import sys,random,bisect from collections import deque,defaultdict,Counter from heapq import heapify,heappop,heappush from itertools import cycle, permutations from math import log,gcd input = lambda :sys.stdin.readline().rstrip() mi = lambda :map(int,input().split()) li = lambda :list(mi()) mod = 998244353 omega = pow(3,119,mod) rev_omega = pow(omega,mod-2,mod) N = 6*10**5 g1 = [1]*(N+1) # 元テーブル g2 = [1]*(N+1) #逆元テーブル inv = [1]*(N+1) #逆元テーブル計算用テーブル for i in range( 2, N + 1 ): g1[i]=( ( g1[i-1] * i ) % mod ) inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod ) g2[i]=( (g2[i-1] * inv[i]) % mod ) inv[0]=0 _fft_mod = 998244353 _fft_imag = 911660635 _fft_iimag = 86583718 _fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899) _fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235) _fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204) _fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681) def _butterfly(a): n = len(a) h = (n - 1).bit_length() len_ = 0 while len_ < h: if h - len_ == 1: p = 1 << (h - len_ - 1) rot = 1 for s in range(1 << len_): offset = s << (h - len_) for i in range(p): l = a[i + offset] r = a[i + offset + p] * rot % _fft_mod a[i + offset] = (l + r) % _fft_mod a[i + offset + p] = (l - r) % _fft_mod if s + 1 != (1 << len_): rot *= _fft_rate2[(~s & -~s).bit_length() - 1] rot %= _fft_mod len_ += 1 else: p = 1 << (h - len_ - 2) rot = 1 for s in range(1 << len_): rot2 = rot * rot % _fft_mod rot3 = rot2 * rot % _fft_mod offset = s << (h - len_) 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) % _fft_mod * _fft_imag a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod if s + 1 != (1 << len_): rot *= _fft_rate3[(~s & -~s).bit_length() - 1] rot %= _fft_mod len_ += 2 def _butterfly_inv(a): n = len(a) h = (n - 1).bit_length() len_ = h while len_: if len_ == 1: p = 1 << (h - len_) irot = 1 for s in range(1 << (len_ - 1)): offset = s << (h - len_ + 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) * irot % _fft_mod if s + 1 != (1 << (len_ - 1)): irot *= _fft_irate2[(~s & -~s).bit_length() - 1] irot %= _fft_mod len_ -= 1 else: p = 1 << (h - len_) irot = 1 for s in range(1 << (len_ - 2)): irot2 = irot * irot % _fft_mod irot3 = irot2 * irot % _fft_mod offset = s << (h - len_ + 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) * _fft_iimag % _fft_mod a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % _fft_mod a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % _fft_mod a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % _fft_mod if s + 1 != (1 << (len_ - 1)): irot *= _fft_irate3[(~s & -~s).bit_length() - 1] irot %= _fft_mod len_ -= 2 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): """It calculates (+, x) convolution in mod 998244353. Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], it calculates the array c of length n + m - 1, defined by > c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353. It returns an empty list if at least one of a and b are empty. Constraints ----------- > len(a) + len(b) <= 8388609 Complexity ---------- > O(n log n), where n = len(a) + len(b). """ n = len(a) m = len(b) if n == 0 or m == 0: return [] if min(n, m) <= 0: return _convolution_naive(a, b) if a is b: return _convolution_square(a) return _convolution_fft(a, b) def taylor_shift(f,a): g = [f[i]*g1[i]%mod for i in range(len(f))][::-1] e = [g2[i] for i in range(len(f))] t = 1 for i in range(1,len(f)): t = t * a % mod e[i] = e[i] * t % mod res = convolution(g,e)[:len(f)] return [res[len(f)-1-i]*g2[i]%mod for i in range(len(f))] def inverse(f,limit): assert(f[0]!=0) l = len(f) L = 1<<((l-1).bit_length()) n = L.bit_length()-1 f = f[:L] f+=[0]*(L-len(f)) res = [pow(f[0],mod-2,mod)] for i in range(1,n+1): h = convolution(res,f[:2**i])[:2**i] h = [(-h[i]) % mod for i in range(2**i)] h[0] = (h[0]+2) % mod res = convolution(res,h)[:2**i] return res[:limit] def integral(f,limit): res = [0]+[(f[i] * inv[i+1]) % mod for i in range(len(f)-1)] return res[:limit] def diff(f,limit): res = [(f[i+1] * (i+1)) % mod for i in range(len(f)-1)]+[0] return res[:limit] def log(f,limit): res = convolution(diff(f,limit),inverse(f,limit))[:limit] return integral(res,limit) def exp(f,limit): l = len(f) L = 1<<((l-1).bit_length()) n = L.bit_length()-1 f = f[:L] f+=[0]*(L-len(f)) res = [1] for i in range(1,n+1): res += [0]*2**(i-1) g = log(res,2**i) h = [(f[j]-g[j])%mod for j in range(2**i)] h[0] = (h[0]+1) % mod res =convolution(res,h)[:2**i] return res[:limit] N = int(input()) A = li() S = sum(A) if S < 999630629: res = S * pow(2,N-1,mod) % mod exit(print(res)) cnt = [0] * (10**4+1) for a in A: cnt[a] += 1 M = S - 999630629 f = [0] * (M+1) for a in range(1,10**4+1): for k in range(a,M+1,a): if (k//a) & 1: f[k] += cnt[a] * inv[k//a] % mod else: f[k] -= cnt[a] * inv[k//a] % mod f[k] %= mod f = exp(f,M+1) res = S * pow(2,N-1,mod) % mod for i in range(M+1): res -= 999630629 * f[i] res %= mod print(res)