結果
問題 | No.2062 Sum of Subset mod 999630629 |
ユーザー |
|
提出日時 | 2022-08-26 23:15:23 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
RE
|
実行時間 | - |
コード長 | 31,567 bytes |
コンパイル時間 | 3,269 ms |
コンパイル使用メモリ | 218,468 KB |
最終ジャッジ日時 | 2025-01-31 05:37:22 |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 10 RE * 19 |
ソースコード
bool TEST = false;using namespace std;#include<bits/stdc++.h>#include<fstream>#define rep(i,n) for(ll (i)=0;(i)<(ll)(n);i++)#define rrep(i,n) for(ll (i)=(ll)(n)-1;(i)>=0;i--)#define range(i,start,end,step) for(ll (i)=start;(i)<(ll)(end);(i)+=(step))#define rrange(i,start,end,step) for(ll (i)=start;(i)>(ll)(end);(i)+=(step))#define dump(x) cerr << "Line " << __LINE__ << ": " << #x << " = " << (x) << "\n";#define spa << " " <<#define fi first#define se second#define all(a) (a).begin(),(a).end()#define allr(a) (a).rbegin(),(a).rend()using ld = long double;using ll = long long;using ull = unsigned long long;using pii = pair<int, int>;using pll = pair<ll, ll>;using pdd = pair<ld, ld>;template<typename T> using V = vector<T>;template<typename T> using VV = V<V<T>>;template<typename T, typename T2> using P = pair<T, T2>;template<typename T, typename T2> using M = map<T, T2>;template<typename T> using S = set<T>;template<typename T, typename T2> using UM = unordered_map<T, T2>;template<typename T> using PQ = priority_queue<T, V<T>, greater<T>>;template<typename T> using rPQ = priority_queue<T, V<T>, less<T>>;template<class T>vector<T> make_vec(size_t a){return vector<T>(a);}template<class T, class... Ts>auto make_vec(size_t a, Ts... ts){return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));}template<class SS, class T> ostream& operator << (ostream& os, const pair<SS, T> v){os << "(" << v.first << ", " << v.second << ")"; return os;}template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }template<class T> ostream& operator<<(ostream& os, const vector<vector<T>> &v){ for(auto &e : v){os << e << "\n";} return os;}struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;template <class T> void UNIQUE(vector<T> &x) {sort(all(x));x.erase(unique(all(x)), x.end());}template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }void fail() { cout << -1 << '\n'; exit(0); }inline int popcount(const int x) { return __builtin_popcount(x); }inline int popcount(const ll x) { return __builtin_popcountll(x); }template<typename T> void debug(vector<vector<T>>&v){for(ll i=0;i<v.size();i++){cerr<<v[i][0];for(ll j=1;j<v[i].size();j++)cerr spa v[i][j];cerr<<"\n";}};template<typename T> void debug(vector<T>&v){if(v.size()!=0)cerr<<v[0];for(ll i=1;i<v.size();i++)cerr spa v[i];cerr<<"\n";};template<typename T> void debug(priority_queue<T>&v){V<T> vals; while(!v.empty()) {cerr << v.top() << " "; vals.push_back(v.top()); v.pop();} cerr<<"\n"; for(auto val: vals) v.push(val);}template<typename T, typename T2> void debug(map<T,T2>&v){for(auto [k,v]: v) cerr << k spa v << "\n"; cerr<<"\n";}template<typename T, typename T2> void debug(unordered_map<T,T2>&v){for(auto [k,v]: v) cerr << k spa v << "\n";cerr<<"\n";}V<int> listrange(int n) {V<int> res(n); rep(i,n) res[i]=i; return res;}template<typename T> P<T,T> divmod(T a, T b) {return make_pair(a/b, a%b);}const ll INF = (1ll<<62);// const ld EPS = 1e-10;// const ld PI = acos(-1.0);template< int mod >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 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< mod >(t);return (is);}static int get_mod() { return mod; }};template<class _Key, class _Tp, class _Hash, bool DOWNSIZE> class