/*                         _
                        _ooOoo_
                       o8888888o
                       88" . "88
                       (| -_- |)
                       O\  =  /O
                    ____/`---'\____
                  .'  \\|     |//  `.
                 /  \\|||  :  |||//  \
                /  _||||| -:- |||||_  \
                |   | \\\  -  /'| |   |
                | \_|  `\`---'//  |_/ |
                \  .-\__ `-. -'__/-.  /
              ___`. .'  /--.--\  `. .'___
           ."" '<  `.___\_<|>_/___.' _> \"".
          | | :  `- \`. ;`. _/; .'/ /  .' ; |
          \  \ `-.   \_\_`. _.'_/_/  -' _.' /
===========`-.`___`-.__\ \___  /__.-'_.'_.-'================

                  Please give me AC.
*/

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <numeric>
#include <string>
#include <sstream>
#include <complex>
#include <bitset>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <deque>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <chrono>
#include <random>

using namespace std;

using int64 = long long;
using uint64 = unsigned long long;
using vi = vector<int>;
using vl = vector<int64>;
using pii = pair<int, int>;
using pll = pair<int64, int64>;

#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define all(v) (v).begin(), (v).end()
#define print(x) cout << (x) << '\n'
#define print2(x, y) cout << (x) << ' ' << (y) << '\n'
#define print3(x, y, z) cout << (x) << ' ' << (y) << ' ' << (z) << '\n'
#define printn(v) rep(i, (v).size() - 1) cout << (v)[i] << ' '; cout << (v)[n - 1] << '\n';
#define debug(x) cerr << #x << ": " << (x) << '\n'
#define debug2(x, y) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << '\n'
#define debug3(x, y, z) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << ", " << #z << ": " << (z) << '\n'
#define dbg(v) for (size_t _ = 0; _ < v.size(); ++_){cerr << #v << "[" << _ << "] : " << v[_] << '\n';}
// constant
const int INF = (1 << 30) - 1;
const int64 INF64 = (1LL << 62) - 1;

template<typename T>
T gcd(T a, T b) {
    if (a < b) return gcd(b, a);
    T r;
    while ((r = a % b)) {
        a = b;
        b = r;
    }
    return b;
}

template<typename T>
T lcm(const T a, const T b) {
    return a / gcd(a, b) * b;
}

template<typename T>
bool chmin(T &a, const T &b) {
    if (a > b) return a = b, true; else return false;
}

template<typename T>
bool chmax(T &a, const T &b) {
    if (a < b) return a = b, true; else return false;
}

// End of template.
// begin fast io

char buf[10000000], OUT[10000000];
int bufi = 0, outi = 0;

template<typename T>
void readui(T &n) {
    n = 0;
    int c = buf[bufi++];
    for (; '0' <= c && c <= '9'; c = buf[bufi++])
        n = 10 * n + c - '0';
}

template<typename T>
void readi(T &n) {
    bool negative = false;
    if (buf[bufi] == '-') negative = true, bufi++;
    readui(n);
    if (negative) n = -n;
}

template<typename T>
void readuf(T &x) {
    x = 0;
    T y = 0;
    int z = 0;
    int c = buf[bufi++];
    for (; '0' <= c && c <= '9'; c = buf[bufi++])
        x = 10 * x + c - '0';
    if (buf[bufi - 1] == '.')
        for (; '0' <= c && c <= '9'; c = buf[bufi++], ++z)
            y = 10 * y + c - '0';
    x += y / pow(10, z);
}

template<typename T>
void readf(T &x) {
    bool negative = false;
    if (buf[bufi] == '-') negative = true, bufi++;
    readuf(x);
    if (negative) x = -x;
}

void reads(string &s) {
    const int begin = bufi;
    int c;
    while (c = buf[bufi++], c != ' ' && c != '\n') {}
    s = string(buf + begin, buf + bufi);
}

void readline(string &s) {
    const int begin = bufi;
    while (buf[bufi++] != '\n') {}
    s = string(buf + begin, buf + bufi);
}

