結果
問題 | No.2360 Path to Integer |
ユーザー |
|
提出日時 | 2023-12-06 11:58:32 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 63 ms / 2,500 ms |
コード長 | 35,835 bytes |
コンパイル時間 | 8,221 ms |
コンパイル使用メモリ | 353,440 KB |
実行使用メモリ | 22,376 KB |
最終ジャッジ日時 | 2024-09-27 01:13:06 |
合計ジャッジ時間 | 9,392 ms |
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 * 2 |
other | AC * 15 |
ソースコード
#ifdef ONLINE_JUDGE#pragma GCC optimize("Ofast,unroll-loops")#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")#endif#include <bits/stdc++.h>#include <ext/rope>#include <ext/pb_ds/assoc_container.hpp>#include <ext/pb_ds/hash_policy.hpp>#include <ext/pb_ds/tree_policy.hpp>#include <ext/pb_ds/trie_policy.hpp>#include <ext/pb_ds/priority_queue.hpp>using namespace std;using namespace __gnu_cxx;using namespace __gnu_pbds;template <class T> using pbds_set = tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;using Trie = trie<string, null_type, trie_string_access_traits<>, pat_trie_tag, trie_prefix_search_node_update>;// template <class T> using heapq = __gnu_pbds::priority_queue<T, greater<T>, pairing_heap_tag>;template <class T> using heapq = std::priority_queue<T, vector<T>, greater<T>>;using ll = long long;using u32 = unsigned int;using u64 = unsigned long long;using i128 = __int128;using u128 = __uint128_t;using f128 = __float128;using ld = long double;using ui = unsigned int;using ull = unsigned long long;using pii = pair<int, int>;using pll = pair<ll, ll>;using pdd = pair<ld, ld>;using vi = vector<int>;using vvi = vector<vector<int>>;using vll = vector<ll>;using vvll = vector<vector<ll>>;using vpii = vector<pii>;using vpll = vector<pll>;template <class T>constexpr T infty = 0;template <>constexpr int infty<int> = 1'000'000'000;template <>constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;template <>constexpr u32 infty<u32> = infty<int>;template <>constexpr u64 infty<u64> = infty<ll>;template <>constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;template <>constexpr double infty<double> = infty<ll>;template <>constexpr long double infty<long double> = infty<ll>;template <class T>using vc = vector<T>;template <class T>using vvc = vector<vc<T>>;template <class T>using vvvc = vector<vvc<T>>;template <class T>using vvvvc = vector<vvvc<T>>;template <class T>using vvvvvc = vector<vvvvc<T>>;template <class T>using pq = std::priority_queue<T>;template <class T>using pqg = std::priority_queue<T, vector<T>, greater<T>>;#define vv(type, name, h, ...) \vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) \vector<vector<vector<type>>> name( \h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...) \vector<vector<vector<vector<type>>>> name( \a, vector<vector<vector<type>>>( \b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))#define lb lower_bound#define ub upper_bound#define pb push_back#define pf push_front#define eb emplace_back#define fi first#define se second#define overload4(_1, _2, _3, _4, name, ...) name#define overload3(_1, _2, _3, name, ...) name#define rep1(n) for(ll _ = 0; _ < n; ++_)#define rep2(i, n) for(ll i = 0; i < n; ++i)#define rep3(i, a, b) for(ll i = a; i < b; ++i)#define rep4(i, a, b, c) for(int i = a; i < b; i += c)#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1) (__VA_ARGS__)#define rrep1(n) for(ll i = n; i--; )#define rrep2(i, n) for(ll i = n; i--; )#define rrep3(i, a, b) for(ll i = a; i > b; i--)#define rrep4(i, a, b, c) for(ll i = a; i > b; i -= c)#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1) (__VA_ARGS__)#define each1(i, a) for(auto&& i : a)#define each2(x, y, a) for(auto&& [x, y] : a)#define