#ifndef MODINT_HPP
#define MODINT_HPP 1

#include <cassert>
#include <iostream>
#include <type_traits>
#include <utility>

#ifndef TYPE_TRAITS_HPP
#define TYPE_TRAITS_HPP 1


#include <istream>
#include <ostream>
#include <type_traits>

namespace kk2 {

template <typename T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value
                                                       or std::is_same<T, __int128>::value,
                                                   std::true_type,
                                                   std::false_type>::type;

template <typename T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value
                                  or std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <typename T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value or is_signed_int128<T>::value
                                  or is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <typename T>
using is_signed = typename std::conditional<std::is_signed<T>::value or is_signed_int128<T>::value,
                                            std::true_type,
                                            std::false_type>::type;

template <typename T>
using is_unsigned =
    typename std::conditional<std::is_unsigned<T>::value or is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <typename T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;

template <typename T>
using to_unsigned =
    typename std::conditional<is_signed_int128<T>::value,
                              make_unsigned_int128<T>,
                              typename std::conditional<std::is_signed<T>::value,
                                                        std::make_unsigned<T>,
                                                        std::common_type<T>>::type>::type;

template <typename T> using is_integral_t = std::enable_if_t<is_integral<T>::value>;
template <typename T> using is_signed_t = std::enable_if_t<is_signed<T>::value>;
template <typename T> using is_unsigned_t = std::enable_if_t<is_unsigned<T>::value>;


template <typename T>
using is_function_pointer =
    typename std::conditional<std::is_pointer_v<T> && std::is_function_v<std::remove_pointer_t<T>>,
                              std::true_type,
                              std::false_type>::type;

template <typename T, std::enable_if_t<is_function_pointer<T>::value> * = nullptr>
struct is_two_args_function_pointer : std::false_type {};

template <typename R, typename T1, typename T2>
struct is_two_args_function_pointer<R (*)(T1, T2)> : std::true_type {};

template <typename T>
using is_two_args_function_pointer_t = std::enable_if_t<is_two_args_function_pointer<T>::value>;

namespace type_traits {

struct istream_tag {};

struct ostream_tag {};

} // namespace type_traits

template <typename T> using is_standard_istream = std::is_same<T, std::istream>;
template <typename T> using is_standard_ostream = std::is_same<T, std::ostream>;
template <typename T> using is_user_defined_istream = std::is_base_of<type_traits::istream_tag, T>;
template <typename T> using is_user_defined_ostream = std::is_base_of<type_traits::ostream_tag, T>;

template <typename T>
using is_istream =
    typename std::conditional<is_standard_istream<T>::value || is_user_defined_istream<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <typename T>
using is_ostream =
    typename std::conditional<is_standard_ostream<T>::value || is_user_defined_ostream<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <typename T> using is_istream_t = std::enable_if_t<is_istream<T>::value>;
template <typename T> using is_ostream_t = std::enable_if_t<is_ostream<T>::value>;


} // namespace kk2

#endif // TYPE_TRAITS_HPP

// #include "../type_traits/type_traits.hpp"

namespace kk2 {

template <int p> struct ModInt {
    using mint = ModInt;

  public:
    static int Mod;

    constexpr static unsigned int getmod() {
        if (p > 0) return p;
        else return Mod;
    }

    static void setmod(int Mod_) {
        assert(1 <= Mod_);
        Mod = Mod_;
    }

    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    constexpr ModInt() : _v(0) {}

    template <class T, is_integral_t<T> * = nullptr> constexpr ModInt(T v) {
        if constexpr (is_signed<T>::value) {
            v %= getmod();
            if (v < 0) v += getmod();
            _v = v;
        } else if constexpr (is_unsigned<T>::value) {
            _v = v %= getmod();
        } else {
            ModInt();
        }
    }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if (_v == getmod()) _v = 0;
        return *this;
    }

    mint &operator--() {
        if (_v == 0) _v = getmod();
        _v--;
        return *this;
    }

