#line 1 "/home/nok0/documents/programming/library/atcoder/dsu.hpp" #include #include #include namespace atcoder { // Implement (union by size) + (path compression) // Reference: // Zvi Galil and Giuseppe F. Italiano, // Data structures and algorithms for disjoint set union problems struct dsu { public: dsu() : _n(0) {} explicit dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } private: int _n; // root node: -1 * component size // otherwise: parent std::vector parent_or_size; }; } // namespace atcoder #line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp" #line 5 "/home/nok0/documents/programming/library/atcoder/modint.hpp" #include #include #ifdef _MSC_VER #include #endif #line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp" #include #ifdef _MSC_VER #include #endif namespace atcoder { 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` explicit 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 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 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 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) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #line 1 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp" #line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp" namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder #line 14 "/home/nok0/documents/programming/library/atcoder/modint.hpp" namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = 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 * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = 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; }; template 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 * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = 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 internal::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder #line 4 "/home/nok0/documents/programming/library/math/factorial.hpp" #line 6 "/home/nok0/documents/programming/library/math/factorial.hpp" template struct factorial { public: static int MAX; static std::vector fac, finv, inv; factorial() {} T binom(int n, int r) { if (n < r or n < 0 or r < 0) return T(0); assert(n < MAX); return fac[n] * finv[r] * finv[n - r]; } T large_binom(int n, int r) { if (n < r or n < 0 or r < 0) return T(0); assert(r < MAX); T ret = finv[r]; for (int i = 1; i <= r; ++i) ret *= (n + 1 - i); return ret; } static void set_size(int n = 3000000) { MAX = (n > 1 ? n : 1) + 1; if ((int)fac.size() >= MAX) return; fac.resize(MAX); finv.resize(MAX); inv.resize(MAX); const int MOD = T::mod(); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * i; inv[i] = (T)MOD - inv[MOD % i] * (MOD / i); finv[i] = finv[i - 1] * inv[i]; } } }; template int factorial::MAX = 0; template std::vector factorial::fac; template std::vector factorial::finv; template std::vector factorial::inv; #line 2 "/home/nok0/documents/programming/library/math/modint_iostream.hpp" #include #line 5 "/home/nok0/documents/programming/library/math/modint_iostream.hpp" template std::istream &std::operator>>(std::istream &is, atcoder::static_modint &a) { long long v; is >> v; a = v; return is; } template std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint &a) { long long v; is >> v; a = v; return is; } template std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint &a) { return os << a.val(); } template std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint &a) { return os << a.val(); } #line 3 "/home/nok0/documents/programming/library/math/osa_k.hpp" struct osa_k { private: std::vector spf, pr; public: osa_k() = default; osa_k(int MAX) : spf(MAX + 1) { for(int i = 2; i <= MAX; i++) { if(spf[i] == 0) { spf[i] = i; pr.push_back(i); } for(int j = 0; j < pr.size() and pr[j] <= spf[i] and i * pr[j] <= MAX; j++) spf[i * pr[j]] = pr[j]; } } std::vector> pair_factorize(int n) { std::vector> divisor; if(n == 1) return divisor; int before = spf[n], cnt = 0; while(n > 1) { if(spf[n] == before) { cnt++; n /= spf[n]; } else { divisor.emplace_back(before, cnt); before = spf[n]; cnt = 1; n /= spf[n]; } } divisor.emplace_back(before, cnt); return divisor; } int smallest_prime_factor(const int n) const { return spf[n]; } bool is_prime(const int n) const { return n == spf[n]; } }; #line 2 "/home/nok0/documents/programming/library/template/header.hpp" #include #line 3 "/home/nok0/documents/programming/library/template/def_const.hpp" const int inf = 1000000000; const long long INF = 1000000000000000000ll; #line 4 "/home/nok0/documents/programming/library/template/debug.hpp" namespace viewer { void view(const long long &e) { if(e == INF) std::cerr << "INF"; else if(e == -INF) std::cerr << "-INF"; else std::cerr << e; } void view(const int &e) { if(e == inf) std::cerr << "inf"; else if(e == -inf) std::cerr << "-inf"; else std::cerr << e; } template