each3(x, y, z, a) for(auto&& [x, y, z] : a)#define each(...) overload4(__VA_ARGS__, each3, each2, each1) (__VA_ARGS__)#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1) (__VA_ARGS__)#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R) (__VA_ARGS__)#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))#define len(x) (int)x.size()#define elif else if#define all1(i) begin(i), end(i)#define all2(i, a) begin(i), begin(i) + a#define all3(i, a, b) begin(i) + a, begin(i) + b#define all(...) overload3(__VA_ARGS__, all3, all2, all1) (__VA_ARGS__)#define rall1(i) rbegin(i), rend(i)#define rall2(i, a) rbegin(i), rbegin(i) + a#define rall3(i, a, b) rbegin(i) + a, rbegin(i) + b#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1) (__VA_ARGS__)#define mst(x, a) memset(x, a, sizeof(x))#define bitcnt(x) (__builtin_popcountll(x))#define endl "\n"#define MIN(v) *min_element(all(v))#define MAX(v) *max_element(all(v))#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()#define SORT(a) sort(all(a))#define REV(a) reverse(all(a))int popcnt(int x) { return __builtin_popcount(x); }int popcnt(u32 x) { return __builtin_popcount(x); }int popcnt(ll x) { return __builtin_popcountll(x); }int popcnt(u64 x) { return __builtin_popcountll(x); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template<class T> auto max(const T& a){ return *max_element(all(a)); }template<class T> auto min(const T& a){ return *min_element(all(a)); }template <typename T, typename U>T ceil(T x, U y) {return (x > 0 ? (x + y - 1) / y : x / y);}template <typename T, typename U>T floor(T x, U y) {return (x > 0 ? x / y : (x - y + 1) / y);}template <typename T, typename U>pair<T, T> divmod(T x, U y) {T q = floor(x, y);return {q, x - q * y};}template <typename T, typename U>T SUM(const vector<U> &A) {T sum = 0;for (auto &&a: A) sum += a;return sum;}template <typename T, typename U>vector<T> cumsum(vector<U> &A, int off = 1) {int N = A.size();vector<T> B(N + 1);for (int i = 0; i < N; i++) B[i + 1] = B[i] + A[i];if (off == 0) B.erase(B.begin());return B;}template <typename T>vector<int> argsort(const vector<T> &A) {vector<int> ids(len(A));iota(all(ids), 0);sort(all(ids),[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });return ids;}template <typename T>vc<T> rearrange(const vc<T> &A, const vc<int> &I) {vc<T> B(len(I));FOR(i, len(I)) B[i] = A[I[i]];return B;}template <typename T>T POP(deque<T> &que) {T a = que.front();que.pop_front();return a;}template <typename T>T POP(pq<T> &que) {T a = que.top();que.pop();return a;}template <typename T>T POP(pqg<T> &que) {assert(!que.empty());T a = que.top();que.pop();return a;}template <typename T>T POP(vc<T> &que) {assert(!que.empty());T a = que.back();que.pop_back();return a;}template <typename F>ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {if (check_ok) assert(check(ok));while (abs(ok - ng) > 1) {auto x = (ng + ok) / 2;(check(x) ? ok : ng) = x;}return ok;}template <typename F>double binary_search_real(F check, double ok, double ng, int iter = 100) {while (iter--) {double x = (ok + ng) / 2;(check(x) ? ok : ng) = x;}return (ok + ng) / 2;}template <class T, class S> inline bool chmax(T &a, const S &b) {return (a < b ? a = b, 1 : 0);}template <class T, class S> inline bool chmin(T &a, const S &b) {return (a > b ? a = b, 1 : 0);}mt19937 rng( chrono::steady_clock::now().time_since_epoch().count() );#define Ran(a, b) rng() % ( (b) - (a) + 1 ) + (a)struct custom_hash {static uint64_t splitmix64(uint64_t x) {// http://xorshift.di.unimi.it/splitmix64.cx += 0x9e3779b97f4a7c15;x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;x = (x ^ (x >> 27)) * 0x94d049bb133111eb;return x ^ (x >> 31);}size_t operator()(uint64_t x) const {static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();return splitmix64(x + FIXED_RANDOM);}size_t operator()(pair<uint64_t,uint64_t> x) const {static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();return splitmix64(x.first + FIXED_RANDOM) ^ (splitmix64(x.second + FIXED_RANDOM) >> 1);}};#define FASTIO#include <unistd.h>// https://judge.yosupo.jp/submission/21623namespace fastio {static constexpr uint32_t SZ = 1 << 17;char ibuf[SZ];char obuf[SZ];char out[100];// pointer of ibuf, obufuint32_t pil = 0, pir = 0, por = 0;struct Pre {char num[10000][4];constexpr Pre() : num() {for (int i = 0; i < 10000; i++) {int n = i;for (int j = 3; j >= 0; j--) {num[i][j] = n % 10 | '0';n /= 10;}}}} constexpr pre;inline void load() {memcpy(ibuf, ibuf + pil, pir - pil);pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);pil = 0;if (pir < SZ) ibuf[pir++] = '\n';}inline void flush() {fwrite(obuf, 1, por, stdout);por = 0;}void rd(char &c) {do {if (pil + 1 > pir) load();c = ibuf[pil++];} while (isspace(c));}void rd(string &x) {x.clear();char c;do {if (pil + 1 > pir) load();c = ibuf[pil++];} while (isspace(c));do {x += c;if (pil == pir) load();c = ibuf[pil++];} while (!isspace(c));}template <typename T>void rd_real(T &x) {string s;rd(s);x = stod(s);}template <typename T>void rd_integer(T &x) {if (pil + 100 > pir) load();char c;doc = ibuf[pil++];while (c < '-');bool minus = 0;if constexpr (is_signed<T>::value || is_same_v<T, i128>) {if (c == '-') { minus = 1, c = ibuf[pil++]; }}x = 0;while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }if constexpr (is_signed<T>::value || is_same_v<T, i128>) {if (minus) x = -x;}}void rd(int &x) { rd_integer(x); }void rd(ll &x) { rd_integer(x); }void rd(i128 &x) { rd_integer(x); }void rd(u32 &x) { rd_integer(x); }void rd(u64 &x) { rd_integer(x); }void rd(u128 &x) { rd_integer(x); }void rd(double &x) { rd_real(x); }void rd(long double &x) { rd_real(x); }void rd(f128 &x) { rd_real(x); }template <class T, class U>void rd(pair<T, U> &p) {return rd(p.first), rd(p.second);}template <size_t N = 0, typename T>void rd_tuple(T &t) {if constexpr (N < std::tuple_size<T>::value) {auto &x = std::get<N>(t);rd(x);rd_tuple<N + 1>(t);}}template <class... T>void rd(tuple<T...> &tpl) {rd_tuple(tpl);}template <size_t N = 0, typename T>void rd(array<T, N> &x) {for (auto &d: x) rd(d);}template <class T>void rd(vc<T> &x) {for (auto &d: x) rd(d);}void read() {}template <class H, class... T>void read(H &h, T &... t) {rd(h), read(t...);}void wt(const char c) {if (por == SZ) flush();obuf[por++] = c;}void wt(const string s) {for (char c: s) wt(c);}void wt(const char *s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) wt(s[i]);}template <typename T>void wt_integer(T x) {if (por > SZ - 100) flush();if (x < 0) { obuf[por++] = '-', x = -x; }int outi;for (outi = 96; x >= 10000; outi -= 4) {memcpy(out + outi, pre.num[x % 10000], 4);x /= 10000;}if (x >= 1000) {memcpy(obuf + por, pre.num[x], 4);por += 4;} else if (x >= 100) {memcpy(obuf + por, pre.num[x] + 1, 3);por += 3;} else if (x >= 10) {int q = (x * 103) >> 10;obuf[por] = q | '0';obuf[por + 1] = (x - q * 10) | '0';por += 2;} elseobuf[por++] = x | '0';memcpy(obuf + por, out + outi + 4, 96 - outi);por += 96 - outi;}template <typename T>void wt_real(T x) {ostringstream oss;oss << fixed << setprecision(15) << double(x);string s = oss.str();wt(s);}void wt(int x) { wt_integer(x); }void wt(ll x) { wt_integer(x); }void wt(i128 