    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }

    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= getmod()) _v -= getmod();
        return *this;
    }

    mint &operator-=(const mint &rhs) {
        _v += getmod() - rhs._v;
        if (_v >= getmod()) _v -= getmod();
        return *this;
    }

    mint &operator*=(const mint &rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        z %= getmod();
        _v = z;
        return *this;
    }

    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }

    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }

    mint inv() const {
        long long s = getmod(), t = _v;
        long long m0 = 0, m1 = 1;

        while (t) {
            long long u = s / t;
            s -= t * u;
            m0 -= m1 * u;

            std::swap(s, t);
            std::swap(m0, m1);
        }
        if (m0 < 0) m0 += getmod() / s;
        return m0;
    }

    friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }

    friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }

    friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }

    friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }

    friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }

    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }

    template <class OStream, is_ostream_t<OStream> * = nullptr>
    friend OStream &operator<<(OStream &os, const mint &mint_) {
        os << mint_._v;
        return os;
    }

    template <class IStream, is_istream_t<IStream> * = nullptr>
    friend IStream &operator>>(IStream &is, mint &mint_) {
        long long x;
        is >> x;
        mint_ = mint(x);
        return is;
    }

  private:
    unsigned int _v;
};

template <int p> int ModInt<p>::Mod = 998244353;


using mint998 = ModInt<998244353>;
using mint107 = ModInt<1000000007>;

} // namespace kk2

#endif // MODINT_HPP

// #include <kk2/modint/modint.hpp>
#ifndef GRAPH_GRAPH_TEMPLATE_HPP
#define GRAPH_GRAPH_TEMPLATE_HPP 1

#include <cassert>
#include <iostream>
#include <type_traits>
#include <utility>
#include <vector>

// #include "../type_traits/type_traits.hpp"

namespace kk2 {

namespace graph {

struct empty {};

template <class T> struct _Edge {
    int from, to, id;
    T cost;

    _Edge(int to_, T cost_, int from_ = -1, int id_ = -1)
        : from(from_),
          to(to_),
          id(id_),
          cost(cost_) {}

    _Edge() : from(-1), to(-1), id(-1), cost() {}

    operator int() const { return to; }

    _Edge rev() const { return _Edge(from, cost, to, id); }

    template <class OStream, is_ostream_t<OStream> * = nullptr>
    friend OStream &operator<<(OStream &os, const _Edge &e) {
        if constexpr (std::is_same_v<T, empty>) return os << e.from << " -> " << e.to;
        else return os << e.from << " -> " << e.to << " : " << e.cost;
    }
};
template <class T> using _Edges = std::vector<_Edge<T>>;

template <class T, bool is_directed> struct AdjacencyList : std::vector<_Edges<T>> {
    using value_type = T;
    using edge_type = _Edge<T>;

    constexpr static bool directed() { return is_directed; }

    AdjacencyList() = default;

    AdjacencyList(int n_) : std::vector<_Edges<T>>(n_) {}

    AdjacencyList(int n_, int m_) : std::vector<_Edges<T>>(n_), edges(m_) {}

    AdjacencyList(int n_, const _Edges<T> &edges_) : std::vector<_Edges<T>>(n_), edges(edges_) {
        for (auto &&e : edges) {
            (*this)[e.from].emplace_back(e);
            if constexpr (!is_directed) (*this)[e.to].emplace_back(e);
        }
    }

