//
//  main.cpp
//

#include <algorithm>
#include <array>
#include <assert.h>
#include <complex>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <math.h>
#include <memory>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

using ll = int64_t;
using ull = uint64_t;
constexpr ll LL_MAX = numeric_limits<ll>::max();
constexpr ull ULL_MAX = numeric_limits<ull>::max();

template<typename T>
vector<T> make_vec_nd(T init, ll size) {
    return vector<T>(size, init);
}
template<typename T, typename... Args>
auto make_vec_nd(T init, ll size, Args... rest) {
    auto inner = make_vec_nd(init, rest...);
    return vector<decltype(inner)>(size, inner);
}

#define rep(i, a, b) for (ll i = (a); i < (b); i++)
#define rrep(i, a, b) for (ll i = (a)-1; i >= (b); i--)

template<typename Monoid>
struct SegmentTree {
    using Op = function<Monoid(const Monoid& lhs, const Monoid& rhs)>;
    ll width;
    vector<Monoid> node;
    Op op;
    Monoid unit;
    
    SegmentTree(ll N, Op op, Monoid unit)
    : SegmentTree(vector<Monoid>(N, unit), op, unit) {}
    SegmentTree(const vector<Monoid>& elems, Op op, Monoid unit)
    : op(op)
    , unit(unit) {
        width = 1;
        while (width < elems.size()) {
            width *= 2;
        }
        node.resize(2 * width - 1, unit);
        for (size_t i = 0; i < elems.size(); i++) {
            node[i + width - 1] = elems[i];
        }
        for (size_t i = width - 2; i != numeric_limits<size_t>::max(); i--) {
            node[i] = op(node[2 * i + 1], node[2 * i + 2]);
        }
    }
    void update(ll idx, Monoid elem) {
        idx += width - 1;
        node[idx] = elem;
        while (idx >= 1) {
            idx = (idx - 1) / 2;
            node[idx] = op(node[2 * idx + 1], node[2 * idx + 2]);
        }
    }
    Monoid query_core(ll a, ll b, ll root, ll left, ll right) const {
        // assert([left, right) = root以下にある範囲)
        assert(0 <= a && b <= width);
        if (right <= a || b <= left) {
            return unit;
        }
        if (a <= left && right <= b) {
            return node[root];
        }
        ll mid = (left + right) / 2;
        Monoid ans_l = query_core(a, b, 2 * root + 1, left, mid);
        Monoid ans_r = query_core(a, b, 2 * root + 2, mid, right);
        return op(ans_l, ans_r);
    }
    Monoid query(ll a, ll b) const {
        assert(0 <= a && b <= width);
        return query_core(a, b, 0, 0, width);
    }
    Monoid operator[](size_t idx) { return query(idx, idx + 1); }
};

void dfs(ll now, ll max_upto, SegmentTree<ll>& seg, vector<ll>& ans, vector<vector<ll>>& tree, vector<ll>& As, vector<bool>& visited) {
    visited[now] = true;
    ll end_now = max((ll)0, seg.query(0, As[now])) + 1;
    max_upto = max(max_upto, end_now);
    ans[now] = max_upto;
    ll bak = seg[As[now]];
    seg.update(As[now], max(bak, end_now));
    for (ll to : tree[now]) {
        if (visited[to]) {
            continue;
        }
        dfs(to, max_upto, seg, ans, tree, As, visited);
    }
    seg.update(As[now], bak);
}

int main() {
    ll N;
    cin >> N;
    vector<ll> As(N);
    rep(i,0,N) {
        cin >> As[i];
    }
    vector<vector<ll>> tree(N);
    rep(i,0,N-1) {
        ll u, v;
        cin >> u >> v;
        u--;
        v--;
        tree[u].push_back(v);
        tree[v].push_back(u);
    }
    set<ll> compress_set;
    rep(i,0,N) {
        compress_set.insert(As[i]);
    }
    unordered_map<ll, ll> compress_map;
    ll value_cnt = 0;
    for (ll val : compress_set) {
        compress_map[val] = value_cnt;
        value_cnt++;
    }
    rep(i,0,N) {
        As[i] = compress_map[As[i]];
    }
    SegmentTree<ll> seg(value_cnt, [](ll lhs, ll rhs){ return max(lhs, rhs); }, numeric_limits<ll>::min());
    vector<ll> ans(N);
    vector<bool> visited(N);
    dfs(0, 0, seg, ans, tree, As, visited);
    rep(i,0,N) {
        cout << ans[i] << endl;
    }
}



Measured memory_bytes: 54920