i]=tmp[i]; } } std::vector<long long> ans(S); for(int i=0;i<S;i++) ans[i]=q[i]; return ans; } //if all zero: // return {0} std::vector<long long> zero_cut(std::vector<long long> &p){ int ind=0; for(int i=0;i<(int)(p.size());i++){ if(p[i]!=0) ind=i; } return slice_vec(p,ind+1); } //return {a,b} (p=aq+b) //https://judge.yosupo.jp/submission/79020 template <unsigned int mod = 998244353> std::pair<std::vector<long long>,std::vector<long long>> div_FPS(std::vector<long long> &p,std::vector<long long> &q){ int N=p.size(),M=q.size(); if(N<M){ return {{0},p}; } auto f=p,g=q; std::reverse(f.begin(),f.end()); std::reverse(g.begin(),g.end()); auto tmp=convolution<mod>(f,inv_FPS(M,N-M+1,g)); auto ans1=slice_vec(tmp,N-M+1); std::reverse(ans1.begin(),ans1.end()); tmp=convolution(ans1,q); std::vector<long long> ans2(M-1); for(int i=0;i<M-1;i++) ans2[i]=(p[i]-tmp[i]+mod)%mod; return std::make_pair(zero_cut(ans1),zero_cut(ans2)); } //return [f(p[0]),f(p[1])...f(p[M-1])] //https://judge.yosupo.jp/submission/79035 template <unsigned int mod = 998244353> std::vector<long long> Multipoint_Evaluation(std::vector<long long> f,std::vector<long long>p){ int M=p.size(); if(M==0){ return {}; } std::vector<int> size={M}; int ind=0; while(size[ind]!=1){ size.push_back((size[ind]+1)/2); ind++; } ind++; std::vector<std::vector<std::vector<long long>>> divisor(ind),remain(ind); for(int i=0;i<ind;i++){ divisor[i].resize(size[i]); if(i==0){ for(int j=0;j<M;j++){ divisor[i][j]={mod-p[j],1}; } }else{ for(int j=0;j<size[i];j++){ if(j!=size[i]-1||size[i-1]%2==0){ divisor[i][j]=convolution<mod>(divisor[i-1][j*2],divisor[i-1][j*2+1]); }else{ divisor[i][j]=divisor[i-1][size[i-1]-1]; } } } } for(int i=ind-1;i>=0;i--){ remain[i].resize(size[i]); if(i==ind-1){ remain[i][0]=div_FPS<mod>(f,divisor[ind-1][0]).second; }else{ for(int j=0;j<size[i];j++){ if(j!=size[i]-1||size[i]%2==0){ remain[i][j]=div_FPS(remain[i+1][j/2],divisor[i][j]).second; }else{ remain[i][j]=remain[i+1][j/2]; } } } } std::vector<long long> ans(M); for(int i=0;i<M;i++) ans[i]=remain[0][i][0]; return ans; } template <unsigned int mod = 998244353> std::vector<long long> multiplication_FPS(std::vector<std::vector<long long>> &p){ std::queue<std::vector<long long>> pq; int N=p.size(); for(int i=0;i<N;i++) pq.push(p[i]); for(int i=1;i<N;i++){ auto l=pq.front(); pq.pop(); auto r=pq.front(); pq.pop(); pq.push(convolution<mod>(l,r)); } return pq.front(); } struct frac_fps{ std::vector<long long> ch; std::vector<long long> mo; }; template <unsigned int mod = 998244353> frac_fps add_frac_fps(frac_fps &l,frac_fps &r){ auto tmp1=convolution<mod>(l.ch,r.mo); auto tmp2=convolution<mod>(l.mo,r.ch); return {add_Polynomial<mod>(tmp1,tmp2),convolution<mod>(l.mo,r.mo)}; } template <unsigned int mod = 998244353> std::vector<long long> Polynomial_Interpolation(std::vector<long long> &x,std::vector<long long> &y){ int N=x.size(); assert(x.size()==y.size()); std::vector<std::vector<long long>> p(N); for(int i=0;i<N;i++){ p[i]={(mod-x[i])%mod,1}; } auto tmp1=multiplication_FPS<mod>(p); auto div=differential_Polynomial<mod>(tmp1); auto