    _Edges<T> edges;

    int num_vertices() const { return (int)this->size(); }

    int num_edges() const { return (int)edges.size(); }

    template <class IStream, is_istream_t<IStream> * = nullptr>
    AdjacencyList &input(IStream &is, bool oneindexed = false) {
        for (int i = 0; i < num_edges(); i++) {
            int u, v;
            T w{};
            is >> u >> v;
            if constexpr (!std::is_same_v<T, empty>) is >> w;
            if (oneindexed) --u, --v;
            _add_edge<true>(u, v, w, i);
        }
        return *this;
    }

    void edge_clear() {
        for (auto &v : *this) v.clear();
        edges.clear();
    }

    void add_edge(int from, int to, T cost = T{}) { _add_edge<false>(from, to, cost, num_edges()); }

  private:
    template <bool update = false>
    void _add_edge(int from, int to, T cost, int id) {
        (*this)[from].emplace_back(to, cost, from, id);
        if constexpr (!is_directed) (*this)[to].emplace_back(from, cost, to, id);
        if constexpr (update) edges[id] = _Edge<T>(to, cost, from, id);
        else edges.emplace_back(to, cost, from, id);
    }
};

template <class T> struct _pair {
    T cost;
    int id;

    _pair(T cost_, int id_) : cost(cost_), id(id_) {}

    _pair() : cost(), id(-1) {}

    operator bool() const { return id != -1; }

    template <class OStream, is_ostream_t<OStream> * = nullptr>
    friend OStream &operator<<(OStream &os, const _pair &p) {
        if constexpr (std::is_same_v<T, empty>) return os;
        else return os << p.cost;
    }
};
template <class T> using _pairs = std::vector<_pair<T>>;

template <class T, bool is_directed> struct AdjacencyMatrix : std::vector<_pairs<T>> {
    using value_type = T;
    using edge_type = _pair<T>;

    constexpr static bool directed() { return is_directed; }

    AdjacencyMatrix() = default;

    AdjacencyMatrix(int n_) : std::vector<_pairs<T>>(n_, _pairs<T>(n_)) {}

    AdjacencyMatrix(int n_, int m_) : std::vector<_pairs<T>>(n_, _pairs<T>(n_)), edges(m_) {}

    AdjacencyMatrix(int n_, const _Edges<T> &edges_)
        : std::vector<_pairs<T>>(n_, _pairs<T>(n_)),
          edges(edges_) {
        for (auto &&e : edges) {
            (*this)[e.from][e.to] = _pair<T>(e.cost, e.id);
            if constexpr (!is_directed) (*this)[e.to][e.from] = _pair<T>(e.cost, e.id);
        }
    }

    template <class IStream, is_istream_t<IStream> * = nullptr>
    AdjacencyMatrix &input(IStream &is, bool oneindexed = false) {
        for (int i = 0; i < num_edges(); i++) {
            int u, v;
            T w{};
            is >> u >> v;
            if constexpr (!std::is_same_v<T, empty>) is >> w;
            if (oneindexed) --u, --v;
            _add_edge<true>(u, v, w, i);
        }
        return *this;
    }

    _Edges<T> edges;

    int num_vertices() const { return (int)this->size(); }

    int num_edges() const { return (int)edges.size(); }

    void edge_clear() {
        for (auto &&e : edges) {
            (*this)[e.from][e.to] = _pair<T>(e.cost, e.id);
            if constexpr (!is_directed) (*this)[e.to][e.from] = _pair<T>(e.cost, e.id);
        }
        edges.clear();
    }

    void add_edge(int from, int to, T cost = T{}) { _add_edge<false>(from, to, cost, num_edges()); }

  private:
    template <bool update = false>
    void _add_edge(int from, int to, T cost, int id) {
        (*this)[from][to] = _pair<T>(cost, id);
        if constexpr (!is_directed) (*this)[to][from] = _pair<T>(cost, id);
        if constexpr (update) edges[id] = _Edge<T>(to, cost, from, id);
        else edges.emplace_back(to, cost, from, id);
    }
};

template <class G>
G reverse(const G &g) {
    G res(g.num_vertices());
    for (auto &&e : g.edges) res.add_edge(e.to, e.from, e.cost);
    return res;
}

template <class T, class IStream, is_istream_t<IStream> * = nullptr>
_Edges<T> &input(_Edges<T> &edges, bool is_one_indexed, IStream &is) {
    for (int i = 0; i < (int)edges.size(); i++) {
        int u, v;
        T w{};
        is >> u >> v;
        if (is_one_indexed) --u, --v;
        if constexpr (!std::is_same_v<T, empty>) is >> w;
        edges[i] = _Edge<T>(v, w, u, i);
    }
    return edges;
}

