We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i. Vertex i has an integer a_i written on it. For every integer k from 1 through N, solve the following problem:

* We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.



Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq a_i \leq 10^9
* 1 \leq u_i , v_i \leq N
* u_i \neq v_i
* The given graph is a tree.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}


Output

Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.

Example

Input

10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10


Output

1
2
3
3
4
4
5
2
2
3
/*
    Author: Anthony Ngene
    Created: 08/08/2020 - 05:53
*/

import java.io.*;
import java.util.*;

public class Main {
    // To live a pure unselfish life, one must count nothing as one's own in the midst of abundance. - Buddha
    static long[] stacks;
    static long[] costs;
    static int n;
    static int[] res;
    static int hi;
    public static void main(String[] args) throws IOException {
        in = new FastScanner();

        n = in.intNext();
        costs = in.nextLongArray(n);
        adj = in.adjacencyList(n, n - 1);
        stacks = new long[n + 1];
        res = new int[n + 1];
        hi = 1;
        dfs(1, new boolean[n + 1]);
        for (int i = 1; i < n + 1; i++) out.println(res[i]);

        out.close();
    }

    static void dfs(int node, boolean[] visited) {
        visited[node] = true;
        int l = 1;
        int h = hi;
        long cost = costs[node - 1];
        int best = 1;
        while (l <= h) {
            int mid = (l + h) / 2;
            if (stacks[mid] == 0 || stacks[mid] >= cost) {
                best = mid;
                h = mid - 1;
            } else {
                l = mid + 1;
            }
        }
        if (best == hi) hi++;
        res[node] = hi - 1;
        long prev = stacks[best];
        stacks[best] = cost;
        for (int child : adj[node]) {
            if (!visited[child]) dfs(child, visited);
        }

        stacks[best] = prev;
        if (stacks[best] == 0) hi--;
    }


private static final FastWriter out = new FastWriter();
private static FastScanner in;
static ArrayList<Integer>[] adj;
private static long e97 = (long)1e9 + 7;
static class FastWriter {
    private static final int IO_BUFFERS = 128 * 1024;
    private final StringBuilder out;
    public FastWriter() {
        out = new StringBuilder(IO_BUFFERS);
    }
    public FastWriter p(Object object) {
        out.append(object);
        return this;
    }
    public FastWriter p(String format, Object... args) {
        out.append(String.format(format, args));
        return this;
    }
    public FastWriter pp(Object... args) {
        for (Object ob : args) {
            out.append(ob).append(" ");
        }
        out.append("\n");
        return this;
    }
    public FastWriter println(Object object) {
        out.append(object).append("\n");
        return this;
    }
    public void toFile(String fileName) throws IOException {
        BufferedWriter writer = new BufferedWriter(new FileWriter(fileName));
        writer.write(out.toString());
        writer.close();
    }
    public void close() throws IOException {
        System.out.print(out);
    }
}
static class FastScanner {
    private InputStream sin = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(){}
    public FastScanner(String filename) throws FileNotFoundException {
        File file = new File(filename);
        sin = new FileInputStream(file);
    }
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = sin.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long longNext() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b) || b == ':'){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int intNext() {
        long nl = longNext();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double doubleNext() { return Double.parseDouble(next());}
    public long[] nextLongArray(final int n){
        final long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = longNext();
        return a;
    }
    public int[] nextIntArray(final int n){
        final int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = intNext();
        return a;
    }
    public ArrayList<Integer>[] getAdj(int n) {
        ArrayList<Integer>[] adj = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
        return adj;
    }

    public ArrayList<Integer>[] adjacencyList(int n, int m) throws IOException {
        adj = getAdj(n);
        for (int i = 0; i < m; i++) {
            int a = intNext(), b = intNext();
            adj[a].add(b);
            adj[b].add(a);
        }
        return adj;
    }
}
}