UnorderedMapIterator;template<class _Key, class _Tp, class _Hash = hash<_Key>, bool DOWNSIZE = false>class UnorderedMap{private:using iterator = UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>;using value_type = _Tp;using data_type = pair<_Key, _Tp>;using aligned_pointer = typename aligned_storage<sizeof(value_type), alignof(value_type)>::type;friend UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>;struct bucket {_Key _key;short int _dist;bool _last, _end;aligned_pointer _value_ptr;bucket() noexcept : _dist(-1), _last(false), _end(false){}bucket& operator=(const bucket& another) noexcept {_key = another._key, _dist = another._dist, _last = another._last, _end = another._end;if(!another.empty()){new(&_value_ptr) value_type(*reinterpret_cast<const value_type*>(&another._value_ptr));}return *this;}~bucket(){ if(!empty()) _delete(); }inline void clear() noexcept { _dist = -1; }inline void _delete(){ _dist = -1, value_ptr()->~value_type(); }inline bool empty() const noexcept { return (_dist == -1); }inline value_type& value() noexcept {return *reinterpret_cast<value_type*>(&_value_ptr);}inline value_type* value_ptr() noexcept {return reinterpret_cast<value_type*>(&_value_ptr);}inline void new_value(value_type&& value){new(&_value_ptr) value_type(move(value));}};inline static unsigned int ceilpow2(unsigned int u) noexcept {if(u == 0u) return 0u;--u, u |= u >> 1, u |= u >> 2, u |= u >> 4, u |= u >> 8;return (u | (u >> 16)) + 1u;}inline static bucket *increment(bucket *cur) noexcept {for(++cur; !cur->_end; ++cur){if(!cur->empty()) break;}return cur;}inline bucket *next_bucket(bucket *cur) const noexcept {return cur->_last ? _buckets : cur + 1;}inline unsigned int make_hash(const _Key& key) const noexcept {return _Hash()(key);}inline float load_rate() const noexcept {return (float)_data_count / _bucket_count;}bucket *insert(bucket *cur, _Key&& key, short int dist, value_type&& value){bucket *ret = cur;bool flag = false;while(true){if(cur->empty()){cur->_key = move(key), cur->_dist = dist, cur->new_value(move(value));if(!flag) ret = cur, flag = true;break;}else if(dist > cur->_dist){swap(key, cur->_key), swap(dist, cur->_dist), swap(value, cur->value());if(!flag) ret = cur, flag = true;}++dist;cur = next_bucket(cur);}return ret;}template<class Key>bucket *_find(Key&& key, bool push = false){unsigned int hash = make_hash(key);bucket *cur = _buckets + (hash & _mask);short int dist = 0;while(dist <= cur->_dist){if(key == cur->_key) return cur;++dist, cur = next_bucket(cur);}if(!push) return _buckets + _bucket_count;++_data_count;if(rehash_check()){cur = _buckets + (hash & _mask), dist = 0;}value_type new_value = value_type();_Key new_key = forward<Key>(key);return insert(cur, move(new_key), dist, move(new_value));}template<class Data>bucket *find_insert(Data&& data){const _Key& key = data.first;unsigned int hash = make_hash(key);bucket *cur = _buckets + (hash & _mask);short int dist = 0;while(dist <= cur->_dist){if(key == cur->_key) return cur;++dist, cur = next_bucket(cur);}++_data_count;if(rehash_check()){cur = _buckets + (hash & _mask), dist = 0;}data_type new_data = forward<Data>(data);return insert(cur, move(new_data.first), dist, move(new_data.second));}template<typename... Args>bucket *emplace(Args&&... args){return find_insert(data_type(forward<Args>(args)...));}bucket *backward_shift(bucket *cur, bool next_ret){bucket *next = next_bucket(cur), *ret = cur;if(next->_dist < 1) return next_ret ? increment(cur) : cur;do {cur->_key = next->_key, cur->_dist = next->_dist - 