} // namespace graph

template <typename T> using WAdjList = graph::AdjacencyList<T, false>;
template <typename T> using DWAdjList = graph::AdjacencyList<T, true>;
using AdjList = graph::AdjacencyList<graph::empty, false>;
using DAdjList = graph::AdjacencyList<graph::empty, true>;

template <typename T> using WAdjMat = graph::AdjacencyMatrix<T, false>;
template <typename T> using DWAdjMat = graph::AdjacencyMatrix<T, true>;
using AdjMat = graph::AdjacencyMatrix<graph::empty, false>;
using DAdjMat = graph::AdjacencyMatrix<graph::empty, true>;

template <typename T> using WEdge = graph::_Edge<T>;
template <typename T> using WEdges = graph::_Edges<T>;
using Edge = graph::_Edge<graph::empty>;
using Edges = graph::_Edges<graph::empty>;
using graph::input;
using graph::reverse;

} // namespace kk2

#endif // GRAPH_GRAPH_TEMPLATE_HPP

// #include <kk2/graph/graph.hpp>
#ifndef TEMPLATE
#define TEMPLATE 1

// #pragma GCC optimize("O3,unroll-loops")

// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// #include "../type_traits/type_traits.hpp"
#ifndef TEMPLATE_FASTIO_HPP
#define TEMPLATE_FASTIO_HPP 1

#include <cctype>
#include <cstdint>
#include <cstdio>
#include <fstream>
#include <iostream>
#include <string>

// #include "../type_traits/type_traits.hpp"

namespace kk2 {

namespace fastio {

#define INPUT_FILE "in.txt"
#define OUTPUT_FILE "out.txt"

struct Scanner : type_traits::istream_tag {
  private:
    static constexpr size_t INPUT_BUF = 1 << 17;
    size_t pos = 0, end = 0;
    static char buf[INPUT_BUF];
    FILE *fp;

  public:
    Scanner() : fp(stdin) {}

    Scanner(const char *file) : fp(fopen(file, "r")) {}

    ~Scanner() {
        if (fp != stdin) fclose(fp);
    }

    char now() {
        if (pos == end) {
            while (!(end = fread(buf, 1, INPUT_BUF, fp))) {}
            if (end != INPUT_BUF) buf[end] = '\0';
            pos = 0;
        }
        return buf[pos];
    }

    void skip_space() {
        while (isspace(now())) ++pos;
    }

    template <class T, is_unsigned_t<T> * = nullptr> T next_unsigned_integral() {
        skip_space();
        T res{};
        while (isdigit(now())) {
            res = res * 10 + (now() - '0');
            ++pos;
        }
        return res;
    }

    template <class T, is_signed_t<T> * = nullptr> T next_signed_integral() {
        skip_space();
        if (now() == '-') {
            ++pos;
            return T(-next_unsigned_integral<typename to_unsigned<T>::type>());
        } else return (T)next_unsigned_integral<typename to_unsigned<T>::type>();
    }

    char next_char() {
        skip_space();
        auto res = now();
        ++pos;
        return res;
    }

    std::string next_string() {
        skip_space();
        std::string res;
        while (true) {
            char c = now();
            if (isspace(c) or c == '\0') break;
            res.push_back(now());
            ++pos;
        }
        return res;
    }

    template <class T, is_unsigned_t<T> * = nullptr> Scanner &operator>>(T &x) {
        x = next_unsigned_integral<T>();
        return *this;
    }

    template <class T, is_signed_t<T> * = nullptr> Scanner &operator>>(T &x) {
        x = next_signed_integral<T>();
        return *this;
    }

    Scanner &operator>>(char &x) {
        x = next_char();
        return *this;
    }

