import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(int M_) { import std.conv : to; alias M = M_; int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { if (a < 0) return (this = inv()^^(-a)); ModInt t2 = this, te = ModInt(1); for (long e = a; e > 0; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op: "-")() const { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; enum LIM = 2 * 10^^5 + 10; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM]; fac = new Mint[LIM]; invFac = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)]; } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } long brute(int N, int A, int B) { long ans; auto perm = iota(N).array; do { int[] simulate(int a) { auto ps = perm.dup; for (; ; ) { foreach (i; 0 .. N) if (ps[i] >= a) { foreach_reverse (j; 0 .. N) if (ps[j] < a) { if (i < j) { swap(ps[i], ps[j]); goto found; } else { goto done; } } } found: } done: return ps; } const ps = simulate(A); const qs = simulate(B); foreach (i; 0 .. N) { if (ps[i] == qs[i]) { ++ans; } } } while (perm.nextPermutation); return ans; } Mint slow(int N, int A, int B) { if (A > B) { swap(A, B); } /* fixed finally: 0...0 (1or2...1or2) (0or1...0or1) 2...2 */ Mint ans0; ans0 += Mint(A)^^2; ans0 += Mint(B - A)^^2; ans0 += Mint(N - B)^^2; ans0 *= fac[N - 1]; debug { writeln(" ans0 = ", ans0); } /* moved ........ 2 ... 0 ........ x0,x1,x2 y0,y1,y2 x1 + x2 = y0 x2 = y0 + y1 ==> (x0, x1, x2, y0, y1, y2) = (c - t, 0, t, t, 0, d - t) */ Mint ans1; foreach (c; 0 .. A) foreach (d; 0 .. N - B) { Mint tmp = 1; tmp *= binom(c + d, c); tmp *= binom(N - (c + d + 2), A - (c + 1)) * binom((N - (c + d + 2)) - (A - (c + 1)), (N - B) - (d + 1)); tmp *= fac[A]; tmp *= fac[B - A]; tmp *= fac[N - B]; ans1 += tmp; } debug { writeln(" ans1 = ", ans1); } return ans0 + 2 * ans1; } Mint solve(int N, int A, int B) { if (A > B) { swap(A, B); } Mint ans0; ans0 += Mint(A)^^2; ans0 += Mint(B - A)^^2; ans0 += Mint(N - B)^^2; ans0 *= fac[N - 1]; debug { writeln(" ans0 = ", ans0); } /* \sum_{c+d=s} 1 / (c! (A - 1 - c)! d! ((N - B) - 1 - d!) = binom(A + (N - B) - 2, s) / ((A - 1)! ((N - B) - 1)!) */ /* Mint ans1; foreach (s; 0 .. (A + (N - B) - 2) + 1) { Mint tmp = 1; tmp *= fac[s]; tmp *= fac[N - 2 - s]; tmp *= invFac[B - A]; tmp *= binom(A + (N - B) - 2, s) * invFac[A - 1] * invFac[(N - B) - 1]; ans1 += tmp; } ans1 *= fac[A]; ans1 *= fac[B - A]; ans1 *= fac[N - B]; */ /* s! (N - 2 - s)! (A + (N - B) - 2)! A! (B - A)! (N - B)! \sum_s ------------------------------------------------------------ (B - A)! s! (A + (N - B) - 2 - s)! (A - 1)! ((N - B) - 1)! (N - 2 - s)! = A (N - B) (A + (N - B) - 2)! \sum_s ------------------------ (A + (N - B) - 2 - s)! = A (N - B) (A + (N - B) - 2)! (B - A)! \sum_s binom(N - 2 - s, B - A) = A (N - B) (A + (N - B) - 2)! (B - A)! \sum_{B-A<=i<=N-2} binom(i, B - A) = A (N - B) (A + (N - B) - 2)! (B - A)! binom(N - 1, B - A + 1) A (N - B) (A + (N - B) - 2)! (B - A)! (N - 1)! = ------------------------------------------------ (B - A + 1)! (N - 2 - (B - A))! */ Mint ans1 = 1; ans1 *= A; ans1 *= (N - B); ans1 *= fac[N - 1]; ans1 *= inv[B - A + 1]; debug { writeln(" ans1 = ", ans1); } return ans0 + 2 * ans1; } void main() { prepare; try { for (; ; ) { const N = readInt(); int A = readInt(); int B = readInt(); const ans = solve(N, A, B); writeln(ans); debug { const slw = slow(N, A, B); writeln("slw = ", slw); assert(ans.x == slw.x); if (N <= 10) { const brt = brute(N, A, B); writeln("brt = ", brt); assert(slw.x == brt); } } } } catch (EOFException e) { } }