#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } MDCONST ModInt() : val_(0) {} MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } MDCONST explicit operator bool() const { return val_ != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val_); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val_ + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val_ % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv().val() % md); } MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; } MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; } MDCONST bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } MDCONST ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST ModInt inv() const { if (this->val_ < std::min(md >> 1, 1 << 21)) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } MDCONST ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } MDCONST ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } MDCONST ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template std::vector> ModInt::facs = {1}; template std::vector> ModInt::facinvs = {1}; template std::vector> ModInt::invs = {0}; using mint = ModInt<998244353>; int experiment1(int a, int b) { vector v(a); v.resize(a + b, 1); int ret = 0; do { int n0 = 0; for (auto x : v) { if (x) { if (n0) --n0, ++ret; } else { ++n0; } } } while (next_permutation(ALL(v))); return ret; } // Count difference mint solve(int N, int A1, int A2) { // no swap -> no swap const int n2 = N - A1, n1 = A1 - A2, n0 = A2; mint n00 = mint(n2).fac() * mint(n1).fac() * mint(n0).fac(); // no swap -> swap (2) mint n02 = mint(n0 + n1).fac() * mint(n2).fac() - n00; // swap -> no swap (2) mint n20 = mint(n0).fac() * mint(n1 + n2).fac() - n00; // swap -> swap same pair (0) mint n_swpfix = 0; if (n0 and n2) { REP(i0in, n0) { n_swpfix += mint(n2).fac() * mint(n1).fac() * mint(n0).fac() * mint(n1 + i0in).nCr(n1) * mint(n1 + i0in + 1 + n2 - 1).nCr(n2 - 1); } } // swap -> swap completely different pair (4) mint n4 = 0; if (n1 > 1) { REP(i0in, n0 + 1) { mint c = 0; if (!i0in) c = 1; else if (n1 >= 1) c = mint(n1 - 2 + i0in).nCr(i0in); n4 += mint(n2).fac() * mint(n1).fac() * mint(n0).fac() * c * (mint(n2 + i0in + n1 - 1).nCr(n2) - 1); } // dbg(n4); // n4 -= mint(n2).fac() * mint(n1).fac() * mint(n0).fac() * (mint(n2 + n1).nCr(n2) - mint(n2 - 1 + n1).nCr(n1)); // dbg(n4); } mint n3 = mint(N).fac() - n00 - n02 - n20 - n_swpfix - n4; dbg(make_tuple(N, A1, A2, n0, n1, n2, n00, n02, n20, n_swpfix, n4, n3)); return n02 * 2 + n20 * 2 + n4 * 4 + n3 * 3; } int main() { // constexpr int D = 12; // REP(i, D) { // REP(j, D) cout << experiment1(i, j) << ' '; // cout << endl; // } // REP(i, D) { // REP(j, D) cout << (mint(i + j + 1).fac() / mint(i).fac() / mint(j).fac() - mint(2).pow(min(i, j) * 2)) / 2 << ' '; // cout << endl; // } int N, A1, A2; cin >> N >> A1 >> A2; if (A1 > A2) swap(A1, A2); auto calc = [&](int n, int w) -> mint { return mint(w) * w * mint(n - 1).fac(); }; // mint ret = solve(N, A1, A2); // mint ret = calc(N, A2 - A1); mint ret = calc(N, A1) + calc(N, A2 - A1) + calc(N, N - A2); const int a = A1, b = N - A2, c = A2 - A1; ret += 2 * mint(a).fac() * mint(b).fac() * mint(c).fac() * mint(a - 1 + b - 1 + c + 1).fac() * mint(a - 1).facinv() * mint(b - 1).facinv() * mint(c + 1).facinv(); // REP(i, A1) REP(j, N - A2) { // int y = i + j; // int ain = A1 - (i + 1); // int bin = N - A2 - (j + 1); // int c = A2 - A1; // mint tmp = mint(i + j).nCr(i) * mint(ain + bin + c).nCr(ain) * mint(bin + c).nCr(c) * mint(A1).fac() * mint(N - A2).fac() * mint(c).fac(); // ret += tmp * 2; // } dbg(make_tuple(N, A1, A2, ret)); // REP(i, min(A1, N - A2)) { ret += mint(2).pow(i) * mint(A1).nPr(i + 1) * mint(N - A2).nPr(i + 1) * mint(N - (i + 1) * 2).fac() * 2; } cout << ret << endl; // cout << mint(N).fac() * N - ret << '\n'; }