#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <array>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <sstream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <list>
#include <numeric>
#include <stack>
#include <iomanip>
#include <random>
#include <complex>
#include <functional>
#include <tuple>

using namespace std;

#define Rep(i,a,b) for(ll i = a; i < b; ++i)
#define rep(i,b) Rep(i,0,b)
#define allof(a) (a).begin(), (a).end()

#define Yes(q) ((q) ? "Yes" : "No")
#define YES(q) ((q) ? "YES" : "NO")
#define Possible(q) ((q) ? "Possible" : "Impossible")
#define POSSIBLE(q) ((q) ? "POSSIBLE" : "IMPOSSIBLE")

using ll = long long;

constexpr int inf = 1e9 + 7;
constexpr ll infll = 1ll << 60ll;
constexpr ll mod = 1e9 + 7;
// 0~3までは右左下上 4~7までは斜め
constexpr int dx[] = { 1, 0, -1, 0, 1, 1, -1, -1 };
constexpr int dy[] = { 0, -1, 0, 1, 1, -1, -1, 1 };

namespace {
    template<typename T> void chmax(T& a, T b) { a = std::max(a, b); }
    template<typename T> void chmin(T& a, T b) { a = std::min(a, b); }
    template<typename T> void chadd(T& a, T b) { a = a + b; }

    void Cout(long long x, const char* end = "\n") { std::cout << x << end; }
    template <typename T> void Cout(const T& x, const char* end = "\n") { std::cout << x << end; }
    template <typename T> void Cout(const std::vector<T>& x, const char* sep = " ", const char* end = "\n") { for (std::size_t i = 0, sz = x.size(); i < sz; i++) { std::cout << x[i] << (i == sz - 1 ? end : sep); } }

    // 標準入出力
    struct inp {
        std::size_t sz;
        inp(std::size_t _sz = 1) : sz(_sz) {}
        template <typename T> operator T () const { T a; std::cin >> a; return a; }
        template <typename T> operator std::vector<T>() const { std::vector<T> a(sz); for (std::size_t i = 0; i < sz; i++) std::cin >> a[i]; return a; }
    };

    // 2次元用の標準入出力
    template<typename T>
    struct inpn {
        std::size_t szi, szj;
        inpn(std::size_t _szi, std::size_t _szj) : szi(_szi), szj(_szj) {}
        operator std::vector<std::vector<T>>() const {
            std::vector<std::vector<T>> a(szi, std::vector<T>(szj));
            for (std::size_t i = 0; i < szi; ++i)
                for (std::size_t j = 0; j < szj; ++j) cin >> a[i][j];
            return a;
        }
    };

    inp inp1; // input one

    struct Edge {
        ll to; // 移動先のノード
        ll cost; // 辺のコスト
        ll hoge; // 任意変更 いらないかも

        Edge(ll _to, ll _cost, ll _hoge = 0) : to(_to), cost(_cost), hoge(_hoge) {};
        bool operator< (const Edge& rhs) const {
            if (cost != rhs.cost) return cost > rhs.cost;
            else return to < rhs.to;
        }
    };

    using Graph = vector<vector<Edge>>;

    void dfs(int s, vector<int>& dp, vector<int>& ans, vector<bool>& used, const Graph& G, const vector<int>& a) {
        used[s] = true;

        int i = lower_bound(allof(dp), a[s]) - dp.begin();
        int prev = dp[i];
        dp[i] = a[s];
        //*lower_bound(allof(dp), a[s]) = a[s];
        int res = lower_bound(allof(dp), inf) - dp.begin();
        chmax(ans[s], res);

        for (auto edge : G[s]) {
            if (used[edge.to]) continue;

            dfs(edge.to, dp, ans, used, G, a);
        }

        // 戻るときに変更を戻す
        dp[i] = prev;
    }
}

int main() {

    int n = inp1;
    vector<int> a = inp(n);
    Graph G(n);
    rep(i, n - 1) {
        int v, u;
        cin >> u >> v;
        --u, --v;
        G[u].push_back(Edge(v, 1));
        G[v].push_back(Edge(u, 1));
    }

    vector<bool> used(n, false);
    vector<int> dp(n, inf);
    vector<int> ans(n, 0);

    dfs(0, dp, ans, used, G, a);

    for (auto x : ans) Cout(x);

    return 0;
}


Measured memory_bytes: 39928