1;cur->new_value(move(next->value()));cur = next, next = next_bucket(cur);}while(next->_dist >= 1);cur->clear();return ret;}bucket *erase_impl(bucket *cur, bool next_ret){assert(static_cast<size_t>(cur - _buckets) != _bucket_count);cur->_delete();--_data_count;return backward_shift(cur, next_ret);}bucket *erase_itr(bucket *cur, bool next_ret = true){const _Key key = cur->_key;return erase_impl(rehash_check() ? _find(key) : cur, next_ret);}size_t erase_key(const _Key& key){rehash_check();bucket *cur = _find(key);if(static_cast<size_t>(cur - _buckets) == _bucket_count){return 0;}else{erase_impl(_find(key), false);return 1;}}bool rehash_check(){if(_bucket_count == 0){rehash(1u);return true;}else if(load_rate() >= MAX_LOAD_RATE){rehash(_bucket_count * 2u);return true;}else if(DOWNSIZE){if(load_rate() <= MIN_LOAD_RATE && _bucket_count >= DOWNSIZE_THRESHOLD){rehash(_bucket_count / 2u);return true;}}return false;}void move_data(bucket *cur){insert(_buckets + (make_hash(cur->_key) & _mask), move(cur->_key), 0, move(cur->value()));}void rehash(unsigned int new_bucket_count){UnorderedMap new_unordered_map(new_bucket_count);new_unordered_map._data_count = _data_count;for(bucket *cur = _buckets; !cur->_end; ++cur){if(!cur->empty()){new_unordered_map.move_data(cur);}}swap(*this, new_unordered_map);}friend void swap(UnorderedMap& ump1, UnorderedMap& ump2){swap(ump1._bucket_count, ump2._bucket_count);swap(ump1._mask, ump2._mask);swap(ump1._data_count, ump2._data_count);swap(ump1._buckets, ump2._buckets);}private:unsigned int _bucket_count, _mask, _data_count;bucket *_buckets;public:const float MAX_LOAD_RATE = 0.5f;const float MIN_LOAD_RATE = 0.1f;const unsigned int DOWNSIZE_THRESHOLD = 16u;UnorderedMap(unsigned int bucket_size = 0u): _bucket_count(ceilpow2(bucket_size)), _mask(_bucket_count - 1),_data_count(0u), _buckets(new bucket[_bucket_count + 1]){if(_bucket_count > 0) _buckets[_bucket_count - 1]._last = true;else _mask = 0;_buckets[_bucket_count]._end = true;}UnorderedMap(const UnorderedMap& another): _bucket_count(another._bucket_count), _mask(another._mask), _data_count(another._data_count){_buckets = new bucket[_bucket_count + 1u];for(unsigned int i = 0u; i <= _bucket_count; ++i){_buckets[i] = another._buckets[i];}}UnorderedMap(UnorderedMap&& another): _bucket_count(move(another._bucket_count)), _mask(move(another._mask)),_data_count(move(another._data_count)), _buckets(another._buckets){another._buckets = nullptr;}UnorderedMap& operator=(const UnorderedMap& another){delete[] _buckets;_bucket_count = another._bucket_count;_mask = another._mask;_data_count = another._data_count;_buckets = new bucket[_bucket_count + 1u];for(unsigned int i = 0u; i <= _bucket_count; ++i){_buckets[i] = another._buckets[i];}return *this;}UnorderedMap& operator=(UnorderedMap&& another){delete[] _buckets;_bucket_count = move(another._bucket_count);_mask = move(another._mask);_data_count = move(another._data_count);_buckets = another._buckets;another._buckets = nullptr;return *this;}void allocate(unsigned int element_size){rehash(ceilpow2(ceil(element_size / MAX_LOAD_RATE) + 1));}~UnorderedMap(){ delete[] _buckets; }friend ostream& operator<< (ostream& os, UnorderedMap& ump) noexcept {for(auto val : ump) os << '{' << val.first << ',' << val.second << "} ";return os;}_Tp& operator[](const _Key& key){ return _find(key, true)->value(); }_Tp& operator[](_Key&& key){ return _find(move(key), true)->value(); }const _Tp& at(const _Key& key){bucket *res = _find(key);if(res == _buckets + _bucket_count) __throw_out_of_range("Unordered_Map::at");return