import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

import static java.lang.Math.max;
import static java.lang.Math.min;

public class Main {
    static In in = new In();
    static Out out = new Out(false, false);
    static final long inf = 0x1fffffffffffffffL;
    static final int iinf = 0x3fffffff;
    static final double eps = 1e-9;
    static long mod = 998244353;

    int[] a;
    int[] ans;
    void solve() {
        int n = in.nextInt();
        a = in.nextIntArray(n);
        ans = new int[n];
        List<List<Integer>> edges = in.nextGraph(n, n - 1, false);
        new CentroidDecomposition(edges) {
            void query(int center, List<List<Integer>> left, List<List<Integer>> right) {
                f(center, left, right);
                f(center, right, left);
            }
        };
        out.println(ans);
    }

    List<Integer> table;
    void f(int s, List<List<Integer>> x, List<List<Integer>> y) {
        table = new ArrayList<>();
        dfs1(s, s, 0, x);
        for (int i = table.size() - 2; i >= 0; i--) {
            table.set(i, min(table.get(i), table.get(i + 1)));
        }
        dfs2(s, s, 0, y);
    }

    void dfs1(int node, int parent, int depth, List<List<Integer>> x) {
        while (table.size() <= depth) {
            table.add(0);
        }
        table.set(depth, min(table.get(depth), -a[node]));
        for (int child : x.get(node)) {
            if (child == parent) continue;
            dfs1(child, node, depth + 1, x);
        }
    }

    void dfs2(int node, int parent, int depth, List<List<Integer>> y) {
        int left = -1;
        int right = table.size();
        while (right - left > 1) {
            int mid = (left + right) / 2;
            if (table.get(mid) <= -a[node]) {
                left = mid;
            } else {
                right = mid;
            }
        }
        if (right >= 1) {
            ans[node] = max(ans[node], depth + right - 1);
        }
        for (int child : y.get(node)) {
            if (child == parent) continue;
            dfs2(child, node, depth + 1, y);
        }
    }

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


abstract class CentroidDecomposition {
    int[] size;
    int[] count;
    int[] sort;
    boolean[] xy;
    int center;
    int n;
    List<List<List<Integer>>> bufLeft = new ArrayList<>();
    List<List<List<Integer>>> bufRight = new ArrayList<>();

    abstract void query(int center, List<List<Integer>> left, List<List<Integer>> right);

    public CentroidDecomposition(List<List<Integer>> edges) {
        this.n = edges.size();
        this.size = new int[n];
        this.count = new int[n];
        this.sort = new int[n];
        this.xy = new boolean[n];
        rec(edges.size(), 0, edges, 0);
    }

    private void rec(int m, int root, List<List<Integer>> edges, int depth) {
        if (m <= 2) {
            return;
        }
        size(root, -1, m, edges);
        int max = 0;
        for (int nei : edges.get(center)) {
            if (size[nei] > size[center]) {
                size[nei] = m - size[center];
            }
            count[size[nei]]++;
            max = max(max, size[nei] + 1);
        }
        for (int i = 1; i < max; i++) {
            count[i] += count[i - 1];
        }
        for (int nei : edges.get(center)) {
            sort[--count[size[nei]]] = nei;
        }
        Arrays.fill(count, 0, max, 0);
        int xs = 0;
        int ys = 0;
        int g = edges.get(center).size();
        for (int i = g - 1; i >= 0; i--) {
            if (xs < ys) {
                xy[sort[i]] = false;
                xs += size[sort[i]];
            } else {
                xy[sort[i]] = true;
                ys += size[sort[i]];
            }
        }
        while (bufLeft.size() <= depth) {
            List<List<Integer>> edgesLeft = new ArrayList<>();
            List<List<Integer>> edgesRight = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                edgesLeft.add(new ArrayList<>());
                edgesRight.add(new ArrayList<>());
            }
            bufLeft.add(edgesLeft);
            bufRight.add(edgesRight);
        }
        List<List<Integer>> left = bufLeft.get(depth);
        List<List<Integer>> right = bufRight.get(depth);
        left.get(center).clear();
        right.get(center).clear();
        for (int nei : edges.get(center)) {
            if (xy[nei]) {
                right.get(center).add(nei);
                build(nei, center, edges, right);
            } else {
                left.get(center).add(nei);
                build(nei, center, edges, left);
            }
        }
        query(center, left, right);
        rec(xs + 1, center, left, depth + 1);
        rec(ys + 1, center, right, depth + 1);
    }

    private void build(int node, int parent, List<List<Integer>> edges, List<List<Integer>> sub) {
        sub.set(node, edges.get(node));
        for (int child : edges.get(node)) {
            if (child != parent) {
                build(child, node, edges, sub);
            }
        }
    }

