#line 1 "main.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
// input output utils
namespace siro53_io {
    // https://maspypy.github.io/library/other/io_old.hpp
    struct has_val_impl {
        template <class T>
        static auto check(T &&x) -> decltype(x.val(), std::true_type{});

        template <class T> static auto check(...) -> std::false_type;
    };

    template <class T>
    class has_val : public decltype(has_val_impl::check<T>(std::declval<T>())) {
    };

    // debug
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void dump(const T t) {
        cerr << t;
    }
    template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
    void dump(const T t) {
        cerr << t;
    }
    template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
    void dump(const T &t) {
        cerr << t.val();
    }
    void dump(__int128_t n) {
        if(n == 0) {
            cerr << '0';
            return;
        } else if(n < 0) {
            cerr << '-';
            n = -n;
        }
        string s;
        while(n > 0) {
            s += (char)('0' + n % 10);
            n /= 10;
        }
        reverse(s.begin(), s.end());
        cerr << s;
    }
    void dump(const string &s) { cerr << s; }
    void dump(const char *s) {
        int n = (int)strlen(s);
        for(int i = 0; i < n; i++) cerr << s[i];
    }
    template <class T1, class T2> void dump(const pair<T1, T2> &p) {
        cerr << '(';
        dump(p.first);
        cerr << ',';
        dump(p.second);
        cerr << ')';
    }
    template <class T> void dump(const vector<T> &v) {
        cerr << '{';
        for(int i = 0; i < (int)v.size(); i++) {
            dump(v[i]);
            if(i < (int)v.size() - 1) cerr << ',';
        }
        cerr << '}';
    }
    template <class T> void dump(const set<T> &s) {
        cerr << '{';
        for(auto it = s.begin(); it != s.end(); it++) {
            dump(*it);
            if(next(it) != s.end()) cerr << ',';
        }
        cerr << '}';
    }
    template <class Key, class Value> void dump(const map<Key, Value> &mp) {
        cerr << '{';
        for(auto it = mp.begin(); it != mp.end(); it++) {
            dump(*it);
            if(next(it) != mp.end()) cerr << ',';
        }
        cerr << '}';
    }
    template <class Key, class Value>
    void dump(const unordered_map<Key, Value> &mp) {
        cerr << '{';
        for(auto it = mp.begin(); it != mp.end(); it++) {
            dump(*it);
            if(next(it) != mp.end()) cerr << ',';
        }
        cerr << '}';
    }
    template <class T> void dump(const deque<T> &v) {
        cerr << '{';
        for(int i = 0; i < (int)v.size(); i++) {
            dump(v[i]);
            if(i < (int)v.size() - 1) cerr << ',';
        }
        cerr << '}';
    }
    template <class T> void dump(queue<T> q) {
        cerr << '{';
        while(!q.empty()) {
            dump(q.front());
            if((int)q.size() > 1) cerr << ',';
            q.pop();
        }
        cerr << '}';
    }

    void debug_print() { cerr << endl; }
    template <class Head, class... Tail>
    void debug_print(const Head &h, const Tail &...t) {
        dump(h);
        if(sizeof...(Tail)) dump(' ');
        debug_print(t...);
    }
    // print
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void print_single(const T t) {
        cout << t;
    }
    template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
    void print_single(const T t) {
        cout << t;
    }
    template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
    void print_single(const T t) {
        cout << t.val();
    }
    void print_single(__int128_t n) {
        if(n == 0) {
            cout << '0';
            return;
        } else if(n < 0) {
            cout << '-';
            n = -n;
        }
        string s;
        while(n > 0) {
            s += (char)('0' + n % 10);
            n /= 10;
        }
        reverse(s.begin(), s.end());
        cout << s;
    }
    void print_single(const string &s) { cout << s; }
    void print_single(const char *s) {
        int n = (int)strlen(s);
        for(int i = 0; i < n; i++) cout << s[i];
    }
    template <class T1, class T2> void print_single(const pair<T1, T2> &p) {
        print_single(p.first);
        cout << ' ';
        print_single(p.second);
    }
    template <class T> void print_single(const vector<T> &v) {
        for(int i = 0; i < (int)v.size(); i++) {
            print_single(v[i]);
            if(i < (int)v.size() - 1) cout << ' ';
        }
    }
    template <class T> void print_single(const set<T> &s) {
        for(auto it = s.begin(); it != s.end(); it++) {
            print_single(*it);
            if(next(it) != s.end()) cout << ' ';
        }
    }
    template <class T> void print_single(const deque<T> &v) {
        for(int i = 0; i < (int)v.size(); i++) {
            print_single(v[i]);
            if(i < (int)v.size() - 1) cout << ' ';
        }
    }
    template <class T> void print_single(queue<T> q) {
        while(!q.empty()) {
            print_single(q.front());
            if((int)q.size() > 1) cout << ' ';
            q.pop();
        }
    }

    void print() { cout << '\n'; }
    template <class Head, class... Tail>
    void print(const Head &h, const Tail &...t) {
        print_single(h);
        if(sizeof...(Tail)) print_single(' ');
        print(t...);
    }

