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); } } /* [x^(N-2)] ((d/dx) x e^x)^N = [x^(N-2)] (e^x (1 + x))^N */ void main() { prepare; try { for (; ; ) { const N = readInt(); Mint ans; Mint nn = 1; foreach (i; 0 .. N - 2 + 1) { ans += invFac[i] * nn * binom(N, N - 2 - i); nn *= N; } ans *= fac[N - 2]; ans /= Mint(N)^^(N - 2); writeln(ans); } } catch (EOFException e) { } }