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(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = cast(uint)(x_ % M); } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; enum LIM_INV = 5010; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM_INV]; fac = new Mint[LIM_INV]; invFac = new Mint[LIM_INV]; inv[1] = 1; foreach (i; 2 .. LIM_INV) { inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]); } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM_INV) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (n < 0) { if (k >= 0) { return (-1)^^(k & 1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (-1)^^((n - k) & 1) * binom(-k - 1, n - k); } else { return Mint(0); } } else { if (0 <= k && k <= n) { assert(n < LIM_INV); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } } void main() { prepare; auto S2 = new Mint[][](LIM_INV, LIM_INV); foreach (n; 0 .. LIM_INV) { S2[n][0] = 0; S2[n][n] = 1; foreach (k; 1 .. n) { S2[n][k] = S2[n - 1][k - 1] + k * S2[n - 1][k]; } } debug { foreach (n; 0 .. 4 + 1) { auto freq = new int[1 << n]; foreach (p; 0 .. 1 << (1 << n)) if (popcnt(p) <= 4) { int[] xs; foreach (x; 0 .. 1 << n) if (p >> x & 1) { xs ~= x; } const xsLen = cast(int)(xs.length); auto xsOr = new int[1 << xsLen]; foreach (i; 0 .. xsLen) foreach (q; 0 .. 1 << i) { xsOr[q | 1 << i] = xsOr[q] | xs[i]; } xsOr.sort; bool ok = true; foreach (q; 1 .. 1 << xsLen) { ok = ok && (xsOr[q - 1] != xsOr[q]); } if (ok) { ++freq[xs.length]; if (n == 3) { writeln(" ", xs); } } } writeln(n, ": ", freq); } } try { for (; ; ) { const N = readInt; Mint ans; foreach (m; 0 .. N + 1) { Mint sum; const two = Mint(2)^^m; Mint pw = 1; foreach_reverse (l; m .. N + 1) { Mint num = 1; num *= S2[l][m]; num *= binom(N, l); num *= pw; pw *= (two - m); sum += num; } debug { if (N <= 10) { writeln(N, " ", m, ": ", sum); } } ans += sum; } writeln(ans); } } catch (EOFException e) { } }