#include <bits/stdc++.h>
using namespace std;

// Define
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <class T> using pvector = vector<pair<T, T>>;
template <class T>
using rpriority_queue = priority_queue<T, vector<T>, greater<T>>;
constexpr const ll dx[4] = {1, 0, -1, 0};
constexpr const ll dy[4] = {0, 1, 0, -1};
constexpr const ll MOD = 1e9 + 7;
constexpr const ll mod = 998244353;
constexpr const ll INF = 1LL << 60;
constexpr const ll inf = 1 << 30;
constexpr const char rt = '\n';
constexpr const char sp = ' ';
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define elif else if
#define all(a, v, ...)                                                         \
    ([&](decltype((v)) w) { return (a)(begin(w), end(w), ##__VA_ARGS__); })(v)
#define rall(a, v, ...)                                                        \
    ([&](decltype((v)) w) { return (a)(rbegin(w), rend(w), ##__VA_ARGS__); })(v)
#define fi first
#define se second

template <class T> bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T> bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}

// Debug
#define debug(...)                                                             \
    {                                                                          \
        cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ";                     \
        for (auto &&X : {__VA_ARGS__}) cerr << "[" << X << "] ";               \
        cerr << rt;                                                            \
    }

#define dump(a, h, w)                                                          \
    {                                                                          \
        cerr << __LINE__ << ": " << #a << " = [" << rt;                        \
        rep(_i, h) {                                                           \
            rep(_j, w) cerr << a[_i][_j] << sp;                                \
            cerr << rt;                                                        \
        }                                                                      \
        cerr << "]" << rt;                                                     \
    }

#define vdump(a, n)                                                            \
    {                                                                          \
        cerr << __LINE__ << ": " << #a << " = [";                              \
        rep(_i, n) if (_i) cerr << sp << a[_i];                                \
        else cerr << a[_i];                                                    \
        cerr << "]" << rt;                                                     \
    }

// Loop
#define inc(i, a, n) for (ll i = (a), _##i = (n); i <= _##i; ++i)
#define dec(i, a, n) for (ll i = (a), _##i = (n); i >= _##i; --i)
#define rep(i, n) for (ll i = 0, _##i = (n); i < _##i; ++i)
#define each(i, a) for (auto &&i : a)

// Stream
#define fout(n) cout << fixed << setprecision(n)
struct io {
    io() { cin.tie(nullptr), ios::sync_with_stdio(false); }
} io;

// Speed
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

// Math
inline constexpr ll gcd(const ll a, const ll b) {
    return b ? gcd(b, a % b) : a;
}
inline constexpr ll lcm(const ll a, const ll b) { return a / gcd(a, b) * b; }

inline constexpr ll modulo(const ll n, const ll m = MOD) {
    ll k = n % m;
    return k + m * (k < 0);
}
inline constexpr ll chmod(ll &n, const ll m = MOD) {
    n %= m;
    return n += m * (n < 0);
}
inline constexpr ll mpow(ll a, ll n, const ll m = MOD) {
    ll r = 1;
    rep(i, 64) {
        if (n & (1LL << i)) r *= a;
        chmod(r, m);
        a *= a;
        chmod(a, m);
    }
    return r;
}
inline ll inv(const ll n, const ll m = MOD) {
    ll a = n, b = m, x = 1, y = 0;
    while (b) {
        ll t = a / b;
        a -= t * b;
        swap(a, b);
        x -= t * y;
        swap(x, y);
    }
    return modulo(x, m);
}

struct RUMQ {
    static const ll n = 1LL << 20;
    vector<ll> node, lazy, flag;
    RUMQ() : node(n * 2 - 1), lazy(n * 2 - 1), flag(n * 2 - 1) {}
    inline void eval(ll i, ll l, ll r) {
        if (flag[i]) {
            node[i] = lazy[i];
            if (r - l > 1) {
                lazy[i * 2 + 1] = lazy[i * 2 + 2] = lazy[i];
                flag[i * 2 + 1] = flag[i * 2 + 2] = true;
            }
            lazy[i] = 0;
            flag[i] = false;
        }
    }
    inline void update(ll a, ll b, ll x, ll i = 0, ll l = 0, ll r = 1LL << 20) {
        eval(i, l, r);
        if (b <= l || r <= a) return;
        if (a <= l && r <= b) {
            lazy[i] = x;
            flag[i] = true;
            eval(i, l, r);
        } else {
            update(a, b, x, i * 2 + 1, l, (l + r) / 2);
            update(a, b, x, i * 2 + 2, (l + r) / 2, r);
            node[i] = std::max(node[i * 2 + 1], node[i * 2 + 2]);
        }
    }
    inline ll max(ll a, ll b, ll i = 0, ll l = 0, ll r = 1LL << 20) {
        if (b <= l || r <= a) return -INF;
        eval(i, l, r);
        if (a <= l && r <= b) return node[i];
        return std::max(max(a, b, i * 2 + 1, l, (l + r) / 2),
                        max(a, b, i * 2 + 2, (l + r) / 2, r));
    }
} seg;

ll A[200000];
vector<ll> G[200000];
map<ll, ll> M;
ll res[200000];
signed main() {
    ll N;
    cin >> N;
    rep(i, N) cin >> A[i], M[A[i]] = 1;
    ll cnt = 0;
    each(i, M) {
        cnt++;
        i.se = cnt;
    }
    rep(i, N - 1) {
        ll a, b;
        cin >> a >> b;
        G[a - 1].pb(b - 1), G[b - 1].pb(a - 1);
    }
    function<void(ll, ll)> dfs = [&](ll t, ll p) {
        res[t] = max(seg.max(0, M[A[t]]) + 1, seg.max(0, M.size() + 1));
        ll mem = seg.max(M[A[t]], M[A[t]] + 1);
        seg.update(M[A[t]], M[A[t]] + 1, max(mem, seg.max(0, M[A[t]]) + 1));
        each(i, G[t]) if (i != p) dfs(i, t);
        seg.update(M[A[t]], M[A[t]] + 1, mem);
    };
    dfs(0, -1);
    rep(i, N) cout << res[i] << rt;
}

// -g -D_GLIBCXX_DEBUG -fsanitize=undefined


Measured memory_bytes: 98148