結果
問題 | No.2360 Path to Integer |
ユーザー |
|
提出日時 | 2023-06-23 23:12:48 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 88 ms / 2,500 ms |
コード長 | 28,166 bytes |
コンパイル時間 | 3,090 ms |
コンパイル使用メモリ | 329,444 KB |
最終ジャッジ日時 | 2025-02-15 01:31:54 |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 15 |
ソースコード
#include <bits/stdc++.h>#ifdef _MSC_VER# include <intrin.h>#else# include <x86intrin.h>#endif#include <limits>#include <type_traits>namespace suisen {// ! utilitytemplate <typename ...Types>using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;template <bool cond_v, typename Then, typename OrElse>constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {if constexpr (cond_v) {return std::forward<Then>(then);} else {return std::forward<OrElse>(or_else);}}// ! functiontemplate <typename ReturnType, typename Callable, typename ...Args>using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;template <typename F, typename T>using is_uni_op = is_same_as_invoke_result<T, F, T>;template <typename F, typename T>using is_bin_op = is_same_as_invoke_result<T, F, T, T>;template <typename Comparator, typename T>using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;// ! integraltemplate <typename T, typename = constraints_t<std::is_integral<T>>>constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;template <typename T, unsigned int n>struct is_nbit { static constexpr bool value = bit_num<T> == n; };template <typename T, unsigned int n>static constexpr bool is_nbit_v = is_nbit<T, n>::value;// ?template <typename T>struct safely_multipliable {};template <>struct safely_multipliable<int> { using type = long long; };template <>struct safely_multipliable<long long> { using type = __int128_t; };template <>struct safely_multipliable<unsigned int> { using type = unsigned long long; };template <>struct safely_multipliable<unsigned long int> { using type = __uint128_t; };template <>struct safely_multipliable<unsigned long long> { using type = __uint128_t; };template <>struct safely_multipliable<float> { using type = float; };template <>struct safely_multipliable<double> { using type = double; };template <>struct safely_multipliable<long double> { using type = long double; };template <typename T>using safely_multipliable_t = typename safely_multipliable<T>::type;template <typename T, typename = void>struct rec_value_type {using type = T;};template <typename T>struct rec_value_type<T, std::void_t<typename T::value_type>> {using type = typename rec_value_type<typename T::value_type>::type;};template <typename T>using rec_value_type_t = typename rec_value_type<T>::type;} // namespace suisen// ! type aliasesusing i128 = __int128_t;using u128 = __uint128_t;template <typename T>using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;// ! macros (internal)#define DETAIL_OVERLOAD2(_1,_2,name,...) name#define DETAIL_OVERLOAD3(_1,_2,_3,name,...) name#define DETAIL_OVERLOAD4(_1,_2,_3,_4,name,...) name#define DETAIL_REP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))#define DETAIL_REP3(i,l,r) DETAIL_REP4(i,l,r,1)#define DETAIL_REP2(i,n) DETAIL_REP3(i,0,n)#define DETAIL_REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))#define DETAIL_REPINF2(i,l) DETAIL_REPINF3(i,l,1)#define DETAIL_REPINF1(i) DETAIL_REPINF2(i,0)#define DETAIL_RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))#define DETAIL_RREP3(i,l,r) DETAIL_RREP4(i,l,r,1)#define DETAIL_RREP2(i,n) DETAIL_RREP3(i,0,n)#define DETAIL_CAT_I(a, b) a##b#define DETAIL_CAT(a, b) DETAIL_CAT_I(a, b)#define DETAIL_UNIQVAR(tag) DETAIL_CAT(tag, __LINE__)// ! macros#define REP(...) DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_REP4 , DETAIL_REP3 , DETAIL_REP2 )(__VA_ARGS__)#define RREP(...) DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_RREP4 , DETAIL_RREP3 , DETAIL_RREP2 )(__VA_ARGS__)#define REPINF(...) DETAIL_OVERLOAD3(__VA_ARGS__, DETAIL_REPINF3, DETAIL_REPINF2, DETAIL_REPINF1)(__VA_ARGS__)#define LOOP(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> DETAIL_UNIQVAR(loop_variable) = n; DETAIL_UNIQVAR(loop_variable) --> 0;)#define ALL(iterable) std::begin(iterable), std::end(iterable)#define INPUT(type, ...) type __VA_ARGS__; read(__VA_ARGS__)// ! debug#ifdef