    private void size(int node, int parent, int m, List<List<Integer>> edges) {
        size[node] = 1;
        int max = 0;
        for (int child : edges.get(node)) {
            if (child != parent) {
                size(child, node, m, edges);
                size[node] += size[child];
                max = max(max, size[child]);
            }
        }
        max = max(max, m - size[node]);
        if (max * 2 <= m) {
            center = node;
        }
    }
}
abstract class CentroidDecomposition2 {
    int[] size;
    int[] count;
    int[] sort;
    int[] parent;
    boolean[] xy;
    int center;
    int n;
    List<List<List<Integer>>> bufLeft = new ArrayList<>();
    List<List<List<Integer>>> bufRight = new ArrayList<>();

    abstract void query(int center, List<List<Integer>> left, List<List<Integer>> right);

    public CentroidDecomposition2(List<List<Integer>> edges) {
        this.n = edges.size();
        this.size = new int[n];
        this.count = new int[n];
        this.sort = new int[n];
        this.xy = new boolean[n];
        this.parent = new int[n];
        rec(edges.size(), 0, edges, 0);
    }

    private void rec(int m, int root, List<List<Integer>> edges, int depth) {
        if (m <= 2) {
            return;
        }
        size(root, -1, m, edges);
        int max = 0;
        for (int nei : edges.get(center)) {
            if (size[nei] > size[center]) {
                size[nei] = m - size[center];
            }
            count[size[nei]]++;
            max = max(max, size[nei] + 1);
        }
        for (int i = 1; i < max; i++) {
            count[i] += count[i - 1];
        }
        for (int nei : edges.get(center)) {
            sort[--count[size[nei]]] = nei;
        }
        Arrays.fill(count, 0, max, 0);
        int xs = 0;
        int ys = 0;
        int g = edges.get(center).size();
        for (int i = g - 1; i >= 0; i--) {
            if (xs < ys) {
                xy[sort[i]] = false;
                xs += size[sort[i]];
            } else {
                xy[sort[i]] = true;
                ys += size[sort[i]];
            }
        }
        while (bufLeft.size() <= depth) {
            List<List<Integer>> edgesLeft = new ArrayList<>();
            List<List<Integer>> edgesRight = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                edgesLeft.add(new ArrayList<>());
                edgesRight.add(new ArrayList<>());
            }
            bufLeft.add(edgesLeft);
            bufRight.add(edgesRight);
        }
        List<List<Integer>> left = bufLeft.get(depth);
        List<List<Integer>> right = bufRight.get(depth);
        left.get(center).clear();
        right.get(center).clear();
        for (int nei : edges.get(center)) {
            if (xy[nei]) {
                right.get(center).add(nei);
                build(nei, center, edges, right);
            } else {
                left.get(center).add(nei);
                build(nei, center, edges, left);
            }
        }
        query(center, left, right);
        rec(xs + 1, center, left, depth + 1);
        rec(ys + 1, center, right, depth + 1);
    }

    private void build(int root, int par, List<List<Integer>> edges, List<List<Integer>> sub) {
        deque.addLast(root);
        parent[root] = par;
        while (!deque.isEmpty()) {
            int u = deque.removeLast();
            sub.set(u, edges.get(u));
            for (int child : edges.get(u)) {
                if (child != parent[u]) {
                    parent[child] = u;
                    deque.addLast(child);
                }
            }
        }
    }

    Deque<Integer> deque = new ArrayDeque<>();
    private void size(int root, int par, int m, List<List<Integer>> edges) {
        deque.addLast(~root);
        deque.addLast(root);
        parent[root] = par;
        size[root] = 1;
        while (!deque.isEmpty()) {
            int u = deque.removeLast();
            if (u < 0) {
                u = ~u;
                if (parent[u] != -1) {
                    size[parent[u]] += size[u];
                }
                int max = 0;
                for (int child : edges.get(u)) {
                    if (child != parent[u]) {
                        max = max(max, size[child]);
                    }
                }
                max = max(max, m - size[u]);
                if (max * 2 <= m) {
                    center = u;
                }
            } else {
                for (int child : edges.get(u)) {
                    if (child != parent[u]) {
                        parent[child] = u;
                        size[child] = 1;
                        deque.addLast(~child);
                        deque.addLast(child);
                    }
                }
            }
        }
    }
}

class In {
    private final BufferedInputStream reader = new BufferedInputStream(System.in);
    private final byte[] buffer = new byte[0x10000];
    private int i = 0;
    private int length = 0;

    public int read() {
        if (i == length) {
            i = 0;
            try {
                length = reader.read(buffer);
            } catch (IOException ignored) {
            }
            if (length == -1) {
                return 0;
            }
        }
        if (length <= i) {
            throw new RuntimeException();
        }
        return buffer[i++];
    }

    public String next() {
        StringBuilder builder = new StringBuilder();
        int b = read();
        while (b < '!' || '~' < b) {
            b = read();
        }
        while ('!' <= b && b <= '~') {
            builder.appendCodePoint(b);
            b = read();
        }
        return builder.toString();
    }