    Scanner &operator>>(std::string &x) {
        x = next_string();
        return *this;
    }
};

struct endl_struct_t {};

struct Printer : type_traits::ostream_tag {
  private:
    static char helper[10000][5];
    static char leading_zero[10000][5];
    constexpr static size_t OUTPUT_BUF = 1 << 17;
    static char buf[OUTPUT_BUF];
    size_t pos = 0;
    FILE *fp;

    template <class T> static constexpr void div_mod(T &a, T &b, T mod) {
        a = b / mod;
        b -= a * mod;
    }

    static void init() {
        buf[0] = '\0';
        for (size_t i = 0; i < 10000; ++i) {
            leading_zero[i][0] = i / 1000 + '0';
            leading_zero[i][1] = i / 100 % 10 + '0';
            leading_zero[i][2] = i / 10 % 10 + '0';
            leading_zero[i][3] = i % 10 + '0';
            leading_zero[i][4] = '\0';

            size_t j = 0;
            if (i >= 1000) helper[i][j++] = i / 1000 + '0';
            if (i >= 100) helper[i][j++] = i / 100 % 10 + '0';
            if (i >= 10) helper[i][j++] = i / 10 % 10 + '0';
            helper[i][j++] = i % 10 + '0';
            helper[i][j] = '\0';
        }
    }

  public:
    Printer() : fp(stdout) { init(); }

    Printer(const char *file) : fp(fopen(file, "w")) { init(); }

    ~Printer() {
        write();
        if (fp != stdout) fclose(fp);
    }

    void write() {
        fwrite(buf, 1, pos, fp);
        pos = 0;
    }

    void flush() {
        write();
        fflush(fp);
    }

    void put_char(char c) {
        if (pos == OUTPUT_BUF) write();
        buf[pos++] = c;
    }

    void put_cstr(const char *s) {
        while (*s) put_char(*(s++));
    }

    void put_u32(uint32_t x) {
        uint32_t y;
        if (x >= 100000000) { // 10^8
            div_mod<uint32_t>(y, x, 100000000);
            put_cstr(helper[y]);
            div_mod<uint32_t>(y, x, 10000);
            put_cstr(leading_zero[y]);
            put_cstr(leading_zero[x]);
        } else if (x >= 10000) { // 10^4
            div_mod<uint32_t>(y, x, 10000);
            put_cstr(helper[y]);
            put_cstr(leading_zero[x]);
        } else put_cstr(helper[x]);
    }

    void put_i32(int32_t x) {
        if (x < 0) {
            put_char('-');
            put_u32(-x);
        } else put_u32(x);
    }

    void put_u64(uint64_t x) {
        uint64_t y;
        if (x >= 1000000000000ull) { // 10^12
            div_mod<uint64_t>(y, x, 1000000000000ull);
            put_u32(y);
            div_mod<uint64_t>(y, x, 100000000ull);
            put_cstr(leading_zero[y]);
            div_mod<uint64_t>(y, x, 10000ull);
            put_cstr(leading_zero[y]);
            put_cstr(leading_zero[x]);
        } else if (x >= 10000ull) { // 10^4
            div_mod<uint64_t>(y, x, 10000ull);
            put_u32(y);
            put_cstr(leading_zero[x]);
        } else put_cstr(helper[x]);
    }

    void put_i64(int64_t x) {
        if (x < 0) {
            put_char('-');
            put_u64(-x);
        } else put_u64(x);
    }

    void put_u128(__uint128_t x) {
        constexpr static __uint128_t pow10_10 = 10000000000ull;
        constexpr static __uint128_t pow10_20 = pow10_10 * pow10_10;