LOCAL# define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)template <class T, class... Args>void debug_internal(const char* s, T&& first, Args&&... args) {constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);((std::cerr << ", " << std::forward<Args>(args)), ...);std::cerr << close_brakets << "\n";}#else# define debug(...) void(0)#endif// ! I/O utilities// __int128_tstd::ostream& operator<<(std::ostream& dest, __int128_t value) {std::ostream::sentry s(dest);if (s) {__uint128_t tmp = value < 0 ? -value : value;char buffer[128];char* d = std::end(buffer);do {--d;*d = "0123456789"[tmp % 10];tmp /= 10;} while (tmp != 0);if (value < 0) {--d;*d = '-';}int len = std::end(buffer) - d;if (dest.rdbuf()->sputn(d, len) != len) {dest.setstate(std::ios_base::badbit);}}return dest;}// __uint128_tstd::ostream& operator<<(std::ostream& dest, __uint128_t value) {std::ostream::sentry s(dest);if (s) {char buffer[128];char* d = std::end(buffer);do {--d;*d = "0123456789"[value % 10];value /= 10;} while (value != 0);int len = std::end(buffer) - d;if (dest.rdbuf()->sputn(d, len) != len) {dest.setstate(std::ios_base::badbit);}}return dest;}// pairtemplate <typename T, typename U>std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {return out << a.first << ' ' << a.second;}// tupletemplate <unsigned int N = 0, typename ...Args>std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& a) {if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return out;else {out << std::get<N>(a);if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) out << ' ';return operator<<<N + 1>(out, a);}}// vectortemplate <typename T>std::ostream& operator<<(std::ostream& out, const std::vector<T>& a) {for (auto it = a.begin(); it != a.end();) {out << *it;if (++it != a.end()) out << ' ';}return out;}// arraytemplate <typename T, size_t N>std::ostream& operator<<(std::ostream& out, const std::array<T, N>& a) {for (auto it = a.begin(); it != a.end();) {out << *it;if (++it != a.end()) out << ' ';}return out;}inline void print() { std::cout << '\n'; }template <typename Head, typename... Tail>inline void print(const Head& head, const Tail &...tails) {std::cout << head;if (sizeof...(tails)) std::cout << ' ';print(tails...);}template <typename Iterable>auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {for (auto it = v.begin(); it != v.end();) {std::cout << *it;if (++it != v.end()) std::cout << sep;}std::cout << end;}__int128_t stoi128(const std::string& s) {__int128_t ret = 0;for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';if (s[0] == '-') ret = -ret;return ret;}__uint128_t stou128(const std::string& s) {__uint128_t ret = 0;for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';return ret;}// __int128_tstd::istream& operator>>(std::istream& in, __int128_t& v) {std::string s;in >> s;v = stoi128(s);return in;}// __uint128_tstd::istream& operator>>(std::istream& in, __uint128_t& v) {std::string s;in >> s;v = stou128(s);return in;}// pairtemplate <typename T, typename U>std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {return in >> a.first >> a.second;}// tupletemplate <unsigned int N = 0, typename ...Args>std::istream& operator>>(std::istream& in, std::tuple<Args...>& a) {if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return in;else return operator>><N + 1>(in >> std::get<N>(a), a);}// vectortemplate <typename T>std::istream& operator>>(std::istream& in, std::vector<T>& a) {for (auto it = a.begin(); it != a.end(); ++it) in >> *it;return in;}// arraytemplate <typename T, size_t N>std::istream& operator>>(std::istream& in, std::array<T, N>& a) {for (auto it = a.begin(); it != a.end(); ++it) in >> *it;return in;}template <typename ...Args>void read(Args &...args) {(std::cin >> ... >> args);}// ! integral utilities// Returns pow(-1, n)template <typename T> constexpr inline int pow_m1(T n) {return -(n & 1) | 1;}// Returns pow(-1, n)template <> constexpr inline int pow_m1<bool>(bool n) {return -int(n) | 1;}// Returns floor(x / y)template <typename T> constexpr inline T fld(const T x, const T y) {return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;}template <typename T> constexpr inline T cld(const T x, const T