val=Multipoint_Evaluation<mod>(div,x); std::queue<frac_fps> q; for(int i=0;i<N;i++) q.push({{y[i]},{(mod-(val[i]*x[i])%mod)%mod,val[i]}}); for(int i=1;i<N;i++){ frac_fps l=q.front(); q.pop(); frac_fps r=q.front(); q.pop(); q.push(add_frac_fps<mod>(l,r)); } long long D=1; auto ans=q.front().ch; for(int i=0;i<N;i++){ D=(D*val[i])%mod; } D=rev(D,mod); for(int i=0;i<N;i++) ans[i]=(ans[i]*D)%mod; return ans; } } namespace po167{ template <class T> struct seg_sum{ int n; int seg_size; std::vector<T> seg; T e; //要素数、単位元 typeは+演算が定義されているもの seg_sum(int k,T e_in){ e=e_in; n=k; seg_size=1; while(seg_size<n) seg_size*=2; seg.resize(seg_size*2-1); for(int i=0;i<seg_size*2-1;i++) seg[i]=e; } T sum_sub(int a,int b,int l,int r,int k){ if(r<=a||b<=l) return e; if(a<=l&&r<=b) return seg[k]; T X=sum_sub(a,b,l,(l+r)/2,k*2+1); T Y=sum_sub(a,b,(l+r)/2,r,k*2+2); return X+Y; } T sum(int a,int b){ //assert(0<=a&&b<n); return sum_sub(a,b,0,seg_size,0); } T get(int index){ assert(0<=index&&index<n); return seg[seg_size-1+index]; } void insert(int index,T a){ assert(0<=index&&index<n); int now_index=index+seg_size-1; seg[now_index]=a; while(now_index!=0){ now_index-=1; now_index/=2; seg[now_index]=seg[now_index*2+1]+seg[now_index*2+2]; } } }; template <class T> //p,qのなかみは、重複ありで内容が同じならおけ long long inversion(std::vector<T> &p,std::vector<T> &q){ int n=p.size(); assert(p.size()==q.size()); po167::seg_sum<int> S(n,0); std::vector<int> p_index(n,-1); std::map<T,std::queue<int>> m; for(int i=0;i<n;i++) m[p[i]].push(i); for(int i=0;i<n;i++){ if(m[q[i]].empty()) return -1; int a=m[q[i]].front(); m[q[i]].pop(); p_index[i]=a; } long long ans=0; for(int i=0;i<n;i++){ ans+=S.sum(p_index[i],n); S.insert(p_index[i],1); } return ans; } template <class T> //qのなかみは、0~nの順列の並び替えである必要がある long long inversion(std::vector<T> &q){ int n=q.size(); po167::seg_sum<int> S(n,0); std::vector<int> p_index(n); for(int i=0;i<n;i++){ p_index[i]=i; } long long ans=0; for(int i=0;i<n;i++){ assert(0<=q[i]&&q[i]<n); assert(S.get(q[i])==0); ans+=S.sum(q[i],n); S.insert(q[i],1); } return ans; } } using po167::inversion; using po167::seg_sum; namespace po167{ struct combination{ int upper; long long MOD; std::vector<long long> fact; std::vector<long long> rev; std::vector<long long> fact_rev; combination(int max,long long mod):upper(max),MOD(mod),fact(max+1),rev(max+1),fact_rev(max+1){ for(long long i=0;i<=max;i++){ if(i<2){ fact[i]=1; fact_rev[i]=1; rev[i]=1; continue; } fact[i]=(fact[i-1]*i)%mod; rev[i]=mod-((mod/i)*rev[mod%i])%mod; fact_rev[i]=(fact_rev[i-1]*rev[i])%mod; } } long long Comb(int x,int y){ assert(upper>=x); if (x<y||y<0||x<0) return 0; return (((fact_rev[y]*fact_rev[x-y])%MOD)*fact[x])%MOD; } }; } using po167::combination; void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,t) solve(); } void solve(){ string S; cin>>S; int N=S.size(),M=26; vector<int> p(M); rep(i,N) p[S[i]-'a']++; combination table(N,mod); vector<ll> dp={1}; rep(i,M){ vector<ll> tmp(p[i]+1); rep(j,p[i]+1) tmp[j]=table.fact_rev[j]; dp=convolution<mod>(dp,tmp); } ll ans=0; rep(i,N+1){ if(i==0) continue; ans=(ans+(table.fact[i]*dp[i]))%mod; } cout<<ans<<"\n"; }