/** * date : 2021-11-19 22:30:10 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &... u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // template void walsh_hadamard_transform(vector& f, bool inverse = false) { int n = f.size(); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { T x = f[j], y = f[j | i]; f[j] = x + y, f[j | i] = x - y; } } } if (inverse) { if constexpr (is_integral::value) { for (auto& x : f) x /= n; } else { T invn = T(1) / T(f.size()); for (auto& x : f) x *= invn; } } } /** * @brief Walsh Hadamard Transform */ template vector xor_convolution(vector a, vector b) { walsh_hadamard_transform(a); walsh_hadamard_transform(b); for (int i = 0; i < (int)a.size(); i++) a[i] *= b[i]; walsh_hadamard_transform(a, true); return a; } /** * @brief XOR Convoluion */ // /** #include "modint/montgomery-modint.hpp" #include "modulo/binomial.hpp" using namespace Nyaan; using mint = LazyMontgomeryModInt<998244353>; // using mint = LazyMontgomeryModInt<1000000007>; Binomial C; //*/ /**/ struct Rational { using R = Rational; using i128 = __int128_t; using i64 = long long; using u64 = unsigned long long; long long x, y; Rational() : x(0), y(1) {} Rational(long long _x, long long _y = 1) : x(_x), y(_y) { assert(y != 0); if (_y != 1) { long long g = gcd(x, y); if (g != 0) x /= g, y /= g; if (y < 0) x = -x, y = -y; } } u64 gcd(i64 A, i64 B) { u64 a = A >= 0 ? A : -A; u64 b = B >= 0 ? B : -B; if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); int m = __builtin_ctzll(b); a >>= n; b >>= m; while (a != b) { int d = __builtin_ctzll(a - b); bool f = a > b; u64 c = f ? a : b; b = f ? b : a; a = (c - b) >> d; } return a << min(n, m); } friend R operator+(const R& l, const R& r) { return R(l.x * r.y + l.y * r.x, l.y * r.y); } friend R operator-(const R& l, const R& r) { return R(l.x * r.y - l.y * r.x, l.y * r.y); } friend R operator*(const R& l, const R& r) { return R(l.x * r.x, l.y * r.y); } friend R operator/(const R& l, const R& r) { assert(r.x != 0); return R(l.x * r.y, l.y * r.x); } R& operator+=(const R& r) { return (*this) = (*this) + r; } R& operator-=(const R& r) { return (*this) = (*this) - r; } R& operator*=(const R& r) { return (*this) = (*this) * r; } R& operator/=(const R& r) { return (*this) = (*this) / r; } R operator-() const { R r; r.x = -x, r.y = y; return r; } R inverse() const { assert(x != 0); R r; r.x = y, r.y = x; if (x < 0) r.x = -r.x, r.y = -r.y; return r; } R pow(long long p) const { R res(1), base(*this); while (p) { if (p & 1) res *= base; base *= base; p >>= 1; } return res; } friend bool operator==(const R& l, const R& r) { return l.x == r.x && l.y == r.y; }; friend bool operator!=(const R& l, const R& r) { return l.x != r.x || l.y != r.y; }; friend bool operator<(const R& l, const R& r) { return i128(l.x) * r.y < i128(l.y) * r.x; }; friend bool operator<=(const R& l, const R& r) { return l < r || l == r; } friend bool operator>(const R& l, const R& r) { return i128(l.x) * r.y > i128(l.y) * r.x; }; friend bool operator>=(const R& l, const R& r) { return l > r || l == r; } friend ostream& operator<<(ostream& os, const R& r) { os << r.x; if (r.x != 0 && r.y != 1) os << "/" << r.y; return os; } long long toMint(long long mod) { assert(mod != 0); i64 a = y, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return i128((u % mod + mod) % mod) * x % mod; } }; struct Binomial { vector fc; Binomial(int = 0) { fc.emplace_back(1); } void extend() { int n = fc.size(); Rational nxt = fc.back() * n; fc.push_back(nxt); } Rational fac(int n) { while ((int)fc.size() <= n) extend(); return fc[n]; } Rational finv(int n) { return fac(n).inverse(); } Rational inv(int n) { return Rational{1, max(n, 1)}; } Rational C(int n, int r) { if (n < 0 or r < 0 or n < r) return Rational{0}; return fac(n) * finv(n - r) * finv(r); } }; using mint = Rational; //*/ using namespace Nyaan; using vm = vector; using vvm = vector; void Nyaan::solve() { auto sol = [](ll, ll S) { mint x = mint{-1} / 3; return (mint{1} - x.pow(S)) / 2; }; inl(N); vl a(N); in(a); if (N == 1) { out(mint{2} / 3); return; } ll S = Sum(a); if (sz(a) % 2 == 0) { mint ans = sol(N, S); trc(ans); out(ans); return; } exit(1); sort(all(a)); reverse(all(a)); each(x, a) { // 奇数個 -> 勝ち if (S % 2 != x % 2) { mint bns = sol(N - 1, S - x); mint ans = bns * 2 / 3; ans += (-bns + 1) * 1 / 3; out(ans); return; } } // 一番小さいものを選ぶ { ll x = a.back(); mint bns = sol(N - 1, S - x); mint ans = bns * 2 / 3; ans += (-bns + 1) * 1 / 3; out(ans); return; } }