x) { wt_integer(x); }void wt(u32 x) { wt_integer(x); }void wt(u64 x) { wt_integer(x); }void wt(u128 x) { wt_integer(x); }void wt(double x) { wt_real(x); }void wt(long double x) { wt_real(x); }void wt(f128 x) { wt_real(x); }template <class T, class U>void wt(const pair<T, U> val) {wt(val.first);wt(' ');wt(val.second);}template <size_t N = 0, typename T>void wt_tuple(const T t) {if constexpr (N < std::tuple_size<T>::value) {if constexpr (N > 0) { wt(' '); }const auto x = std::get<N>(t);wt(x);wt_tuple<N + 1>(t);}}template <class... T>void wt(tuple<T...> tpl) {wt_tuple(tpl);}template <class T, size_t S>void wt(const array<T, S> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) wt(' ');wt(val[i]);}}template <class T>void wt(const vector<T> val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) wt(' ');wt(val[i]);}}void print() { wt('\n'); }template <class Head, class... Tail>void print(Head &&head, Tail &&... tail) {wt(head);if (sizeof...(Tail)) wt(' ');print(forward<Tail>(tail)...);}// gcc expansion. called automaticall after main.void __attribute__((destructor)) _d() { flush(); }} // namespace fastiousing fastio::read;using fastio::print;using fastio::flush;#define INT(...) \int __VA_ARGS__; \read(__VA_ARGS__)#define LL(...) \ll __VA_ARGS__; \read(__VA_ARGS__)#define U32(...) \u32 __VA_ARGS__; \read(__VA_ARGS__)#define U64(...) \u64 __VA_ARGS__; \read(__VA_ARGS__)#define STR(...) \string __VA_ARGS__; \read(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \read(__VA_ARGS__)#define DBL(...) \double __VA_ARGS__; \read(__VA_ARGS__)#define VEC(type, name, size) \vector<type> name(size); \read(name)#define VV(type, name, h, w) \vector<vector<type>> name(h, vector<type>(w)); \read(name)void YES(bool t = 1) { print(t ? "YES" : "NO"); }void NO(bool t = 1) { YES(!t); }void Yes(bool t = 1) { print(t ? "Yes" : "No"); }void No(bool t = 1) { Yes(!t); }void yes(bool t = 1) { print(t ? "yes" : "no"); }void no(bool t = 1) { yes(!t); }const i128 ONE = 1;template <typename Iterable>auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(fastio::wt(*v.begin())) {for (auto it = v.begin(); it != v.end();) {fastio::wt(*it);if (++it != v.end()) fastio::wt(sep);}fastio::wt(end);}ll gcd(ll x, ll y) {if(!x) return y;if(!y) return x;int t = __builtin_ctzll(x | y);x >>= __builtin_ctzll(x);do {y >>= __builtin_ctzll(y);if (x > y) swap(x, y);y -= x;} while (y);return x << t;}ll lcm(ll x, ll y) { return x * y / gcd(x, y); }ll exgcd(ll a, ll b, ll &x, ll &y) {if(!b) return x = 1, y = 0, a;ll d = exgcd(b, a % b, x, y);ll t = x;x = y;y = t - a / b * x;return d;}ll max(ll x, ll y) { return x > y ? x : y; }ll min(ll x, ll y) { return x < y ? x : y; }ll Mod(ll x, int mod) { return (x % mod + mod) % mod; }ll pow(ll x, ll y, ll mod){ll res = 1, cur = x;while (y) {if (y & 1) res = res * cur % mod;cur = ONE * cur * cur % mod;y >>= 1;}return res % mod;}ll probabilityMod(ll x, ll y, ll mod) {return x * pow(y, mod-2, mod) % mod;}vvi getGraph(int n, int m, bool directed = false) {vvi res(n);rep(_, 0, m) {INT(u, v);u--, v--;res[u].emplace_back(v);if(!directed) res[v].emplace_back(u);}return res;}vector<vpii> getWeightedGraph(int n, int m, bool directed = false) {vector<vpii> res(n);rep(_, 0, m) {INT(u, v, w);u--, v--;res[u].emplace_back(v, w);if(!directed) res[v].emplace_back(u, w);}return res;}template <class... Args> auto ndvector(size_t n, Args &&...args) {if constexpr (sizeof...