#include <bits/stdc++.h>  // clang-format off
using Int = long long;
#define REP_(i, a_, b_, a, b, ...) for (Int i = (a), lim##i = (b); i < lim##i; i++)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
struct SetupIO { SetupIO() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(13); } } setup_io;
#ifndef dump
#define dump(...)
#endif  // clang-format on

/**
 *    author:  knshnb
 *    created: Sat May  2 21:57:02 JST 2020
 **/

/// @docs src/DataStructure/SegmentTree.md
template <class T, class F> struct SegmentTree {
    const F op;
    const T e;
    SegmentTree(F op_, T e_) : op(op_), e(e_) {}
    int n;
    std::vector<T> t;
    void set_by_identity(int n_) {
        n = n_;
        t.clear(), t.resize(2 * n, e);
    }
    void set_by_vector(const std::vector<T>& a) {
        n = a.size();
        t.clear(), t.resize(2 * n, e);
        for (int i = 0; i < n; i++) t[i + n] = a[i];
        build();
    }
    void build() {
        for (int i = n - 1; i; --i) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    T& operator[](int i) { return t[i + n]; }
    // [l, r)
    T query(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        T resl = e, resr = e;
        for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
            if (l & 1) resl = op(resl, t[l++]);
            if (r & 1) resr = op(t[--r], resr);
        }
        return op(resl, resr);
    }
    // i番目をxに変更
    void update(int i, const T& x) {
        assert(0 <= i && i < n);
        t[i += n] = x;
        while (i >>= 1) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    // i番目にxを作用 (a[i] = op(a[i], x))
    void operate(int i, const T& x) {
        assert(0 <= i && i < n);
        i += n;
        t[i] = op(t[i], x);
        while (i >>= 1) t[i] = op(t[2 * i], t[2 * i + 1]);
    }
    friend std::string to_string(const SegmentTree<T, F>& seg) {
        return to_string(std::vector<T>(seg.t.begin() + seg.n, seg.t.end()));
    }
};
template <class T, class F> auto make_segment_tree(F op, T e) { return SegmentTree<T, F>(op, e); }

template <class T> struct Compressor {
    std::vector<T> val;
    void insert(T x) { val.push_back(x); }
    void build() {
        std::sort(val.begin(), val.end());
        val.erase(std::unique(val.begin(), val.end()), val.end());
    }
    int operator[](T x) { return std::lower_bound(val.begin(), val.end(), x) - val.begin(); }
    int size() { return val.size(); }
};

signed main() {
    int n;
    std::cin >> n;
    Compressor<Int> c;
    std::vector<Int> a(n);
    REP(i, n) std::cin >> a[i], c.insert(a[i]);
    c.build();
    REP(i, n) a[i] = c[a[i]];
    std::vector<std::vector<int>> g(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v;
        std::cin >> u >> v;
        u--, v--;
        g[u].push_back(v);
        g[v].push_back(u);
    }

    auto seg = make_segment_tree<Int>([&](Int x, Int y) { return std::max(x, y); }, 0);
    seg.set_by_identity(n);
    std::vector<Int> ans(n);
    auto dfs = [&](auto f, int v, int prv) -> void {
        Int bef = seg[a[v]];
        seg.update(a[v], seg.query(0, a[v]) + 1);
        ans[v] = seg.query(0, n);
        for (int s : g[v]) {
            if (s == prv) continue;
            f(f, s, v);
        }
        seg.update(a[v], bef);
    };
    dfs(dfs, 0, -1);
    for (Int x : ans) {
        std::cout << x << "\n";
    }
}


Measured memory_bytes: 47612