#Pythonで通るかチェック #https://judge.yosupo.jp/submission/152016 from collections import deque from __pypy__.builders import StringBuilder import sys from os import read as os_read, write as os_write from atexit import register as atexist_register from typing import Generic, Iterator, List, Tuple, Dict, Iterable, Sequence, Callable, Union, Optional, TypeVar T = TypeVar('T') Pair = Tuple[int, int] Graph = List[List[int]] Poly = List[int] Vector = List[int] Matrix = List[List[int]] Func10 = Callable[[int], None] Func20 = Callable[[int, int], None] Func11 = Callable[[int], int] Func21 = Callable[[int, int], int] Func31 = Callable[[int, int, int], int] class Fastio: ibuf = bytes() pil = pir = 0 sb = StringBuilder() def load(self): self.ibuf = self.ibuf[self.pil:] self.ibuf += os_read(0, 131072) self.pil = 0; self.pir = len(self.ibuf) def flush_atexit(self): os_write(1, self.sb.build().encode()) def flush(self): os_write(1, self.sb.build().encode()) self.sb = StringBuilder() def fastin(self): if self.pir - self.pil < 64: self.load() minus = x = 0 while self.ibuf[self.pil] < 45: self.pil += 1 if self.ibuf[self.pil] == 45: minus = 1; self.pil += 1 while self.ibuf[self.pil] >= 48: x = x * 10 + (self.ibuf[self.pil] & 15) self.pil += 1 if minus: return -x return x def fastin_string(self): if self.pir - self.pil < 64: self.load() while self.ibuf[self.pil] <= 32: self.pil += 1 res = bytearray() while self.ibuf[self.pil] > 32: if self.pir - self.pil < 64: self.load() res.append(self.ibuf[self.pil]) self.pil += 1 return res def fastout(self, x): self.sb.append(str(x)) def fastoutln(self, x): self.sb.append(str(x)); self.sb.append('\n') fastio = Fastio() rd = fastio.fastin; rds = fastio.fastin_string; wt = fastio.fastout; wtn = fastio.fastoutln; flush = fastio.flush atexist_register(fastio.flush_atexit) sys.stdin = None; sys.stdout = None def rdl(n): return [rd() for _ in range(n)] def wtnl(l): wtn(' '.join(map(str, l))) def wtn_yes(): wtn("Yes") def wtn_no(): wtn("No") def print(*arg): wtnl(arg) def modinv(a: int, m: int) -> int: '''return x s.t. x == a^(-1) (mod m)''' b = m; u = 1; v = 0 while b: t = a // b a, b = b, a - t * b u, v = v, u - t * v u %= m return u MOD = 998244353 _IMAG = 911660635 _IIMAG = 86583718 _rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0) _rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0) _irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0) class NTT: @staticmethod def _fft(a: Vector) -> None: n = len(a) h = (n - 1).bit_length() le = 0 for le in range(0, h - 1, 2): p = 1 << (h - le - 2) rot = 1 for s in range(1 << le): rot2 = rot * rot % MOD rot3 = rot2 * rot % MOD offset = s << (h - le) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] * rot a2 = a[i + offset + p * 2] * rot2 a3 = a[i + offset + p * 3] * rot3 a1na3imag = (a1 - a3) % MOD * _IMAG a[i + offset] = (a0 + a2 + a1 + a3) % MOD a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD rot = rot * _rate3[(~s & -~s).bit_length()] % MOD if h - le & 1: rot = 1 for s in range(1 << (h - 1)): offset = s << 1 l = a[offset] r = a[offset + 1] * rot a[offset] = (l + r) % MOD a[offset + 1] = (l - r) % MOD rot = rot * _rate2[(~s & -~s).bit_length()] % MOD @staticmethod def _ifft(a: Vector) -> None: n = len(a) h = (n - 1).bit_length() le = h for le in range(h, 1, -2): p = 1 << (h - le) irot = 1 for s in range(1 << (le - 2)): irot2 = irot * irot % MOD irot3 = irot2 * irot % MOD offset = s << (h - le + 2) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] a2 = a[i + offset + p * 2] a3 = a[i + offset + p * 3] a2na3iimag = (a2 - a3) * _IIMAG % MOD a[i + offset] = (a0 + a1 + a2 + a3) % MOD a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD irot = irot * _irate3[(~s & -~s).bit_length()] % MOD if le & 1: p = 1 << (h - 1) for i in range(p): l = a[i] r = a[i + p] a[i] = l + r if l + r < MOD else l + r - MOD a[i + p] = l - r if l - r >= 0 else l - r + MOD @classmethod def ntt(cls, a: Vector) -> None: if len(a) <= 1: return cls._fft(a) @classmethod def intt(cls, a:Vector) -> None: if len(a) <= 1: return cls._ifft(a) iv = modinv(len(a), MOD) for i, x in enumerate(a): a[i] = x * iv % MOD @classmethod def multiply(cls, s: Vector, t: Vector) -> Vector: n, m = len(s), len(t) l = n + m - 1 if min(n, m) <= 60: a = [0] * l for i, x in enumerate(s): for j, y in enumerate(t): a[i + j] = (a[i + j] + x * y) % MOD return a z = 1 << (l - 1).bit_length() a = s + [0] * (z - n) b = t + [0] * (z - m) cls._fft(a) cls._fft(b) for i, x in enumerate(b): a[i] = a[i] * x % MOD cls._ifft(a) a[l:] = [] iz = modinv(z, MOD) return [x * iz % MOD for x in a] @classmethod def pow2(cls, s: Vector) -> Vector: n = len(s) l = (n << 1) - 1 if n <= 60: a = [0] * l for i, x in enumerate(s): for j, y in enumerate(s): a[i + j] += x * y return [x % MOD for x in a] z = 1 << (l - 1).bit_length() a = s + [0] * (z - n) cls._fft(a) for i, x in enumerate(a): a[i] = x * x % MOD cls._ifft(a) a[l:] = [] iz = modinv(z, MOD) return [x * iz % MOD for x in a] @classmethod def ntt_doubling(cls, a: Vector) -> None: M = len(a) b = a[:] cls.intt(b) r = 1 zeta = pow(3, (MOD - 1) // (M << 1), MOD) for i, x in enumerate(b): b[i] = x * r % MOD r = r * zeta % MOD cls.ntt(b) a += b N=rd() A=rdl(N) q = deque() for i in A: q.append([1,i]) while len(q) >= 2: q.append(NTT.multiply(q.popleft(), q.popleft())) res=q.popleft() ans=0 for i in range(1,N+1): ans+=pow(i,N-i,998244353)*res[i]%998244353 ans%=998244353 print(ans)