結果

問題 No.2360 Path to Integer
ユーザー suisen
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 15
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#ifdef _MSC_VER
#  include <intrin.h>
#else
#  include <x86intrin.h>
#endif
#include <limits>
#include <type_traits>
namespace suisen {
// ! utility
template <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);
    }
}
// ! function
template <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>;
// ! integral
template <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 aliases
using 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_t
std::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_t
std::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;
}
// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <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);
    }
}
// vector
template <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;
}
// array
template <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_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
    std::string s;
    in >> s;
    v = stoi128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = stou128(s);
    return in;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {
    return in >> a.first >> a.second;
}
// tuple
template <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);
}
// vector
template <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;
}
// array
template <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; }
// ! container
template <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 suisen
using 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;
}
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