y) {return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;}template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }template <typename T> constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }template <typename T> constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }template <typename T> constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }template <typename T> constexpr inline int parity(const T x) { return popcount(x) & 1; }// ! containertemplate <typename T, typename Comparator>auto priqueue_comp(const Comparator comparator) {return std::priority_queue<T, std::vector<T>, Comparator>(comparator);}template <typename Container>void sort_unique_erase(Container& a) {std::sort(a.begin(), a.end());a.erase(std::unique(a.begin(), a.end()), a.end());}template <typename InputIterator, typename BiConsumer>auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);}template <typename Container, typename BiConsumer>auto foreach_adjacent_values(Container &&c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) {foreach_adjacent_values(c.begin(), c.end(), f);}// ! other utilities// x <- min(x, y). returns true iff `x` has chenged.template <typename T>inline bool chmin(T& x, const T& y) {return y >= x ? false : (x = y, true);}// x <- max(x, y). returns true iff `x` has chenged.template <typename T>inline bool chmax(T& x, const T& y) {return y <= x ? false : (x = y, true);}template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>std::string bin(T val, int bit_num = -1) {std::string res;if (bit_num != -1) {for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);} else {for (; val; val >>= 1) res += '0' + (val & 1);std::reverse(res.begin(), res.end());}return res;}template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>std::vector<T> digits_low_to_high(T val, T base = 10) {std::vector<T> res;for (; val; val /= base) res.push_back(val % base);if (res.empty()) res.push_back(T{ 0 });return res;}template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>std::vector<T> digits_high_to_low(T val, T base = 10) {auto res = digits_low_to_high(val, base);std::reverse(res.begin(), res.end());return res;}template <typename T>std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {std::ostringstream ss;for (auto it = v.begin(); it != v.end();) {ss << *it;if (++it != v.end()) ss << sep;}ss << end;return ss.str();}template <typename Func, typename Seq>auto transform_to_vector(const Func &f, const Seq &s) {std::vector<std::invoke_result_t<Func, typename Seq::value_type>> v;v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f);return v;}template <typename T, typename Seq>auto copy_to_vector(const Seq &s) {std::vector<T> v;v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v));return v;}template <typename Seq>Seq concat(Seq s, const Seq &t) {s.reserve(std::size(s) + std::size(t));std::copy(std::begin(t), std::end(t), std::back_inserter(s));return s;}template <typename Seq>std::vector<Seq> split(const Seq s, typename Seq::value_type delim) {std::vector<Seq> res;for (auto itl = std::begin(s), itr = itl;; itl = ++itr) {while (itr != std::end(s) and *itr != delim) ++itr;res.emplace_back(itl, itr);if (itr == std::end(s)) return res;}}int digit_to_int(char c) { return c - '0'; }int lowercase_to_int(char c) { return c - 'a'; }int uppercase_to_int(char c) { return c - 'A'; }std::vector<int> digit_str_to_ints(const std::string &s) {return transform_to_vector(digit_to_int, s);}std::vector<int> lowercase_str_to_ints(const std::string &s) {return transform_to_vector(lowercase_to_int, s);}std::vector<int> uppercase_str_to_ints(const std::string &s) {return transform_to_vector(uppercase_to_int, s);}template <typename T, typename ToKey, typename CompareValue = std::less<>,std::enable_if_t<std::conjunction_v<std::is_invocable<ToKey, T>,std::is_invocable_r<bool, CompareValue, std::invoke_result_t<ToKey, T>, std::invoke_result_t<ToKey, T>>>, std::nullptr_t> = nullptr>auto comparator(const ToKey &to_key, const CompareValue &compare_value = std::less<>()) {return [to_key, compare_value](const T& x, const T& y) { return compare_value(to_key(x), to_key(y)); };}template <typename