        __uint128_t y;
        if (x >= pow10_20) { // 10^20
            div_mod<__uint128_t>(y, x, pow10_20);
            put_u64(uint64_t(y));
            div_mod<__uint128_t>(y, x, __uint128_t(10000000000000000ull));
            put_cstr(leading_zero[y]);
            div_mod<__uint128_t>(y, x, __uint128_t(1000000000000ull));
            put_cstr(leading_zero[y]);
            div_mod<__uint128_t>(y, x, __uint128_t(100000000ull));
            put_cstr(leading_zero[y]);
            div_mod<__uint128_t>(y, x, __uint128_t(10000ull));
            put_cstr(leading_zero[y]);
            put_cstr(leading_zero[x]);
        } else if (x >= __uint128_t(10000)) { // 10^4
            div_mod<__uint128_t>(y, x, __uint128_t(10000));
            put_u64(uint64_t(y));
            put_cstr(leading_zero[x]);
        } else put_cstr(helper[x]);
    }

    void put_i128(__int128_t x) {
        if (x < 0) {
            put_char('-');
            put_u128(-x);
        } else put_u128(x);
    }

    template <class T, is_unsigned_t<T> * = nullptr> Printer &operator<<(T x) {
        if constexpr (sizeof(T) <= 4) put_u32(x);
        else if constexpr (sizeof(T) <= 8) put_u64(x);
        else put_u128(x);
        return *this;
    }

    template <class T, is_signed_t<T> * = nullptr> Printer &operator<<(T x) {
        if constexpr (sizeof(T) <= 4) put_i32(x);
        else if constexpr (sizeof(T) <= 8) put_i64(x);
        else put_i128(x);
        return *this;
    }

    Printer &operator<<(char x) {
        put_char(x);
        return *this;
    }

    Printer &operator<<(const std::string &x) {
        for (char c : x) put_char(c);
        return *this;
    }

    Printer &operator<<(const char *x) {
        put_cstr(x);
        return *this;
    }

    // std::cout << std::endl; は関数ポインタを渡しているらしい
    Printer &operator<<(endl_struct_t) {
        put_char('\n');
        flush();
        return *this;
    }
};

char Scanner::buf[Scanner::INPUT_BUF];
char Printer::buf[Printer::OUTPUT_BUF];
char Printer::helper[10000][5];
char Printer::leading_zero[10000][5];

} // namespace fastio

#if defined(INTERACTIVE) || defined(USE_STDIO)
auto &kin = std::cin;
auto &kout = std::cout;
auto (*kendl)(std::ostream &) = std::endl<char, std::char_traits<char>>;
#elif defined(KK2)
fastio::Scanner kin(INPUT_FILE);
fastio::Printer kout(OUTPUT_FILE);
fastio::endl_struct_t kendl;
#else
fastio::Scanner kin;
fastio::Printer kout;
fastio::endl_struct_t kendl;
#endif

} // namespace kk2

#endif // TEMPLATE_FASTIO_HPP

// #include "fastio.hpp"

using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

using pi = std::pair<int, int>;
using pl = std::pair<i64, i64>;
using pil = std::pair<int, i64>;
using pli = std::pair<i64, int>;

template <class T> using vc = std::vector<T>;
template <class T> using vvc = std::vector<vc<T>>;
template <class T> using vvvc = std::vector<vvc<T>>;
template <class T> using vvvvc = std::vector<vvvc<T>>;

template <class T> using pq = std::priority_queue<T>;
template <class T> using pqi = std::priority_queue<T, std::vector<T>, std::greater<T>>;

template <class T> constexpr T infty = 0;
template <> constexpr int infty<int> = (1 << 30) - 123;
template <> constexpr i64 infty<i64> = (1ll << 62) - (1ll << 31);
template <> constexpr i128 infty<i128> = (i128(1) << 126) - (i128(1) << 63);
template <> constexpr u32 infty<u32> = infty<int>;
template <> constexpr u64 infty<u64> = infty<i64>;
template <> constexpr u128 infty<u128> = infty<i128>;
template <> constexpr double infty<double> = infty<i64>;
template <> constexpr long double infty<long double> = infty<i64>;