void view(const T &e) { std::cerr << e; } template void view(const std::pair &p) { std::cerr << "("; view(p.first); std::cerr << ", "; view(p.second); std::cerr << ")"; } template void view(const std::tuple &p) { std::cerr << "("; view(std::get<0>(p)); std::cerr << ", "; view(std::get<1>(p)); std::cerr << ", "; view(std::get<2>(p)); std::cerr << ")"; } template void view(const std::tuple &p) { std::cerr << "("; view(std::get<0>(p)); std::cerr << ", "; view(std::get<1>(p)); std::cerr << ", "; view(std::get<2>(p)); std::cerr << ", "; view(std::get<3>(p)); std::cerr << ")"; } template void view(const std::set &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::unordered_set &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::multiset &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::unordered_multiset &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::array &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector> &vv) { std::cerr << "{\n"; for(const auto &v : vv) { std::cerr << "\t"; view(v); std::cerr << '\n'; } std::cerr << "}"; } template void view(const std::vector> &v) { std::cerr << "{\n"; for(const auto &c : v) { std::cerr << "\t("; view(c.first); std::cerr << ", "; view(c.second); std::cerr << ")\n"; } std::cerr << "}"; } template void view(const std::vector> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << '{'; for(const auto &t : v) { std::cerr << "\n\t"; view(t); std::cerr << ","; } std::cerr << "\n}"; } template void view(const std::vector> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << '{'; for(const auto &t : v) { std::cerr << "\n\t"; view(t); std::cerr << ","; } std::cerr << "\n}"; } template void view(const std::map &m) { std::cerr << "{\n"; for(const auto &t : m) { std::cerr << "\t["; view(t.first); std::cerr << "] : "; view(t.second); std::cerr << '\n'; } std::cerr << "}"; } template void view(const std::unordered_map &m) { std::cerr << "{\n"; for(const auto &t : m) { std::cerr << "\t["; view(t.first); std::cerr << "] : "; view(t.second); std::cerr << '\n'; } std::cerr << "}"; } } // namespace viewer // when compiling : g++ foo.cpp -DLOCAL #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { viewer::view(H); std::cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ std::cerr << "\b\b]\n"; \ } while(0) #define dump(x) \ do { \ std::cerr << __LINE__ << " " << #x << " : "; \ viewer::view(x); \ std::cerr << '\n'; \ } while(0) #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #line 3 "/home/nok0/documents/programming/library/template/def_name.hpp" #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define popcnt(x) __builtin_popcountll(x) template using V = std::vector; template using VV = std::vector>; template using pqup = std::priority_queue, std::greater>; using ll = long long; using ld = long double; using int128 = __int128_t; using pii = std::pair; using pll = std::pair; #line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp" struct fast_io { fast_io() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(15); } } fast_io_; #line 3 "/home/nok0/documents/programming/library/template/input.hpp" template std::istream &operator>>(std::istream &is, std::pair &p) { is >> p.first >> p.second; return is; } template std::istream &operator>>(std::istream &is, std::vector &v) { for (T &i : v) is >> i; return is; } std::istream &operator>>(std::istream &is, __int128_t &a) { std::string s; is >> s; __int128_t ret = 0; for (int i = 0; i < (int)s.length(); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; a = ret * (s[0] == '-' ? -1 : 1); return is; } namespace scanner { void scan(int &a) { std::cin >> a; } void scan(long long &a) { std::cin >> a; } void scan(std::string &a) { std::cin >> a; } void scan(char &a) { std::cin >> a; } void scan(char a[]) { std::scanf("%s", a); } void scan(double &a) { std::cin >> a; } void scan(long double &a) { std::cin >> a; } template void scan(std::pair &p) { std::cin >> p; } template void scan(std::vector &a) { std::cin >> a; } void INPUT() {} template void INPUT(Head &head, Tail &...tail) { scan(head); INPUT(tail...); } } // namespace scanner #define VEC(type, name, size) \ std::vector name(size); \ scanner::INPUT(name) #define VVEC(type, name, h, w) \ std::vector> name(h, std::vector(w)); \ scanner::INPUT(name) #define INT(...) \ int __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #line 3 "/home/nok0/documents/programming/library/template/math.hpp" template inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template T divup(T x, T y) { return (x + y - 1) / y; } template T POW(T a, long long n) { T ret = 1; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } long long POW(long long a, long long n, const int mod) { long long ret = 1; a = (a % mod + mod) % mod; while(n) { if(n & 1) (ret *= a) %= mod; (a *= a) %= mod; n >>= 1; } return ret; } template