ToKey, std::enable_if_t<std::is_invocable_v<ToKey, int>, std::nullptr_t> = nullptr>std::vector<int> sorted_indices(int n, const ToKey &to_key) {std::vector<int> p(n);std::iota(p.begin(), p.end(), 0);std::sort(p.begin(), p.end(), comparator<int>(to_key));return p;}template <typename Compare, std::enable_if_t<std::is_invocable_r_v<bool, Compare, int, int>, std::nullptr_t> = nullptr>std::vector<int> sorted_indices(int n, const Compare &compare) {std::vector<int> p(n);std::iota(p.begin(), p.end(), 0);std::sort(p.begin(), p.end(), compare);return p;}const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO";namespace suisen {}using namespace suisen;using namespace std;struct io_setup {io_setup(int precision = 20) {std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout << std::fixed << std::setprecision(precision);}} io_setup_ {};// ! code from here#include <atcoder/modint>using mint = atcoder::modint998244353;namespace atcoder {std::istream& operator>>(std::istream& in, mint &a) {long long e; in >> e; a = e;return in;}std::ostream& operator<<(std::ostream& out, const mint &a) {out << a.val();return out;}} // namespace atcoder#include <vector>namespace suisen {template <int base_as_int, typename mint>struct static_pow_mods {static_pow_mods() {}static_pow_mods(int n) { ensure(n); }const mint& operator[](int i) const {ensure(i);return pows[i];}static void ensure(int n) {int sz = pows.size();if (sz > n) return;pows.resize(n + 1);for (int i = sz; i <= n; ++i) pows[i] = base * pows[i - 1];}private:static inline std::vector<mint> pows { 1 };static inline mint base = base_as_int;static constexpr int mod = mint::mod();};template <typename mint>struct pow_mods {pow_mods() {}pow_mods(mint base, int n) : base(base) { ensure(n); }const mint& operator[](int i) const {ensure(i);return pows[i];}void ensure(int n) const {int sz = pows.size();if (sz > n) return;pows.resize(n + 1);for (int i = sz; i <= n; ++i) pows[i] = base * pows[i - 1];}private:mutable std::vector<mint> pows { 1 };mint base;static constexpr int mod = mint::mod();};}#include <cassert>#include <tuple>#include <variant>namespace suisen {namespace internal::rerooting {using void_weight = std::monostate;template <typename VertexWeight, typename EdgeWeight>struct Rerooting {using vertex_weight = VertexWeight;using edge_weight = EdgeWeight;private:using is_vertex_weight_void = std::is_same<vertex_weight, void_weight>;using is_edge_weight_void = std::is_same<edge_weight, void_weight>;static constexpr bool is_vertex_weight_void_v = is_vertex_weight_void::value;static constexpr bool is_edge_weight_void_v = is_edge_weight_void::value;template <typename DP, typename AddSubtreeRoot>using is_add_subtree_root = std::conditional_t<std::negation_v<is_vertex_weight_void>,std::conditional_t<std::negation_v<is_edge_weight_void>,std::is_invocable_r<DP, AddSubtreeRoot, DP, vertex_weight, edge_weight>,std::is_invocable_r<DP, AddSubtreeRoot, DP, vertex_weight>>,std::conditional_t<std::negation_v<is_edge_weight_void>,std::is_invocable_r<DP, AddSubtreeRoot, DP, edge_weight>,std::is_invocable_r<DP, AddSubtreeRoot, DP>>>;template <typename DP, typename AddRoot>using is_add_root = std::conditional_t<std::negation_v<is_vertex_weight_void>,std::is_invocable_r<DP, AddRoot, DP, vertex_weight>,std::is_invocable_r<DP, AddRoot, DP>>;public:Rerooting() : _w{} {}explicit Rerooting(int n) : _w(n) {}explicit Rerooting(const std::vector<vertex_weight>& w) : _w(w) {}void reserve(int n) {_w.reserve(n);}void add_vertex(const vertex_weight& w) {_w.emplace_back(w);}void add_edge(int u, int v, const edge_weight& w = {}) {const int n = _w.size();assert(0 <= u and u < n);assert(0 <= v and v < n);_e.emplace_back(u, v, w);}void set_vertex_weights(const std::vector<vertex_weight>& w) {assert(w.size() == _w.size());_w = w;}/*** op : (T, T) -> T // commutative monoid* e : () -> T // identity* add_subtree_root : (T, vertex_weight, edge_weight) -> T // add subroot, edge to parent* add_root : (T, vertex_weight) -> T // add root*/template <typename Op, typename E, typename AddSubtreeRoot, typename AddRoot,typename DP = std::decay_t<std::invoke_result_t<E>>,std::enable_if_t<std::conjunction_v<std::is_invocable_r<DP, Op, DP, DP>,std::is_invocable_r<DP, E>,is_add_subtree_root<DP, AddSubtreeRoot>,is_add_root<DP, AddRoot>>, std::nullptr_t> = nullptr>std::vector<DP> run_dp(const