    // input
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void input_single(T &t) {
        cin >> t;
    }
    template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
    void input_single(T &t) {
        cin >> t;
    }
    template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
    void input_single(T &t) {
        cin >> t;
    }
    void input_single(__int128_t &n) {
        string s;
        cin >> s;
        if(s == "0") {
            n = 0;
            return;
        }
        bool is_minus = false;
        if(s[0] == '-') {
            s = s.substr(1);
            is_minus = true;
        }
        n = 0;
        for(int i = 0; i < (int)s.size(); i++) n = n * 10 + (int)(s[i] - '0');
        if(is_minus) n = -n;
    }
    void input_single(string &s) { cin >> s; }
    template <class T1, class T2> void input_single(pair<T1, T2> &p) {
        input_single(p.first);
        input_single(p.second);
    }
    template <class T> void input_single(vector<T> &v) {
        for(auto &e : v) input_single(e);
    }
    void input() {}
    template <class Head, class... Tail> void input(Head &h, Tail &...t) {
        input_single(h);
        input(t...);
    }
}; // namespace siro53_io
#ifdef DEBUG
#define debug(...)                                                             \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debug_print(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
// io setup
struct Setup {
    Setup() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} __Setup;
using namespace siro53_io;
// types
using ll = long long;
using i128 = __int128_t;
// input macros
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    ll __VA_ARGS__;                                                            \
    input(__VA_ARGS__)
#define STRING(...)                                                            \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define CHAR(...)                                                              \
    char __VA_ARGS__;                                                          \
    input(__VA_ARGS__)
#define DBL(...)                                                               \
    double __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define LD(...)                                                                \
    long double __VA_ARGS__;                                                   \
    input(__VA_ARGS__)
#define UINT(...)                                                              \
    unsigned int __VA_ARGS__;                                                  \
    input(__VA_ARGS__)
#define ULL(...)                                                               \
    unsigned long long __VA_ARGS__;                                            \
    input(__VA_ARGS__)
#define VEC(name, type, len)                                                   \
    vector<type> name(len);                                                    \
    input(name);
#define VEC2(name, type, len1, len2)                                           \
    vector name(len1, vector<type>(len2));                                     \
    input(name);
// other macros
// https://trap.jp/post/1224/
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define UNIQUE(v)                                                              \
    sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()), v.shrink_to_fit()
#define REV(v) reverse(ALL(v))
#define SZ(v) ((int)(v).size())
#define MIN(v) (*min_element(ALL(v)))
#define MAX(v) (*max_element(ALL(v)))
// util const
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
// util functions
void Case(int i) { cout << "Case #" << i << ": "; }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
template <class T> inline bool chmax(T &a, T b) {
    return (a < b ? a = b, true : false);
}
template <class T> inline bool chmin(T &a, T b) {
    return (a > b ? a = b, true : false);
}
template <class T, int dim>
auto make_vector_impl(vector<int>& sizes, const T &e) {
    if constexpr(dim == 1) {
        return vector(sizes[0], e);
    } else {
        int n = sizes[dim - 1];
        sizes.pop_back();
        return vector(n, make_vector_impl<T, dim - 1>(sizes, e));
    }
}
template <class T, int dim>
auto make_vector(const int (&sizes)[dim], const T &e = T()) {
    vector<int> s(dim);
    for(int i = 0; i < dim; i++) s[i] = sizes[dim - i - 1];
    return make_vector_impl<T, dim>(s, e);
}
vector<int> iota_gen(int n, int start = 0) {
    vector<int> ord(n);
    iota(ord.begin(), ord.end(), start);
    return ord;
}
template<typename T>
vector<int> ord_sort(const vector<T>& v, bool greater = false) {
    auto ord = iota_gen((int)v.size());
    sort(ALL(ord), [&](int i, int j) {
        if(greater) return v[i] > v[j];
        return v[i] < v[j];
    });
    return ord;
}
#pragma endregion Macros