res->value();}void clear(){UnorderedMap new_unordered_map(0u);swap(*this, new_unordered_map);}size_t size() const noexcept { return _data_count; }size_t bucket_count() const noexcept { return _bucket_count; }bool empty() const noexcept { return (_data_count == 0); }iterator begin() noexcept {return (_buckets->empty() && _bucket_count > 0) ? iterator(increment(_buckets)) : iterator(_buckets);}iterator end() noexcept { return iterator(_buckets + _bucket_count); }iterator find(const _Key& key){ return iterator(_find(key)); }iterator insert(const data_type& data){ return iterator(find_insert(data)); }iterator insert(data_type&& data){ return iterator(find_insert(move(data))); }template<typename... Args>iterator emplace(Args&&... args){ return iterator(_emplace(forward<Args>(args)...)); }size_t erase(const _Key& key){ return erase_key(key); }iterator erase(const iterator& itr){ return iterator(erase_itr(itr.bucket_ptr)); }void simple_erase(const _Key& key){ erase_key(key); }void simple_erase(const iterator& itr){ erase_itr(itr.bucket_ptr, false); }// DEBUG 用short int maximum_distance() const noexcept {short int ret = -1;for(bucket *cur = _buckets; !cur->_end; ++cur){ret = max(ret, cur->_dist);}return ret;}};template<class _Key, class _Tp, class _Hash, bool DOWNSIZE>class UnorderedMapIterator {private:friend UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>;typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *bucket_ptr;using iterator_category = forward_iterator_tag;using value_type = pair<const _Key, _Tp>;using difference_type = ptrdiff_t;using reference = pair<const _Key&, _Tp&>;private:UnorderedMapIterator(typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *_bucket_ptr)noexcept : bucket_ptr(_bucket_ptr){}public:UnorderedMapIterator() noexcept : bucket_ptr(){}UnorderedMapIterator(const UnorderedMapIterator& itr) noexcept : bucket_ptr(itr.bucket_ptr){}UnorderedMapIterator& operator=(const UnorderedMapIterator& itr)& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }UnorderedMapIterator& operator=(const UnorderedMapIterator&& itr)& noexcept { return bucket_ptr = itr.bucket_ptr, *this; }reference operator*() const noexcept { return {bucket_ptr->_key, bucket_ptr->value()}; }UnorderedMapIterator& operator++() noexcept {return bucket_ptr = UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(bucket_ptr), *this;}UnorderedMapIterator operator++(int) const noexcept {return UnorderedMapIterator(UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(this->bucket_ptr));}bool operator==(const UnorderedMapIterator& itr) const noexcept { return !(*this != itr); };bool operator!=(const UnorderedMapIterator& itr) const noexcept { return bucket_ptr != itr.bucket_ptr; }};// UnorderedMapusing m17 = ModInt<1'000'000'007>;using m98 = ModInt<998'244'353>;using MOD = m98;ll mod = 998'244'353;// using MOD = m17;// ll mod = 1'000'000'007;const int _B = 500500;V<MOD> g1(_B);V<MOD> g2(_B);V<MOD> inverse(_B);void prepare() {g1[0] = g1[1] = g2[0] = g2[1] = 1;inverse[0] = 0;inverse[1] = 1;range(i,2,_B,1) {g1[i] = g1[i-1]*i;inverse[i] = -inverse[mod%i]*(mod/i);g2[i] = g2[i-1]*inverse[i];}}template<typename T>MOD cmb(T n, T r) {assert(g1[0]==1);if (r<0 || r>n) return 0;if (g1.size()<=n) {int s = g1.size();g1.resize(n+1);g2.resize(n+1);inverse.resize(n+1);range(i, s, n+1, 1) {g1[i] = g1[i-1]*i;inverse[i] = -inverse[mod%i]*(mod/i);g2[i] = g2[i-1]*inverse[i];}}r = min(r, n-r);return g1[n]*g2[r]*g2[n-r];}template<typename T>MOD perm(T n, T r) {if (r<0 || r>n) return 0;return g1[n]*g2[n-r];}template< typename