T bin_search(T ok, T ng, const F &f) { while(abs(ok - ng) > 1) { T mid = (ok + ng) >> 1; (f(mid) ? ok : ng) = mid; } return ok; } template T bin_search(T ok, T ng, const F &f, int loop) { for(int i = 0; i < loop; i++) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } #line 3 "/home/nok0/documents/programming/library/template/output.hpp" template std::ostream &operator<<(std::ostream &os, const std::pair &p) { os << p.first << " " << p.second; return os; } template std::ostream &operator<<(std::ostream &os, const std::vector &a) { for (int i = 0; i < int(a.size()); ++i) { if (i) os << " "; os << a[i]; } return os; } std::ostream &operator<<(std::ostream &dest, __int128_t &value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } template void print(const T a) { std::cout << a << '\n'; } template void print(Head H, Tail... T) { std::cout << H << ' '; print(T...); } template void printel(const T a) { std::cout << a << '\n'; } template void printel(const std::vector &a) { for (const auto &v : a) std::cout << v << '\n'; } template void printel(Head H, Tail... T) { std::cout << H << '\n'; printel(T...); } void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); } void No() { std::cout << "No\n"; } void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); } void NO() { std::cout << "NO\n"; } #line 2 "/home/nok0/documents/programming/library/template/rep.hpp" #define foa(v, a) for (auto &v : a) #define repname(a, b, c, d, e, ...) e #define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__) #define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter) #define rep1(i, x) for (int i = 0; i < (x); ++i) #define rep2(i, l, r) for (int i = (l); i < (r); ++i) #define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c)) #define repsname(a, b, c, ...) c #define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__) #define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter) #define reps1(i, x) for (int i = 1; i <= (x); ++i) #define rrepname(a, b, c, ...) c #define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__) #define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter) #define rrep1(i, x) for (int i = (x)-1; i >= 0; --i) #line 3 "/home/nok0/documents/programming/library/template/vector.hpp" template int lb(const std::vector &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); } template int ub(const std::vector &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); } template void UNIQUE(std::vector &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template std::vector press(std::vector &a) { auto res = a; UNIQUE(res); for(auto &v : a) v = lb(res, v); return res; } #define SORTname(a, b, c, ...) c #define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__) #define SORT0(a) std::sort((a).begin(), (a).end()) #define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; }) template void ADD(std::vector &a, const T x = 1) { for(auto &v : a) v += x; } template void SUB(std::vector &a, const T x = 1) { for(auto &v : a) v -= x; } template struct cum_vector { public: cum_vector() = default; template cum_vector(const std::vector &vec) : cum((int)vec.size() + 1) { for(int i = 0; i < (int)vec.size(); i++) cum[i + 1] = cum[i] + vec[i]; } T prod(int l, int r) { return cum[r] - cum[l]; } private: std::vector cum; }; std::vector> rle(const std::string &s) { const int n = s.size(); std::vector> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and s[l] == s[r]; r++) {} ret.emplace_back(s[l], r - l); l = r; } return ret; } template std::vector> rle(const std::vector &v) { int n = v.size(); std::vector> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and v[l] == v[r]; r++) {} ret.emplace_back(v[l], r - l); l = r; } return ret; } std::vector iota(int n) { std::vector p(n); std::iota(p.begin(), p.end(), 0); return p; } #line 11 "/home/nok0/documents/programming/library/template/all" using namespace std; #line 5 "e.cpp" using mint = atcoder::modint998244353; void main_(); int main() { int t = 1; while(t--) main_(); } ll test(int n, int p, int q) { set> st; auto vec = iota(n); queue> que; que.push(vec); st.insert(vec); while(SZ(que)) { auto v = que.front(); que.pop(); { auto c = v; reverse(c.begin(), c.begin() + p); if(!st.count(c)) { st.insert(c); que.push(c); } } { auto c = v; reverse(c.begin() + n - q, c.begin() + n); if(!st.count(c)) { st.insert(c); que.push(c); } } } ll res = 1; reps(i, n) res *= i; return SZ(st); } void main_() { osa_k pf(200000); INT(n, p, q); if(p == 1 and q == 1) { print(1); return; } atcoder::dsu uf(n); rep(i, p) { uf.merge(i, p - 1 - i); } rep(i, q) { uf.merge(n - 1 - i, n - 1 - (q - 1 - i)); } V<> cnt(200001); foa(g, uf.groups()) { auto pv = pf.pair_factorize(SZ(g)); for(auto [x, c] : pv) { chmax(cnt[x], c); } } mint res = 1; rep(i, 2, 200001) { res *= mint(i).pow(cnt[i]); } print(res * 2); }