(args) == 1) {return vector(n, args...);} else {return vector(n, ndvector(args...));}}const ll LINF = 0x1fffffffffffffff;const ll MINF = 0x7fffffffffff;const int INF = 0x3fffffff;const int MOD = 1000000007;const int MODD = 998244353;const int N = 1e6 + 10;#line 2 "mod/modint_common.hpp"struct has_mod_impl {template <class T>static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});template <class T>static auto check(...) -> std::false_type;};template <class T>class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};template <typename mint>mint inv(int n) {static const int mod = mint::get_mod();static vector<mint> dat = {0, 1};assert(0 <= n);if (n >= mod) n %= mod;while (len(dat) <= n) {int k = len(dat);int q = (mod + k - 1) / k;dat.eb(dat[k * q - mod] * mint::raw(q));}return dat[n];}template <typename mint>mint fact(int n) {static const int mod = mint::get_mod();assert(0 <= n && n < mod);static vector<mint> dat = {1, 1};while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));return dat[n];}template <typename mint>mint fact_inv(int n) {static vector<mint> dat = {1, 1};if (n < 0) return mint(0);while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));return dat[n];}template <class mint, class... Ts>mint fact_invs(Ts... xs) {return (mint(1) * ... * fact_inv<mint>(xs));}template <typename mint, class Head, class... Tail>mint multinomial(Head &&head, Tail &&... tail) {return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);}template <typename mint>mint C_dense(int n, int k) {static vvc<mint> C;static int H = 0, W = 0;auto calc = [&](int i, int j) -> mint {if (i == 0) return (j == 0 ? mint(1) : mint(0));return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);};if (W <= k) {FOR(i, H) {C[i].resize(k + 1);FOR(j, W, k + 1) { C[i][j] = calc(i, j); }}W = k + 1;}if (H <= n) {C.resize(n + 1);FOR(i, H, n + 1) {C[i].resize(W);FOR(j, W) { C[i][j] = calc(i, j); }}H = n + 1;}return C[n][k];}template <typename mint, bool large = false, bool dense = false>mint C(ll n, ll k) {assert(n >= 0);if (k < 0 || n < k) return 0;if constexpr (dense) return C_dense<mint>(n, k);if constexpr (!large) return multinomial<mint>(n, k, n - k);k = min(k, n - k);mint x(1);FOR(i, k) x *= mint(n - i);return x * fact_inv<mint>(k);}template <typename mint, bool large = false>mint C_inv(ll n, ll k) {assert(n >= 0);assert(0 <= k && k <= n);if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);return mint(1) / C<mint, 1>(n, k);}// [x^d](1-x)^{-n}template <typename mint, bool large = false, bool dense = false>mint C_negative(ll n, ll d) {assert(n >= 0);if (d < 0) return mint(0);if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }return C<mint, large, dense>(n + d - 1, d);}#line 3 "mod/modint.hpp"template <int mod>struct modint {static constexpr u32 umod = u32(mod);static_assert(umod < u32(1) << 31);u32 val;static modint raw(u32 v) {modint x;x.val = v;return x;}constexpr modint() : val(0) {}constexpr modint(u32 x) : val(x % umod) {}constexpr modint(u64 x) : val(x % umod) {}constexpr modint(u128 x) : val(x % umod) {}constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};bool operator<(const modint &other) const { return val < other.val; }modint &operator+=(const modint &p) {if ((val += p.val) >= umod) val -= umod;return *this;}modint &operator-=(const modint &p) {if ((val += umod - p.val) >= umod) val -= umod;return *this;}modint &operator*=(const modint &p) {val = u64(val) * p.val % umod;return *this;}modint &operator/=(const modint &p) {*this *= p.inverse();return *this;}modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }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 val == p.val; }bool operator!