const char digit_pairs[] = {
        "00010203040506070809"
        "10111213141516171819"
        "20212223242526272829"
        "30313233343536373839"
        "40414243444546474849"
        "50515253545556575859"
        "60616263646566676869"
        "70717273747576777879"
        "80818283848586878889"
        "90919293949596979899"
};

template<typename T>
void writeui(T n) {
    if (n == 0) OUT[outi++] = '0';
    int size;
    if (n >= 1e12) {
        if (n >= 1e16) {
            if (n >= 1e18) {
                if (n >= 1e19) size = 20;
                else size = 19;
            } else {
                if (n >= 1e17) size = 18;
                else size = 17;
            }
        } else {
            if (n >= 1e14) {
                if (n >= 1e15) size = 16;
                else size = 15;
            } else {
                if (n >= 1e13) size = 14;
                else size = 13;
            }
        }
    } else if (n >= 1e4) {
        if (n >= 1e8) {
            if (n >= 1e10) {
                if (n >= 1e11) size = 12;
                else size = 11;
            } else {
                if (n >= 1e9) size = 10;
                else size = 9;
            }
        } else {
            if (n >= 1e6) {
                if (n >= 1e7) size = 8;
                else size = 7;
            } else {
                if (n >= 1e5) size = 6;
                else size = 5;
            }
        }
    } else {
        if (n >= 1e2) {
            if (n >= 1e3) size = 4;
            else size = 3;
        } else {
            if (n >= 1e1) size = 2;
            else size = 1;
        }
    }
    char *c = OUT + outi + size;
    outi += size;
    while (n >= 100) {
        int x = n % 100;
        n /= 100;
        *--c = digit_pairs[2 * x + 1];
        *--c = digit_pairs[2 * x];
    }
    while (n > 0) {
        *--c = '0' + (n % 10);
        n /= 10;
    }
}


// end fast io


/*
 * Array of linked list. N is max size of array. M is max total size of linked list.
 * An instance must be global variable to zero fill arrays.
*/
template<typename T, int N, int M>
class List {
    int k = 0;
public:
    int head[N];
    pair<int, T> nodes[M];

    class ListNode {
        List<T, N, M> &list;
        int i;
        int pointer;
    public:
        ListNode(List<T, N, M> &list, int i, int pointer = -1) : list(list) {
            this->i = i, this->pointer = pointer;
        }

        void push_back(T x) {
            list.nodes[++list.k].first = list.head[i];
            list.head[i] = list.k;
            list.nodes[list.k].second = x;
        }

        T &operator*() { return list.nodes[pointer].second; }

        bool operator==(ListNode &other) { return pointer == other.pointer; }

        bool operator!=(ListNode &other) { return !pointer == other.pointer; }

        void operator++() { pointer = list.nodes[pointer].first; }

        ListNode begin() {
            return ListNode(list, i, list.head[i]);
        }

        ListNode end() {
            return ListNode(list, i, 0);
        }
    };

    ListNode operator[](int i) {
        return ListNode(*this, i, head[i]);
    }
};

int depth = 0;
List<int, 200100, 400200> vec;
int a[200200];
int arr[200200];
int ans[200200];

void dfs(int i, int p) {
    ++depth;
    const auto it = lower_bound(begin(arr), begin(arr) + depth, a[i]);
    int x = it - begin(arr);
    int hist = arr[x];
    arr[x] = a[i];
    ans[i] = lower_bound(begin(arr) + x, begin(arr) + depth, INF) - begin(arr);
    for (int j : vec[i]) {
        if (j != p) {
            dfs(j, i);
        }
    }
    arr[x] = hist;
    --depth;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cin.read(buf, sizeof buf); // 注意: ./a.out < in か pbp | ./a.out で入力すること

    fill(begin(arr), end(arr), INF);
    int n;
    readui(n);
    rep(i, n) readui(a[i]);
    rep(i, n - 1) {
        int u, v;
        readui(u), readui(v);
        --u, --v;
        vec[u].push_back(v);
        vec[v].push_back(u);
    }

    dfs(0, -1);
    rep(i, n) writeui(ans[i]), OUT[outi++] = '\n';

    cout.write(OUT, outi);

    return 0;
}



Measured memory_bytes: 28284