#include using namespace std; //using namespace atcoder; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for(int i=(begin);i<(end);i++) #define REP(i, n) FOR(i,0,n) #define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--) #define IREP(i, n) IFOR(i,0,n) #define Sort(v) sort(v.begin(), v.end()) #define Reverse(v) reverse(v.begin(), v.end()) #define all(v) v.begin(),v.end() #define SZ(v) ((int)v.size()) #define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x)) #define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x)) #define chmax(a, b) a = max(a, b) #define chmin(a, b) a = min(a, b) #define bit(n) (1LL<<(n)) #define debug(x) cout << #x << "=" << x << endl; #define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, (int)v.size()){ cout << v[i_debug] << ","; } cout << endl; } #define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, (int)m.size()){ REP(j_debug, (int)m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;} } #define pb push_back #define fi first #define se second #define int long long #define INF 1000000000000000000 template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, vector &v){ for(int i = 0; i < (int)v.size(); i++) { cout << v[i]; if(i != (int)v.size() - 1) cout << endl; }; return os; } template ostream &operator<<(ostream &os, pair p){ cout << '(' << p.first << ',' << p.second << ')'; return os; } template void Out(T x) { cout << x << endl; } template void chOut(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); } using vec = vector; using mat = vector; using Pii = pair; using v_bool = vector; using v_Pii = vector; //int dx[4] = {1,0,-1,0}; //int dy[4] = {0,1,0,-1}; //char d[4] = {'D','R','U','L'}; //const int mod = 1000000007; const int mod = 998244353; template struct ModInt{ using ll = long long; ll val; void setval(ll v) { val = v % MOD; }; ModInt(): val(0) {} ModInt(ll v) { setval(v); }; ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); } ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); } ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); } ModInt operator/(const ModInt &x) const { return *this * x.inv(); } ModInt operator-() const { return ModInt(MOD - val); } ModInt operator+=(const ModInt &x) { return *this = *this + x; } ModInt operator-=(const ModInt &x) { return *this = *this - x; } ModInt operator*=(const ModInt &x) { return *this = *this * x; } ModInt operator/=(const ModInt &x) { return *this = *this / x; } bool operator==(const ModInt &x) const { return (*this).val == x.val; } friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; } friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; } ModInt pow(ll n) const { ModInt a = 1; if(n == 0) return a; int i0 = 64 - __builtin_clzll(n); for(int i = i0 - 1; i >= 0; i--){ a = a * a; if((n >> i) & 1) a *= (*this); } return a; } ModInt inv() const { return this->pow(MOD - 2); } void add_product(ModInt a, ModInt b){ (val += a.val * b.val) %= MOD; } void sbt_product(ModInt a, ModInt b){ (val -= a.val * b.val) %= MOD; if(val < 0) val += MOD; } }; using mint = ModInt; mint pow(mint x, long long n) { return x.pow(n); } //using mint = double; //for debug using mvec = vector; using mmat = vector; struct Combination{ vector fact, invfact; Combination(int N){ fact = vector({mint(1)}); invfact = vector({mint(1)}); fact_initialize(N); } void fact_initialize(int N){ int i0 = fact.size(); if(i0 >= N + 1) return; fact.resize(N + 1); invfact.resize(N + 1); for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i; invfact[N] = (mint)1 / fact[N]; for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); } mint nCr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if((int)fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[r] * invfact[n - r]; } mint nPr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if((int)fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[n - r]; } mint Catalan(int n){ if(n < 0) return 0; else if(n == 0) return 1; if((int)fact.size() < 2 * n + 1) fact_initialize(2 * n); return fact[2 * n] * invfact[n + 1] * invfact[n]; } }; template struct edge{ int to; T cost; int id; }; template struct Graph { int N; vector>> E; vec A; mvec dp, dq; const mint inv2 = 499122177; Graph(int N): N(N){ E = vector>>(N, vector>(0)); dp.resize(N); dq.resize(N); } void add_Directed_edge(int from, int to, T cost = 1, int id = 0){ E[from].push_back(edge({ to, cost, id })); } void add_Undirected_edge(int v1, int v2, T cost = 1, int id = 0){ add_Directed_edge(v1, v2, cost, id); add_Directed_edge(v2, v1, cost, id); } void dfs1(int v, int x, int p = -1){ if(A[v] < x) dp[v] = 1; else dp[v] = 0; for(auto e: E[v]) if(e.to != p){ dfs1(e.to, x, v); dp[v] *= (mint)1 - ((mint)1 - dp[e.to]) * inv2; } } void dfs2(int v, int x, mint &ans, int p = -1){ if(p == -1) dq[v] = 1; vec ch; for(auto e: E[v]) if(e.to != p){ ch.pb(e.to); } int n = SZ(ch); mint q0 = (mint)1 - ((mint)1 - dq[v]) * inv2; if(A[v] < x){ mvec dl(n + 1, 0), dr(n + 1, 0); dl[0] = dr[0] = 1; REP(i, n){ mint q = (mint)1 - ((mint)1 - dp[ch[i]]) * inv2; dl[i + 1] = dl[i] * q; } REP(i, n){ mint q = (mint)1 - ((mint)1 - dp[ch[n - 1 - i]]) * inv2; dr[i + 1] = dr[i] * q; } REP(i, n){ dq[ch[i]] = dl[i] * dr[n - 1 - i] * q0; } }else{ REP(i, n){ dq[ch[i]] = 0; } } REP(i, n) dfs2(ch[i], x, ans, v); ans += (mint)1 - dp[v] * q0; } }; signed main(){ int N; cin >> N; vec A(N); cin >> A; Graph G(N); REP(i, N - 1){ int u, v; cin >> u >> v; u--; v--; G.add_Undirected_edge(u, v); } G.A = A; mint ans = 0; FOR(x, 1, 1001){ G.dfs1(0, x); G.dfs2(0, x, ans); } ans *= pow((mint)2, N - 1); Out(ans); return 0; }