_fft_mod = 998244353 _fft_sum_e = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0, 0, 0, 0, 0, 0, 0, 0) _fft_sum_ie = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0, 0, 0, 0, 0, 0, 0, 0) def _butterfly(a): n = len(a) h = (n - 1).bit_length() for ph in range(1, h + 1): w = 1 << (ph - 1) p = 1 << (h - ph) now = 1 for s in range(w): offset = s << (h - ph + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] * now % _fft_mod a[i + offset] = (l + r) % _fft_mod a[i + offset + p] = (l - r) % _fft_mod now *= _fft_sum_e[(~s & -~s).bit_length() - 1] now %= _fft_mod def _butterfly_inv(a): n = len(a) h = (n - 1).bit_length() for ph in range(h, 0, -1): w = 1 << (ph - 1) p = 1 << (h - ph) inow = 1 for s in range(w): offset = s << (h - ph + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] a[i + offset] = (l + r) % _fft_mod a[i + offset + p] = (l - r) * inow % _fft_mod inow *= _fft_sum_ie[(~s & -~s).bit_length() - 1] inow %= _fft_mod def _convolution_naive(a, b): n = len(a) m = len(b) ans = [0] * (n + m - 1) if n < m: for j in range(m): for i in range(n): ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod else: for i in range(n): for j in range(m): ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod return ans def _convolution_fft(a, b): a = a.copy() b = b.copy() n = len(a) m = len(b) z = 1 << (n + m - 2).bit_length() a += [0] * (z - n) _butterfly(a) b += [0] * (z - m) _butterfly(b) for i in range(z): a[i] = a[i] * b[i] % _fft_mod _butterfly_inv(a) a = a[:n + m - 1] iz = pow(z, _fft_mod - 2, _fft_mod) for i in range(n + m - 1): a[i] = a[i] * iz % _fft_mod return a def _convolution_square(a): a = a.copy() n = len(a) z = 1 << (2 * n - 2).bit_length() a += [0] * (z - n) _butterfly(a) for i in range(z): a[i] = a[i] * a[i] % _fft_mod _butterfly_inv(a) a = a[:2 * n - 1] iz = pow(z, _fft_mod - 2, _fft_mod) for i in range(2 * n - 1): a[i] = a[i] * iz % _fft_mod return a def convolution(a, b): n = len(a) m = len(b) if n == 0 or m == 0: return [] if min(n, m) <= 60: return _convolution_naive(a, b) if a is b: return _convolution_square(a) return _convolution_fft(a, b) MOD = 998244353 def main(): import sys input = sys.stdin.readline table_len = 10 ** 5 + 10 fac = [1, 1] for i in range(2, table_len): fac.append(fac[-1] * i % MOD) finv = [0] * table_len finv[-1] = pow(fac[-1], MOD - 2, MOD) for i in range(table_len-1, 0, -1): finv[i - 1] = finv[i] * i % MOD N = int(input()) f = [(i + 1) * finv[i] % MOD for i in range(N)] ans = [0] * N ans[0] = 1 first = True for d in (format(N, 'b')): if first: first = False else: ans = convolution(ans, ans)[:N] if d == '1': ans = convolution(ans, f)[:N] print(ans[N - 2] * fac[N - 2] % MOD * pow(N, MOD - N + 1, MOD) % MOD) main()