=(const modint &p) const { return val != p.val; }modint inverse() const {int a = val, 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(ll n) const {assert(n >= 0);modint ret(1), mul(val);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}static constexpr int get_mod() { return mod; }// (n, r), r は 1 の 2^n 乗根static constexpr pair<int, int> ntt_info() {if (mod == 120586241) return {20, 74066978};if (mod == 167772161) return {25, 17};if (mod == 469762049) return {26, 30};if (mod == 754974721) return {24, 362};if (mod == 880803841) return {23, 211};if (mod == 943718401) return {22, 663003469};if (mod == 998244353) return {23, 31};if (mod == 1045430273) return {20, 363};if (mod == 1051721729) return {20, 330};if (mod == 1053818881) return {20, 2789};return {-1, -1};}static constexpr bool can_ntt() { return ntt_info().fi != -1; }};#ifdef FASTIOtemplate <int mod>void rd(modint<mod> &x) {fastio::rd(x.val);assert(0 <= x.val && x.val < mod);}template <int mod>void wt(modint<mod> x) {fastio::wt(x.val);}#endifusing modint107 = modint<1000000007>;using modint998 = modint<998244353>;#line 2 "graph/base.hpp"template <typename T>struct Edge {int frm, to;T cost;int id;};template <typename T = int, bool directed = false>struct Graph {static constexpr bool is_directed = directed;int N, M;using cost_type = T;using edge_type = Edge<T>;vector<edge_type> edges;vector<int> indptr;vector<edge_type> csr_edges;vc<int> vc_deg, vc_indeg, vc_outdeg;bool prepared;class OutgoingEdges {public:OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}const edge_type* begin() const {if (l == r) { return 0; }return &G->csr_edges[l];}const edge_type* end() const {if (l == r) { return 0; }return &G->csr_edges[r];}private:const Graph* G;int l, r;};bool is_prepared() { return prepared; }Graph() : N(0), M(0), prepared(0) {}Graph(int N) : N(N), M(0), prepared(0) {}void build(int n) {N = n, M = 0;prepared = 0;edges.clear();indptr.clear();csr_edges.clear();vc_deg.clear();vc_indeg.clear();vc_outdeg.clear();}void add(int frm, int to, T cost = 1, int i = -1) {assert(!prepared);assert(0 <= frm && 0 <= to && to < N);if (i == -1) i = M;auto e = edge_type({frm, to, cost, i});edges.eb(e);++M;}#ifdef FASTIO// wt, offvoid read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }void read_graph(int M, bool wt = false, int off = 1) {for (int m = 0; m < M; ++m) {INT(a, b);a -= off, b -= off;if (!wt) {add(a, b);} else {T c;read(c);add(a, b, c);}}build();}#endifvoid build() {assert(!prepared);prepared = true;indptr.assign(N + 1, 0);for (auto&& e: edges) {indptr[e.frm + 1]++;if (!directed) indptr[e.to + 1]++;}for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }auto counter = indptr;csr_edges.resize(indptr.back() + 1);for (auto&& e: edges) {csr_edges[counter[e.frm]++] = e;if (!directed)csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});}}OutgoingEdges operator[](int v) const {assert(prepared);return {this, indptr[v], indptr[v + 1]};}vc<int> deg_array() {if (vc_deg.empty()) calc_deg();return vc_deg;}pair<vc<int>, vc<int>> deg_array_inout() {if (vc_indeg.empty()) calc_deg_inout();return {vc_indeg, vc_outdeg};}int deg(int v) {if (vc_deg.empty()) calc_deg();return vc_deg[v];}int in_deg(int v) {if (vc_indeg.empty()) calc_deg_inout();return vc_indeg[v];}int out_deg(int v) {if (vc_outdeg.empty()) calc_deg_inout();return vc_outdeg[v];}#ifdef FASTIOvoid debug() {print("Graph");if (!prepared) {print("frm to cost id");for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);} else {print("indptr", indptr);print("frm to cost id");FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);}}#endifvc<int> new_idx;vc<bool> used_e;// G における頂点 V[i] が、新しいグラフで i