#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif


#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

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


        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

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

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

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

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class 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;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _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 >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        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 {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    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;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _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 >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        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 {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    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;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

using mint = atcoder::modint998244353;

template <class E, class V, E (*merge)(E, E), E (*e)(), E (*put_edge)(V, int), V (*put_vertex)(E, int)>
struct RerootingDP {
    struct edge {
        int to, idx, xdi;
    };
    RerootingDP(int n_ = 0) : n(n_), inner_edge_id(0) {
        es.resize(2*n-2);
        start.resize(2*n-2);
        if (n == 1) es_build();
    }
    void add_edge(int u, int v, int idx, int xdi){
        start[inner_edge_id] = u;
        es[inner_edge_id] = {v,idx,xdi};
        inner_edge_id++;
        start[inner_edge_id] = v;
        es[inner_edge_id] = {u,xdi,idx};
        inner_edge_id++;
        if (inner_edge_id == 2*n-2){
            es_build();
        }
    }
    vector<V> build(int root_ = 0){
        root = root_;
        vector<V> subdp(n); subdp[0] = put_vertex(e(),0);
        outs.resize(n);
        vector<int> geta(n+1,0);
        for (int i = 0; i < n; i++) geta[i+1] = start[i+1] - start[i] - 1;
        geta[root+1]++;
        for (int i = 0; i < n; i++) geta[i+1] += geta[i];
        auto dfs = [&](auto sfs, int v, int f) -> void {
            E val = e();
            for (int i = start[v]; i < start[v+1]; i++){
                if (es[i].to == f){
                    swap(es[start[v+1]-1],es[i]);
                }
                if (es[i].to == f) continue;
                sfs(sfs,es[i].to,v);
                E nval = put_edge(subdp[es[i].to],es[i].idx);
                outs[geta[v]++] = nval;
                val = merge(val,nval);
            }
            subdp[v] = put_vertex(val, v);
        };
        dfs(dfs,root,-1);
        return subdp;
    }
    vector<V> reroot(){
        vector<E> reverse_edge(n);
        reverse_edge[root] = e();
        vector<V> answers(n);
        auto dfs = [&](auto sfs, int v) -> void {
            int le = outs_start(v);
            int ri = outs_start(v+1);
            int siz = ri - le;
            vector<E> rui(siz+1);
            rui[siz] = e();
            for (int i = siz-1; i >= 0; i--){
                rui[i] = merge(outs[le+i],rui[i+1]);
            }
            answers[v] = put_vertex(merge(rui[0],reverse_edge[v]),v);
            E lui = e();
            for (int i = 0; i < siz; i++){
                V rdp = put_vertex(merge(merge(lui,rui[i+1]),reverse_edge[v]),v);
                reverse_edge[es[start[v]+i].to] = put_edge(rdp,es[start[v]+i].xdi);
                lui = merge(lui,outs[le+i]);
                sfs(sfs,es[start[v]+i].to);
            }
        };
        dfs(dfs,root);
        return answers;
    }
    private:
    int n, root, inner_edge_id;
    vector<E> outs;
    vector<edge> es;
    vector<int> start;
    int outs_start(int v){
        int res = start[v] - v;
        if (root < v) res++;
        return res;
    }
    void es_build(){
        vector<edge> nes(2*n-2);
        vector<int> nstart(n+2,0);
        for (int i = 0; i < 2*n-2; i++) nstart[start[i]+2]++;
        for (int i = 0; i < n; i++) nstart[i+1] += nstart[i];
        for (int i = 0; i < 2*n-2; i++) nes[nstart[start[i]+1]++] = es[i];
        swap(es,nes);
        swap(start,nstart);
    }
};

int N;
vector<int> A;

mint merge(mint a, mint b){
    return a + b;
}
mint e(){
    return mint(0);
}
mint put_edge(mint v, int i){
    return v;
}
mint put_vertex(mint e, int v){
    return mint(A[v]) * (e + 1);
}

void solve() {
    cin >> N;
    A.resize(N);
    REP(i, N) cin >> A[i];
    RerootingDP<mint, mint, merge, e, put_edge, put_vertex> rdp(N);
    REP(i, N-1) {
        INT(u, v);
        u--, v--;
        rdp.add_edge(u, v, i, i);
    }
    rdp.build();
    auto res = rdp.reroot();
    mint ans = 0;
    REP(i, N) ans += res[i];
    REP(i, N) ans -= A[i];
    ans /= 2;
    print(ans);
}

int main() {
    int T = 1;
    // cin >> T;
    while(T--) solve();
}