#nullable enable var n = int.Parse(Console.ReadLine()!); var mod = (int)FPSNTT.Mod; FPSNTT.MaxLength = n + 2; var f0 = new FPSNTT(); f0[0] = f0[1] = 1; var f = new FPSNTT(); f[1] = f[2] = 1; var fac = new long[n + 1]; fac[0] = 1; for (var i = 1; i <= n; i++) fac[i] = fac[i - 1] * i % mod; // { // var t = 1L; // for (var i = 1; i <= n; i++) // { // f[i] = t; // f.DivAt(i, fac[i]); // t = t * 2 % mod; // } // } var ans = 0L; var g = f0 * f0; for (var k = 1; k <= n; k++) { ans += g[n - k] * fac[n - k] % mod * fac[k] % mod; g *= f; } Console.WriteLine(ans); class FPSNTT { public static int MaxLength = -6; public const uint Mod = (1 << P) * K + 1; const int P = 23; const int K = 119; const int R = 3; uint[] _data = [0]; int _length = 1; public FPSNTT() { } public static FPSNTT From(ReadOnlySpan a) { var res = new FPSNTT(); for (var i = 0; i < a.Length; i++) res[i] = a[i]; return res; } public long this[int i] { get => i < _length ? _data[i] : 0; set { Resize(i); _data[i] = Rem(value); } } public long[] Slice(int start, int length) { var res = new long[length]; for (var i = 0; i < length; i++) res[i] = this[start + i]; return res; } public static FPSNTT operator *(FPSNTT f, long k) { k = Rem(k); var a = new uint[f._data.Length]; for (var i = 0; i < f._length; i++) a[i] = (uint)(f[i] * k % Mod); return new(a, f._length); } public static FPSNTT operator /(FPSNTT f, long k) => f * Pow(k, -1); public void DivAt(int i, long k) => this[i] *= Pow(k, -1); public static FPSNTT AdditiveIdentity => new([0]); public static FPSNTT operator +(FPSNTT l, FPSNTT r) { if (l._length < r._length) (l, r) = (r, l); var (llen, rlen) = (l._length, r._length); var a = new uint[l._data.Length]; for (var i = 0; i < rlen; i++) a[i] = (uint)(l[i] + r[i]) % Mod; for (var i = rlen; i < llen; i++) a[i] = (uint)l[i]; return new(a, llen); } public FPSNTT AdditiveInverse() => this * -1; public static FPSNTT operator -(FPSNTT l, FPSNTT r) => l + r * -1; public static FPSNTT MultiplicativeIdentity => new([1]); public static FPSNTT operator *(FPSNTT f, FPSNTT g) => new(Mul(f.ToSpan(), g.ToSpan()), f._length + g._length - 1); public FPSNTT MultiplicativeInverse() { if (_data[0] == 0) throw new Exception("the constant term must not be zero"); return new(Inv(ToSpan(), MaxLength)); } public static FPSNTT operator /(FPSNTT l, FPSNTT r) => l * r.MultiplicativeInverse(); ReadOnlySpan ToSpan() => _data.AsSpan()[.._length]; void Resize(int idx) { _length = Math.Max(_length, idx + 1); var len = _data.Length; if (idx < len) return; if (idx >= MaxLength) throw new IndexOutOfRangeException(); var len2 = len; while (idx >= len2) len2 <<= 1; var (data, data2) = (_data, new uint[len2]); for (var i = 0; i < len; i++) data2[i] = data[i]; _data = data2; } static uint[] Expanded(ReadOnlySpan data, int level) { var res = new uint[1 << level]; data.CopyTo(res); return res; } FPSNTT(uint[] data, int length) { _data = data; _length = Math.Min(length, MaxLength); } FPSNTT(uint[] data) { _data = data; _length = Math.Min(data.Length, MaxLength); } static uint Rem(long v) { var res = v % Mod; return (uint)(res < 0 ? res + Mod : res); } static uint Pow(long n, long m) { if (m < 0) m = (m % (Mod - 1)) + Mod - 1; var (res, k) = (1L, n); while (m > 0) { if ((m & 1) > 0) res = res * k % Mod; k = k * k % Mod; m >>= 1; } return Rem(res); } static readonly ulong[] _r1, _r2; static readonly int[][] _butterfly; static FPSNTT() { var r1 = new ulong[P + 1]; var r2 = new ulong[P + 1]; var u = Pow(R, K); (r1[P], r2[P]) = (u, Pow(u, -1)); for (var i = P; i > 0; i--) { r1[i - 1] = r1[i] * r1[i] % Mod; r2[i - 1] = r2[i] * r2[i] % Mod; } (_r1, _r2, _butterfly) = (r1, r2, new int[P + 1][]); } static int[] Butterfly(int level) { if (_butterfly[level] != null) return _butterfly[level]; var n = 1 << level; var b = new int[n]; for (int p = 1, d = n >> 1; p < n; p <<= 1, d >>= 1) for (var k = 0; k < p; ++k) b[k | p] = b[k] | d; return _butterfly[level] = b; } static void FastModuloTransform(Span f, int level, bool reverse) { var n = f.Length; if (n < 2) return; var b = Butterfly(level); for (var i = 0; i < n; i++) { var j = b[i]; if (i < j) (f[i], f[j]) = (f[j], f[i]); } var rotations = reverse ? _r1 : _r2; for (var k = 1; k <= level; k++) { var l = 1 << k; var h = l >> 1; var root = rotations[k]; for (var i = 0; i < n; i += l) { var rotation = 1UL; for (var j = 0; j < h; j++) { var (ui, vi) = (i + j, i + j + h); var (u, v) = (f[ui], (uint)(f[vi] * rotation % Mod)); (f[ui], f[vi]) = ((u + v) % Mod, (Mod + u - v) % Mod); rotation = rotation * root % Mod; } } } } static uint[] Mul(ReadOnlySpan f, ReadOnlySpan g, int len = -1) { if (len < 0) len = f.Length + g.Length - 1; var (n, level) = (1, 0); while (n < len) (n, level) = (n << 1, level + 1); var ft = Expanded(f, level); var gt = Expanded(g, level); FastModuloTransform(ft, level, false); FastModuloTransform(gt, level, false); for (var i = 0; i < n; i++) ft[i] = (uint)((ulong)ft[i] * gt[i] % Mod); FastModuloTransform(ft, level, true); var nInverse = Pow(n, -1); for (var i = 0; i < len; i++) ft[i] = (uint)((ulong)ft[i] * nInverse % Mod); for (var i = len; i < n; i++) ft[i] = 0; return ft; } static uint[] InvStep(ReadOnlySpan f, ReadOnlySpan g) { var l1 = g.Length; var l2 = l1 << 1; var flen = Math.Min(f.Length, l2); var h = Mul(f[..flen], g, l2); h.AsSpan()[..l1].Clear(); h = Mul(h, g, l2); for (var i = 0; i < l1; i++) h[i] = g[i]; for (var i = l1; i < l2; i++) h[i] = (Mod - h[i]) % Mod; return h; } static uint[] Inv(ReadOnlySpan f, int tl) { var g = new[]{ Pow(f[0], -1) }; if (f.Length == 1) return g; while (g.Length < tl) g = InvStep(f, g); return g; } }