Op& op, const E& e, const AddSubtreeRoot& add_subtree_root, const AddRoot& add_root) const {auto add_subtree_root_ = [&add_subtree_root](const DP &val, const vertex_weight& vw, const edge_weight& ew) {if constexpr (std::negation_v<is_vertex_weight_void>) {if constexpr (std::negation_v<is_edge_weight_void>) {return add_subtree_root(val, vw, ew);} else {return add_subtree_root(val, vw);}} else {if constexpr (std::negation_v<is_edge_weight_void>) {return add_subtree_root(val, ew);} else {return add_subtree_root(val);}}};auto add_root_ = [&add_root](const DP &val, const vertex_weight& vw) {if constexpr (std::negation_v<is_vertex_weight_void>) {return add_root(val, vw);} else {return add_root(val);}};const int n = _w.size();GraphCSR g(n, _e);std::vector<DP> dp(n, e());[dfs = [&, this](auto dfs, int u, int p) -> void {for (const auto& [v, w] : g[u]) if (v != p) {dfs(dfs, v, u);dp[u] = op(dp[u], add_subtree_root_(dp[v], _w[v], w));}}] { dfs(dfs, 0, -1); }();dp[0] = add_root_(dp[0], _w[0]);[dfs = [&, this](auto dfs, int u, int p, const DP& sum_p) -> void {auto get_sum = [&](int v) {return v == p ? sum_p : dp[v];};const int siz = g[u].size();std::vector<DP> sum_r(siz + 1, e());for (int i = siz - 1; i >= 0; --i) {const auto& [v, w] = g[u][i];sum_r[i] = op(sum_r[i + 1], add_subtree_root_(get_sum(v), _w[v], w));}DP sum_l = e();for (int i = 0; i < siz; ++i) {const auto& [v, w] = g[u][i];DP nxt_sum_l = op(sum_l, add_subtree_root_(get_sum(v), _w[v], w));if (v != p) {DP sum_lr = op(sum_l, sum_r[i + 1]);DP sum_v = op(dp[v], add_subtree_root_(sum_lr, _w[u], w));dp[v] = add_root_(sum_v, _w[v]);dfs(dfs, v, u, sum_lr);}sum_l = std::move(nxt_sum_l);}}, &e] { dfs(dfs, 0, -1, e()); }();return dp;}private:std::vector<vertex_weight> _w;std::vector<std::tuple<int, int, edge_weight>> _e;struct GraphCSR {GraphCSR(int n, const std::vector<std::tuple<int, int, edge_weight>>& edges) : _n(n), _m(edges.size()), _edges(2 * _m), _start(_n + 1) {for (const auto& [u, v, w] : edges) {++_start[u];++_start[v];}for (int i = 1; i <= _n; ++i) {_start[i] += _start[i - 1];}for (const auto& [u, v, w] : edges) {_edges[--_start[u]] = { v, w };_edges[--_start[v]] = { u, w };}}private:using edge_type = std::pair<int, edge_weight>;using iterator = typename std::vector<edge_type>::const_iterator;struct AdjacentListView {AdjacentListView(const iterator& l, const iterator& r) : _l(l), _r(r) {}int size() const { return _r - _l; }const edge_type& operator[](int i) const { return *(_l + i); }iterator begin() const { return _l; }iterator end() const { return _r; }private:iterator _l, _r;};public:AdjacentListView operator[](int u) const {return AdjacentListView(_edges.begin() + _start[u], _edges.begin() + _start[u + 1]);}private:int _n, _m;std::vector<std::pair<int, edge_weight>> _edges;std::vector<int> _start;};};}using Rerooting = internal::rerooting::Rerooting<internal::rerooting::void_weight, internal::rerooting::void_weight>;template <typename VertexWeight>using RerootingVertexWeighted = internal::rerooting::Rerooting<VertexWeight, internal::rerooting::void_weight>;template <typename EdgeWeight>using RerootingEdgeWeighted = internal::rerooting::Rerooting<internal::rerooting::void_weight, EdgeWeight>;template <typename VertexWeight, typename EdgeWeighted>using RerootingWeighted = internal::rerooting::Rerooting<VertexWeight, EdgeWeighted>;} // namsepace suisenusing S = pair<mint, int>;int main() {int n;read(n);static_pow_mods<10, mint> pow10(100);vector<S> a(n);REP(i, n) {string s;read(s);a[i] = { mint(stoll(s)), int(s.size()) };}RerootingVertexWeighted<S> g(a);REP(i, n - 1) {int u, v;read(u, v);--u, --v;g.add_edge(u, v);}vector<S> ans = g.run_dp([](const S& x, const S& y) { return S{ x.first + y.first, x.second + y.second }; },[]{ return S{ 0, 0 }; },[&pow10](S sum, S w) { return S { sum.first * pow10[w.second] + w.first * (sum.second + 1), sum.second + 1 }; },[&pow10](S sum, S w) { return S { sum.first * pow10[w.second] + w.first * (sum.second + 1), sum.second + 1 }; });mint sum_ans = 0;for (auto [sum, siz] : ans) {assert(siz == n);sum_ans += sum;}print(sum_ans);return 0;}