になるようにする// {G, es}Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {if (len(new_idx) != N) new_idx.assign(N, -1);if (len(used_e) != M) used_e.assign(M, 0);int n = len(V);FOR(i, n) new_idx[V[i]] = i;Graph<T, directed> G(n);vc<int> history;FOR(i, n) {for (auto&& e: (*this)[V[i]]) {if (used_e[e.id]) continue;int a = e.frm, b = e.to;if (new_idx[a] != -1 && new_idx[b] != -1) {history.eb(e.id);used_e[e.id] = 1;int eid = (keep_eid ? e.id : -1);G.add(new_idx[a], new_idx[b], e.cost, eid);}}}FOR(i, n) new_idx[V[i]] = -1;for (auto&& eid: history) used_e[eid] = 0;G.build();return G;}private:void calc_deg() {assert(vc_deg.empty());vc_deg.resize(N);for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;}void calc_deg_inout() {assert(vc_indeg.empty());vc_indeg.resize(N);vc_outdeg.resize(N);for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }}};#line 2 "graph/tree.hpp"#line 4 "graph/tree.hpp"// HLD euler tour をとっていろいろ。template <typename GT>struct Tree {using Graph_type = GT;GT &G;using WT = typename GT::cost_type;int N;vector<int> LID, RID, head, V, parent, VtoE;vc<int> depth;vc<WT> depth_weighted;Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); }void build(int r = 0, bool hld = 1) {if (r == -1) return; // build を遅延したいときN = G.N;LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r);V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);depth.assign(N, -1), depth_weighted.assign(N, 0);assert(G.is_prepared());int t1 = 0;dfs_sz(r, -1, hld);dfs_hld(r, t1);}void dfs_sz(int v, int p, bool hld) {auto &sz = RID;parent[v] = p;depth[v] = (p == -1 ? 0 : depth[p] + 1);sz[v] = 1;int l = G.indptr[v], r = G.indptr[v + 1];auto &csr = G.csr_edges;// 使う辺があれば先頭にするfor (int i = r - 2; i >= l; --i) {if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);}int hld_sz = 0;for (int i = l; i < r; ++i) {auto e = csr[i];if (depth[e.to] != -1) continue;depth_weighted[e.to] = depth_weighted[v] + e.cost;VtoE[e.to] = e.id;dfs_sz(e.to, v, hld);sz[v] += sz[e.to];if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }}}void dfs_hld(int v, int ×) {LID[v] = times++;RID[v] += LID[v];V[LID[v]] = v;bool heavy = true;for (auto &&e: G[v]) {if (depth[e.to] <= depth[v]) continue;head[e.to] = (heavy ? head[v] : e.to);heavy = false;dfs_hld(e.to, times);}}vc<int> heavy_path_at(int v) {vc<int> P = {v};while (1) {int a = P.back();for (auto &&e: G[a]) {if (e.to != parent[a] && head[e.to] == v) {P.eb(e.to);break;}}if (P.back() == a) break;}return P;}int heavy_child(int v) {int k = LID[v] + 1;if (k == N) return -1;int w = V[k];return (parent[w] == v ? w : -1);}int e_to_v(int eid) {auto e = G.edges[eid];return (parent[e.frm] == e.to ? e.frm : e.to);}int v_to_e(int v) { return VtoE[v]; }int ELID(int v) { return 2 * LID[v] - depth[v]; }int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }// 目標地点へ進む個数が kint LA(int v, int k) {assert(k <= depth[v]);while (1) {int u = head[v];if (LID[v] - k >= LID[u]) return V[LID[v] - k];k -= LID[v] - LID[u] + 1;v = parent[u];}}int la(int u, int v) { return LA(u, v); }int LCA(int u, int v) {for (;; v = parent[head[v]]) {if (LID[u] > LID[v]) swap(u, v);if (head[u] == head[v]) return u;}}// root を根とした場合の lcaint LCA_root(int u, int v, int root) {return LCA(u, v) ^ LCA(u, root) ^ LCA(v, root);}int lca(int u, int v) { return LCA(u, v); }int lca_root(int u, int v, int root) { return LCA_root(u, v, root); }int subtree_size(int v, int root = -1) {if (root == -1) return RID[v] - LID[v];if (v == root) return N;int x = jump(v, root, 1);if (in_subtree(v, x)) return RID[v] - LID[v];return N - RID[x] + LID[x];}int dist(int a, int b) {int c = LCA(a, b);return depth[a] + depth[b] - 2 * depth[c];}WT dist_weighted(int a, int b) {int c = LCA(a, b);return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];}// a is in bbool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }int jump(int a, int b, ll k) {if (k == 1) {if (a == b) return -1;return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);}int c = LCA(a, b);int d_ac = depth[a] - depth[c];int d_bc = depth[b] - depth[c];if (k > d_ac + d_bc) return -1;if (k <= d_ac) return LA(a, k);return LA(b, d_ac + d_bc - k);}vc<int> collect_child(int v) {vc<int> res;for (auto &&e: G[v])if (e.to != parent[v]) res.eb(e.to);return res;}vc<int> collect_light(int v) {vc<int> res;bool skip = true;for (auto &&e: G[v])if (e.to != parent[v]) {if (!skip) res.eb(e.to);skip = false;}return res;}vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {// [始点, 終点] の"閉"区間列。vc<pair<int, int>> up, down;while (1) {if (head[u] == head[v]) break;if (LID[u] < LID[v]) {down.eb(LID[head[v]], LID[v]);v = parent[head[v]];} else {up.eb(LID[u], LID[head[u]]);u = parent[head[u]];}}if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);reverse(all(down));up.insert(up.end(), all(down));return up;}vc<int> restore_path(int u, int v) {vc<int> P;for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {if (a <= b) {FOR(i, a, b + 1) P.eb(V[i]);} else {FOR_R(i, b, a + 1) P.eb(V[i]);}}return P;}};#line 4 "graph/tree_dp/rerooting_dp.hpp"template <typename TREE, typename Data>struct Rerooting_dp {static_assert(!TREE::Graph_type::is_directed);TREE& tree;vc<Data> dp_1; // 辺 pv に対して、部分木 vvc<Data> dp_2; // 辺 pv に対して、部分木 pvc<Data> dp; // full treetemplate <typename F1, typename F2, typename F3>Rerooting_dp(TREE& tree, F1 f_ee, F2 f_ev, F3 f_ve, const Data unit): tree(tree) {build(f_ee, f_ev, f_ve, unit);}// v を根としたときの full treeData operator[](int v) { return dp[v]; }// root を根としたときの部分木 vData get(int v, int root) {if (root == v) return dp[v];if (!tree.in_subtree(root, v)) { return dp_1[v]; }int w = tree.jump(v, root, 1);return dp_2[w];}template <typename F1, typename F2, typename F3>void build(F1 f_ee, F2 f_ev, F3 f_ve, const Data unit) {int N = tree.N;// dp1: subtreedp_1.assign(N, unit);FOR_R(i, N) {int v = tree.V[i];for (auto&& e: tree.G[v]) {if (e.to == tree.parent[v]) continue;dp_1[v] = f_ee(dp_1[v], f_ve(dp_1[e.to], e));}dp_1[v] = f_ev(dp_1[v], v);}// dp2[v]: subtree of p, rooted at vdp_2.assign(N, unit);// dp[v]: fulltree, rooted at vdp.assign(N, unit);FOR(i, N) {int p = tree.V[i];vc<int> ch;vc<Data> ch_data;Data x = unit;for (auto&& e: tree.G[p]) {if (e.to == tree.parent[p]) {x = f_ve(dp_2[p], e);} else {ch.eb(e.to);ch_data.eb(f_ve(dp_1[e.to], e));}}int n = len(ch);if (!n) {dp[p] = f_ev(x, p);continue;}vc<Data> prod_left(n, x);FOR(i, n - 1) prod_left[i + 1] = f_ee(prod_left[i], ch_data[i]);Data prod_right = unit;FOR_R(i, n) {dp_2[ch[i]] = f_ev(f_ee(prod_left[i], prod_right), p);prod_right = f_ee(prod_right, ch_data[i]);}dp[p] = f_ev(f_ee(x, prod_right), p);}}};using mint = modint998;void solve() {INT(n);VEC(ll, a, n);Graph G(n);G.read_tree();Tree tree(G);using Data = pair<mint, mint>;Data unit = {mint(0), mint(0)};auto fee = [&](Data x, Data y) -> Data {return {x.fi + y.fi, x.se + y.se};};auto fev = [&](Data x, int v) -> Data {return {x.fi + 1, x.se * mint(10).pow(len(to_string(a[v]))) + mint(a[v]) * (x.fi + 1)};};auto fve = [&](Data x, auto& e) -> Data {return x;};Rerooting_dp<decltype(tree), Data> dp(tree, fee, fev, fve, unit);mint ans = 0;rep(i, n) ans += dp[i].se;print(ans);}signed main() {int T = 1;// read(T);while (T--) {solve();}return 0;}