Mint >struct NumberTheoreticTransformFriendlyModInt {static vector< Mint > dw, idw;static int max_base;static Mint root;NumberTheoreticTransformFriendlyModInt() = default;static void init() {if(dw.empty()) {const unsigned mod = Mint::get_mod();assert(mod >= 3 && mod % 2 == 1);auto tmp = mod - 1;max_base = 0;while(tmp % 2 == 0) tmp >>= 1, max_base++;root = 2;while(root.pow((mod - 1) >> 1) == 1) root += 1;assert(root.pow(mod - 1) == 1);dw.resize(max_base);idw.resize(max_base);for(int i = 0; i < max_base; i++) {dw[i] = -root.pow((mod - 1) >> (i + 2));idw[i] = Mint(1) / dw[i];}}}static void ntt(vector< Mint > &a) {init();const int n = (int) a.size();assert((n & (n - 1)) == 0);assert(__builtin_ctz(n) <= max_base);for(int m = n; m >>= 1;) {Mint w = 1;for(int s = 0, k = 0; s < n; s += 2 * m) {for(int i = s, j = s + m; i < s + m; ++i, ++j) {auto x = a[i], y = a[j] * w;a[i] = x + y, a[j] = x - y;}w *= dw[__builtin_ctz(++k)];}}}static void intt(vector< Mint > &a, bool f = true) {init();const int n = (int) a.size();assert((n & (n - 1)) == 0);assert(__builtin_ctz(n) <= max_base);for(int m = 1; m < n; m *= 2) {Mint w = 1;for(int s = 0, k = 0; s < n; s += 2 * m) {for(int i = s, j = s + m; i < s + m; ++i, ++j) {auto x = a[i], y = a[j];a[i] = x + y, a[j] = (x - y) * w;}w *= idw[__builtin_ctz(++k)];}}if(f) {Mint inv_sz = Mint(1) / n;for(int i = 0; i < n; i++) a[i] *= inv_sz;}}static vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {int need = a.size() + b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;int sz = 1 << nbase;a.resize(sz, 0);b.resize(sz, 0);ntt(a);ntt(b);Mint inv_sz = Mint(1) / sz;for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;intt(a, false);a.resize(need);return a;}};template< typename Mint >vector< Mint > NumberTheoreticTransformFriendlyModInt< Mint >::dw = vector< Mint >();template< typename Mint >vector< Mint > NumberTheoreticTransformFriendlyModInt< Mint >::idw = vector< Mint >();template< typename Mint >int NumberTheoreticTransformFriendlyModInt< Mint >::max_base = 0;template< typename Mint >Mint NumberTheoreticTransformFriendlyModInt< Mint >::root = Mint();template< typename T >struct FormalPowerSeriesFriendlyNTT : vector< T > {using vector< T >::vector;using P = FormalPowerSeriesFriendlyNTT;using NTT = NumberTheoreticTransformFriendlyModInt< T >;P pre(int deg) const {return P(begin(*this), begin(*this) + min((int) this->size(), deg));}P rev(int deg = -1) const {P ret(*this);if(deg != -1) ret.resize(deg, T(0));reverse(begin(ret), end(ret));return ret;}void shrink() {while(this->size() && this->back() == T(0)) this->pop_back();}P operator+(const P &r) const { return P(*this) += r; }P operator+(const T &v) const { return P(*this) += v; }P operator-(const P &r) const { return P(*this) -= r; }P operator-(const T &v) const { return P(*this) -= v; }P operator*(const P &r) const { return P(*this) *= r; }P operator*(const T &v) const { return P(*this) *= v; }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) {if(r.size() > this->size()) this->resize(r.size());for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];return *this;}P &operator-=(const P &r) {if(r.size() > this->size()) this->resize(r.size());for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];return *this;}// https://judge.yosupo.jp/problem/convolution_modP &operator*=(const P &r) {if(this->empty() || r.empty()) {this->clear();return *this;}auto ret = NTT::multiply(*this, r);return *this = {begin(ret), end(ret)};}P &operator/=(const P &r) {if(this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);}P &operator%=(const P &r) {*this -= *this / r * r;shrink();return *this;}// https://judge.yosupo.jp/problem/division_of_polynomialspair< P, P > div_mod(const P &r) {P q = *this / r;P x = *this - q * r;x.shrink();return make_pair(q, x);}P operator-() const {P ret(this->size());for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];return ret;}P &operator+=(const T &r) {if(this->empty()) this->resize(1);(*this)[0] += r;return *this;}P &operator-=(const T &r) {if(this->empty()) this->resize(1);(*this)[0] -= r;return *this;}P &operator*=(const T &v) {for(int i = 0; i < this->size(); i++) (*this)[i] *= v;return *this;}P dot(P r) const {P ret(min(this->size(), r.size()));for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}P operator>>(int sz) const {if(this->size() <= sz) return {};P ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}P operator<<(int sz) const {P ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}T operator()(T x) const {T r = 0, w = 1;for(auto &v : *this) {r += w * v;w *= x;}return r;}P diff() const {const int n = (int) this->size();P ret(max(0, n - 1));for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);return ret;}P integral() const {const int n = (int) this->size();P ret(n + 1);ret[0] = T(0);for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);return ret;}// https://judge.yosupo.jp/problem/inv_of_formal_power_series// F(0) must not be 0P inv(int deg = -1) const {assert(((*this)[0]) != T(0));const int n = (int) this->size();if(deg == -1) deg = n;P res(deg);res[0] = {T(1) / (*this)[0]};for(int d = 1; d < deg; d <<= 1) {P f(2 * d), g(2 * d);for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j];for(int j = 0; j < d; j++) g[j] = res[j];NTT::ntt(f);NTT::ntt(g);f = f.dot(g);NTT::intt(f);for(int j = 0; j < d; j++) f[j] = 0;NTT::ntt(f);for(int j = 0; j < 2 * d; j++) f[j] *= g[j];NTT::intt(f);for(int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];}return res;}// https://judge.yosupo.jp/problem/log_of_formal_power_series// F(0) must be 1P log(int deg = -1) const {assert((*this)[0] == T(1));const int n = (int) this->size();if(deg == -1) deg = n;return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}// https://judge.yosupo.jp/problem/sqrt_of_formal_power_seriesP sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {const int n = (int) this->size();if(deg == -1) deg = n;if((*this)[0] == T(0)) {for(int i = 1; i < n; i++) {if((*this)[i] != T(0)) {if(i & 1) return {};if(deg - i / 2 <= 0) break;auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);if(ret.empty()) return {};ret = ret << (i / 2);if(ret.size() < deg) ret.resize(deg, T(0));return ret;}}return P(deg, 0);}auto sqr = T(get_sqrt((*this)[0]));if(sqr * sqr != (*this)[0]) return {};P ret{sqr};T inv2 = T(1) / T(2);for(int i = 1; i < deg; i <<= 1) {ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;}return ret.pre(deg);}P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const {return sqrt(deg, get_sqrt);}// https://judge.yosupo.jp/problem/exp_of_formal_power_series// F(0) must be 0P exp(int deg = -1) const {if(deg == -1) deg = this->size();assert((*this)[0] == T(0));P inv;inv.reserve(deg + 1);inv.push_back(T(0));inv.push_back(T(1));auto inplace_integral = [&](P &F) -> void {const int n = (int) F.size();auto mod = T::get_mod();while((int) inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), T(0));for(int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_diff = [](P &F) -> void {if(F.empty()) return;F.erase(begin(F));T coeff = 1, one = 1;for(int i = 0; i < (int) F.size(); i++) {F[i] *= coeff;coeff += one;}};P b{1, 1 < (int) this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for(int m = 2; m < deg; m *= 2) {auto y = b;y.resize(2 * m);NTT::ntt(y);z1 = z2;P z(m);for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i];NTT::intt(z);fill(begin(z), begin(z) + m / 2, T(0));NTT::ntt(z);for(int i = 0; i < m; ++i) z[i] *= -z1[i];NTT::intt(z);c.insert(end(c), begin(z) + m / 2, end(z));z2 = c;z2.resize(2 * m);NTT::ntt(z2);P x(begin(*this), begin(*this) + min< int >(this->size(), m));inplace_diff(x);x.push_back(T(0));NTT::ntt(x);for(int i = 0; i < m; ++i) x[i] *= y[i];NTT::intt(x);x -= b.diff();x.resize(2 * m);for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = T(0);NTT::ntt(x);for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i];NTT::intt(x);x.pop_back();inplace_integral(x);for(int i = m; i < min< int >(this->size(), 2 * m); ++i) x[i] += (*this)[i];fill(begin(x), begin(x) + m, T(0));NTT::ntt(x);for(int i = 0; i < 2 * m; ++i) x[i] *= y[i];NTT::intt(x);b.insert(end(b), begin(x) + m, end(x));}return P{begin(b), begin(b) + deg};}// https://judge.yosupo.jp/problem/pow_of_formal_power_seriesP pow(int64_t k, int deg = -1) const {const int n = (int) this->size();if(deg == -1) deg = n;for(int i = 0; i < n; i++) {if((*this)[i] != T(0)) {T rev = T(1) / (*this)[i];P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));if(i * k > deg) return P(deg, T(0));ret = (ret << (i * k)).pre(deg);if(ret.size() < deg) ret.resize(deg, T(0));return ret;}}return *this;}P mod_pow(int64_t k, P g) const {P modinv = g.rev().inv();auto get_div = [&](P base) {if(base.size() < g.size()) {base.clear();return base;}int n = base.size() - g.size() + 1;return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);};P x(*this), ret{1};while(k > 0) {if(k & 1) {ret *= x;ret -= get_div(ret) * g;ret.shrink();}x *= x;x -= get_div(x) * g;x.shrink();k >>= 1;}return ret;}// https://judge.yosupo.jp/problem/polynomial_taylor_shiftP taylor_shift(T c) const {int n = (int) this->size();vector< T > fact(n), rfact(n);fact[0] = rfact[0] = T(1);for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i);rfact[n - 1] = T(1) / fact[n - 1];for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i);P p(*this);for(int i = 0; i < n; i++) p[i] *= fact[i];p = p.rev();P bs(n, T(1));for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];p = (p * bs).pre(n);p = p.rev();for(int i = 0; i < n; i++) p[i] *= rfact[i];return p;}};using FPS = FormalPowerSeriesFriendlyNTT< MOD >;// usage:// FPS f, g;// f.reserve(s+1);// g.reserve(s+1);// rep(j,s+1) {// f.emplace_back(dpa[i][j]);// g.emplace_back(dpb[n-i][j]);// }// auto h = f*g;// multiply functionsvoid Main(){ll n;cin >> n;V<ll> a(n);ll t = 0;rep(i,n) {cin >> a[i];t += a[i];}MOD ans = MOD(2).pow(n-1) * t;ll M = 999630629;if (t>=M) {ll m = t - M;V<FPS> fs;using PI = P<ll,ll>;priority_queue<PI, V<PI>, greater<PI>> q;for (auto v : a) q.emplace(v,1);while (q.size()>=2) {auto [s,i] = q.top();q.pop();auto [t,j] = q.top();q.pop();fs[i] = fs[i] * fs[j];int ss = fs[i].size();if (ss>m) rep(i,ss-m) fs[i].pop_back();q.push(make_pair(fs[i].size(), i));// cout << i spa j spa fs[i].size() << endl;}auto [ss,ii] = q.top();auto f = fs[ii];MOD val = 0;rep(i,m+1) val += f[i];ans -= MOD(M) * val;}cout << ans << "\n";}int main(void){std::ifstream in("tmp_in");if (TEST) {std::cin.rdbuf(in.rdbuf());std::cout << std::fixed << std::setprecision(15);} else {std::cin.tie(nullptr);std::ios_base::sync_with_stdio(false);std::cout << std::fixed << std::setprecision(15);}Main();}