import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class Main {
    static In in = new In();
    static Out out = new Out();
    static final long mod = 1000000007;
    static final long inf = 0xfffffffffffffffL;
    static final int iinf = 2000000000;
    static final int[] da = {-1, 0, 1, 0, -1, 1, 1, -1, -1};

    int n;
    int[] a;
    List<List<Integer>> edges;
    void solve() {
        n = in.nextInt();
        edges = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            edges.add(new ArrayList<>());
        }
        a = in.nextIntArray(n);
        for (int i = 1; i < n; i++) {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            edges.get(u).add(v);
            edges.get(v).add(u);
        }
        ans = new int[n];
        table = new int[n + 1];
        Arrays.fill(table, iinf);
        table[0] = 0;
        dfs(0, 0);
        for (int i : ans) {
            out.println(i);
        }
    }

    int[] ans;
    int[] table;
    void dfs(int node, int parent) {
        int left = -1, right = n;
        while (right - left > 1) {
            int mid = (left + right) / 2;
            if (table[mid] < a[node]) {
                left = mid;
            } else {
                right = mid;
            }
        }
        int old = table[right];
        table[right] = a[node];
        int left1 = -1;
        int right1 = n + 1;
        while (right1 - left1 > 1) {
            int mid = (left1 + right1) / 2;
            if (table[mid] == iinf) {
                right1 = mid;
            } else {
                left1 = mid;
            }
        }
        ans[node] = left1;
        for (int v : edges.get(node)) {
            if (v != parent) {
                dfs(v, node);
            }
        }
        table[right] = old;
    }

    public static void main(String[]$) {
        new Main().solve();
        out.flush();
    }
}

class In {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    char[][] nextCharArray(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }
}

class Out {
    private PrintWriter out = new PrintWriter(System.out);
    boolean autoFlush = false;

    void println(Object... a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (Object obj : a) {
            joiner.add(String.valueOf(obj));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (int i : a) {
            joiner.add(Integer.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (long i : a) {
            joiner.add(Long.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void flush() {
        out.flush();
    }
}


Measured memory_bytes: 97024