    public String nextLine() {
        StringBuilder builder = new StringBuilder();
        int b = read();
        while (b != 0 && b != '\r' && b != '\n') {
            builder.appendCodePoint(b);
            b = read();
        }
        if (b == '\r') {
            read();
        }
        return builder.toString();
    }

    public int nextInt() {
        long val = nextLong();
        if (val < Integer.MIN_VALUE || Integer.MAX_VALUE < val) {
            throw new NumberFormatException();
        }
        return (int)val;
    }

    public long nextLong() {
        int b = read();
        while (b < '!' || '~' < b) {
            b = read();
        }
        boolean neg = false;
        if (b == '-') {
            neg = true;
            b = read();
        }
        long n = 0;
        int c = 0;
        while ('0' <= b && b <= '9') {
            n = n * 10 + b - '0';
            b = read();
            c++;
        }
        if (c == 0 || c >= 2 && n == 0) {
            throw new NumberFormatException();
        }
        return neg ? -n : n;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public char[] nextCharArray() {
        return next().toCharArray();
    }

    public String[] nextStringArray(int n) {
        String[] s = new String[n];
        for (int i = 0; i < n; i++) {
            s[i] = next();
        }
        return s;
    }

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

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

    public 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;
    }

    public int[][] nextIntMatrix(int h, int w) {
        int[][] a = new int[h][w];
        for (int i = 0; i < h; i++) {
            a[i] = nextIntArray(w);
        }
        return a;
    }

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

    public 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;
    }

    public long[][] nextLongMatrix(int h, int w) {
        long[][] a = new long[h][w];
        for (int i = 0; i < h; i++) {
            a[i] = nextLongArray(w);
        }
        return a;
    }

    public List<List<Integer>> nextGraph(int n, int m, boolean directed) {
        List<List<Integer>> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            res.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int u = nextInt() - 1;
            int v = nextInt() - 1;
            res.get(u).add(v);
            if (!directed) {
                res.get(v).add(u);
            }
        }
        return res;
    }
}

class Out {
    private final PrintWriter out = new PrintWriter(System.out);
    private final PrintWriter err = new PrintWriter(System.err);
    public boolean autoFlush;
    public boolean enableDebug;

    public Out(boolean autoFlush, boolean enableDebug) {
        this.autoFlush = autoFlush;
        this.enableDebug = enableDebug;
    }

    public void debug(Object... args) {
        if (!enableDebug) {
            return;
        }
        if (args == null || args.getClass() != Object[].class) {
            args = new Object[] {args};
        }
        err.println(Arrays.stream(args).map(obj -> format(obj, true)).collect(Collectors.joining(" ")));
        err.flush();
    }

    private String format(Object obj, boolean canMultiline) {
        if (obj == null) return "null";
        Class<?> clazz = obj.getClass();
        if (clazz == Double.class) return String.format("%.10f", obj);
        if (clazz == int[].class) return Arrays.toString((int[])obj);
        if (clazz == long[].class) return Arrays.toString((long[])obj);
        if (clazz == char[].class) return String.valueOf((char[])obj);
        if (clazz == boolean[].class) return IntStream.range(0, ((boolean[])obj).length).mapToObj(i -> ((boolean[])obj)[i] ? "1" : "0").collect(Collectors.joining());
        if (clazz == double[].class) return Arrays.toString(Arrays.stream((double[])obj).mapToObj(a -> format(a, false)).toArray());
        if (canMultiline && clazz.isArray() && clazz.componentType().isArray()) return Arrays.stream((Object[])obj).map(a -> format(a, false)).collect(Collectors.joining("\n"));
        if (clazz == Object[].class) return Arrays.toString(Arrays.stream((Object[])obj).map(a -> format(a, false)).toArray());
        if (clazz.isArray()) return Arrays.toString((Object[])obj);
        return String.valueOf(obj);
    }

    public void println(Object... args) {
        if (args == null || args.getClass() != Object[].class) {
            args = new Object[] {args};
        }
        out.println(Arrays.stream(args)
                .map(obj -> obj instanceof Double ? String.format("%.10f", obj) : String.valueOf(obj))
                .collect(Collectors.joining(" ")));
        if (autoFlush) {
            out.flush();
        }
    }

    public void println(char a) {
        out.println(a);
        if (autoFlush) {
            out.flush();
        }
    }

    public void println(int a) {
        out.println(a);
        if (autoFlush) {
            out.flush();
        }
    }

    public void println(long a) {
        out.println(a);
        if (autoFlush) {
            out.flush();
        }
    }

    public void println(double a) {
        out.println(String.format("%.10f", a));
        if (autoFlush) {
            out.flush();
        }
    }

    public void println(String s) {
        out.println(s);
        if (autoFlush) {
            out.flush();
        }
    }

    public void println(char[] s) {
        out.println(String.valueOf(s));
        if (autoFlush) {
            out.flush();
        }
    }

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

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

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