constexpr int mod = 998244353;
constexpr int modu = 1e9 + 7;
constexpr long double PI = 3.14159265358979323846;

namespace kk2 {

template <class T, class... Sizes> auto make_vector(int first, Sizes... sizes) {
    if constexpr (sizeof...(sizes) == 0) {
        return std::vector<T>(first);
    } else {
        return std::vector<decltype(make_vector(sizes...))>(first, make_vector(sizes...));
    }
}

template <class T, class U> void fill_all(std::vector<T> &v, const U &x) {
    std::fill(std::begin(v), std::end(v), T(x));
}

template <class T, class U> void fill_all(std::vector<std::vector<T>> &v, const U &x) {
    for (auto &u : v) fill_all(u, x);
}

} // namespace kk2

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);
}

#define rep1(a) for (i64 _ = 0; _ < (i64)(a); ++_)
#define rep2(i, a) for (i64 i = 0; i < (i64)(a); ++i)
#define rep3(i, a, b) for (i64 i = (a); i < (i64)(b); ++i)
#define repi2(i, a) for (i64 i = (a) - 1; i >= 0; --i)
#define repi3(i, a, b) for (i64 i = (a) - 1; i >= (i64)(b); --i)
#define overload3(a, b, c, d, ...) d
#define rep(...) overload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi(...) overload3(__VA_ARGS__, repi3, repi2, rep1)(__VA_ARGS__)

#define fi first
#define se second
#define all(p) std::begin(p), std::end(p)

using kk2::kendl;
using kk2::kin;
using kk2::kout;

struct IoSetUp {
    IoSetUp() {
        std::cin.tie(nullptr);
        std::ios::sync_with_stdio(false);
    }
} iosetup;

template <class OStream, class T, class U, kk2::is_ostream_t<OStream> * = nullptr>
OStream &operator<<(OStream &os, const std::pair<T, U> &p) {
    os << p.first << ' ' << p.second;
    return os;
}

template <class IStream, class T, class U, kk2::is_istream_t<IStream> * = nullptr>
IStream &operator>>(IStream &is, std::pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}

template <class OStream, class T, kk2::is_ostream_t<OStream> * = nullptr>
OStream &operator<<(OStream &os, const std::vector<T> &v) {
    for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); }
    return os;
}

template <class IStream, class T, kk2::is_istream_t<IStream> * = nullptr>
IStream &operator>>(IStream &is, std::vector<T> &v) {
    for (auto &x : v) is >> x;
    return is;
}

void Yes(bool b = 1) {
    kout << (b ? "Yes\n" : "No\n");
}

void No(bool b = 1) {
    kout << (b ? "No\n" : "Yes\n");
}

void YES(bool b = 1) {
    kout << (b ? "YES\n" : "NO\n");
}

void NO(bool b = 1) {
    kout << (b ? "NO\n" : "YES\n");
}

void yes(bool b = 1) {
    kout << (b ? "yes\n" : "no\n");
}

void no(bool b = 1) {
    kout << (b ? "no\n" : "yes\n");
}

#endif // TEMPLATE

// #include <kk2/template/template.hpp>
using namespace std;

void solve() {
    int n;
    kin >> n;
    vc<kk2::mint998> a(n);
    kin >> a;
    kk2::AdjList g(n, n - 1);
    g.input(kin, true);

    kk2::mint998 res = 0;
    auto dfs = [&](auto self, int now, int pre) -> kk2::mint998 {
        kk2::mint998 sum = 0, sqsum = 0;
        for (auto e : g[now]) {
            if (e.to == pre) continue;
            auto tmp = self(self, e.to, now);
            sum += tmp;
            sqsum += tmp * tmp;
        }
        res += a[now] / 2 * (sum * sum - sqsum) + sum * a[now];
        return sum * a[now] + a[now];
    };
    dfs(dfs, 0, -1);
    kout << res << kendl;
}

int main() {
    int t = 1;
    // kin >> t;
    rep (t) solve();

    return 0;
}

// converted!!