#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #if __has_include() #include #endif #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define _rep(i, n) _rep2(i, 0, n) #define _rep2(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rep(...) GET_MACRO(__VA_ARGS__, _rep2, _rep)(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define UNIQUE(x) \ std::sort((x).begin(), (x).end()); \ (x).erase(std::unique((x).begin(), (x).end()), (x).end()) using i64 = long long; template bool chmin(T& a, const U& b) { return (b < a) ? (a = b, true) : false; } template bool chmax(T& a, const U& b) { return (b > a) ? (a = b, true) : false; } template inline void YesNo(bool f = 0, const T yes = "Yes", const U no = "No") { if (f) std::cout << yes << "\n"; else std::cout << no << "\n"; } namespace io { template istream& operator>>(istream& i, vector& v) { rep(j, v.size()) i >> v[j]; return i; } template string join(vector& v) { stringstream s; rep(i, v.size()) s << ' ' << v[i]; return s.str().substr(1); } template ostream& operator<<(ostream& o, vector& v) { if (v.size()) o << join(v); return o; } template string join(vector>& vv) { string s = "\n"; rep(i, vv.size()) s += join(vv[i]) + "\n"; return s; } template ostream& operator<<(ostream& o, vector>& vv) { if (vv.size()) o << join(vv); return o; } template istream& operator>>(istream& i, pair& p) { i >> p.first >> p.second; return i; } template ostream& operator<<(ostream& o, pair& p) { o << p.first << " " << p.second; return o; } void OUT() { std::cout << "\n"; } template void OUT(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail)) std::cout << ' '; OUT(std::forward(tail)...); } void OUTL() { std::cout << std::endl; } template void OUTL(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail)) std::cout << ' '; OUTL(std::forward(tail)...); } void IN() {} template void IN(Head&& head, Tail&&... tail) { cin >> head; IN(std::forward(tail)...); } } // namespace io using namespace io; namespace useful { long long modpow(long long a, long long b, long long mod) { long long res = 1; while (b) { if (b & 1) res *= a, res %= mod; a *= a; a %= mod; b >>= 1; } return res; } bool is_pow2(long long x) { return x > 0 && (x & (x - 1)) == 0; } template void rearrange(vector& a, vector& p) { vector b = a; for (int i = 0; i < int(a.size()); i++) { a[i] = b[p[i]]; } return; } template vector> rle_sequence(T& a) { vector> res; int n = a.size(); if (n == 1) return vector>{{a[0], 1}}; int l = 1; rep(i, n - 1) { if (a[i] == a[i + 1]) l++; else { res.emplace_back(a[i], l); l = 1; } } res.emplace_back(a.back(), l); return res; } vector> rle_string(string a) { vector> res; int n = a.size(); if (n == 1) return vector>{{a[0], 1}}; int l = 1; rep(i, n - 1) { if (a[i] == a[i + 1]) l++; else { res.emplace_back(a[i], l); l = 1; } } res.emplace_back(a.back(), l); return res; } vector linear_sieve(int n) { vector primes; vector res(n + 1); iota(all(res), 0); for (int i = 2; i <= n; i++) { if (res[i] == i) primes.emplace_back(i); for (auto j : primes) { if (j * i > n) break; res[j * i] = j; } } return res; // return primes; } template vector dijkstra(vector>>& graph, int start) { int n = graph.size(); vector res(n, 2e18); res[start] = 0; priority_queue, vector>, greater>> que; que.push({0, start}); while (!que.empty()) { auto [c, v] = que.top(); que.pop(); if (res[v] < c) continue; for (auto [nxt, cost] : graph[v]) { auto x = c + cost; if (x < res[nxt]) { res[nxt] = x; que.push({x, nxt}); } } } return res; } } // namespace useful using namespace useful; template struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt& operator+=(const ModInt& p) { if ((x += p.x) >= mod) x -= mod; return *this; } ModInt& operator-=(const ModInt& p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt& operator*=(const ModInt& p) { x = (int)(1LL * x * p.x % mod); return *this; } ModInt& operator/=(const ModInt& p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+() const { return ModInt(*this); } ModInt operator+(const ModInt& p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt& p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt& p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt& p) const { return ModInt(*this) /= p; } bool operator==(const ModInt& p) const { return x == p.x; } bool operator!=(const ModInt& p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream& operator<<(ostream& os, const ModInt& p) { return os << p.x; } friend istream& operator>>(istream& is, ModInt& a) { int64_t t; is >> t; a = ModInt(t); return (is); } int get() const { return x; } static constexpr int get_mod() { return mod; } }; using mint = ModInt<998244353>; vector fact_calc(int x) { vector res(x + 1); res[0] = 1; for (int i = 0; i < x; i++) { res[i + 1] = res[i] * (i + 1); } return res; } vector ifact_calc(int x) { vector res(x + 1); mint t = 1; for (int i = 1; i <= x; i++) { t *= i; } res[x] = t.inverse(); // res[x] = t.inv(); for (int i = x; i > 0; i--) { res[i - 1] = res[i] * i; } return res; } auto fact = fact_calc(2000005); auto ifact = ifact_calc(2000005); mint comb(int x, int y) { if (x < 0 || y < 0 || x - y < 0) return 0; return fact[x] * ifact[y] * ifact[x - y]; } mint perm(int x, int y) { if (x < 0 || x - y < 0) return 0; return fact[x] * ifact[x - y]; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; IN(n); vector a(n); IN(a); mint ans = 0; vector f(n + 10), g(n + 10); rep(i, n + 10) { f[i] = (ifact[i] * (i + 1)).x; g[i] = (ifact[i]).x; } auto cv = atcoder::convolution(f, g); rep(i, n) { mint tmp1 = 0, tmp2 = 0; int m = n - i - 1; // rep(l, i + 1) tmp1 += comb(i, l) * (l + 1); // rep(r, m + 1) tmp2 += comb(m, r) * (r + 1); tmp1 = fact[i] * cv[i]; tmp2 = fact[m] * cv[m]; mint tmp = tmp1 * tmp2; ans += tmp * a[i]; } OUT(ans); }