#include <iostream>
#include <array>
#include <vector>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <algorithm>
#include <math.h>
#include <string>
#include <climits>
#include <assert.h>
#include <iomanip>
#include <bitset>
#include <queue>
#include <deque>
#include <stack>
#include <functional>
#include <fstream>
#include <random>

#define LEN(x) (long long)(x.size())
#define FOR(i,a,n) for(int i=(a);i<(n); ++i)
#define FOE(i,a) for(auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v,x) (std::find(v.begin(), v.end(), x) != v.end())
#define BIT_COUNT(bit) (__builtin_popcount(bit))

typedef long long LL;
template<typename T> std::vector<T> make_v(size_t a){return std::vector<T>(a);}
template<typename T,typename... Ts> auto make_v(size_t a, Ts... ts){ return std::vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));}    // C++14
template<typename T,typename V> typename std::enable_if<std::is_class<T>::value==0>::type fill_v(T &t,const V &v){t=v;}
template<typename T,typename V> typename std::enable_if<std::is_class<T>::value!=0>::type fill_v(T &t,const V &v){for(auto &e:t) fill_v(e,v);}
template<class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }
void print() { std::cout << std::endl; }
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) { std::cout << head; if (sizeof...(tail) != 0) {std::cout << " ";} print(std::forward<Tail>(tail)...); }
template <class T> void print(std::vector<T> &v) {for (auto& a : v) { std::cout << a; if (&a != &v.back()) {std::cout << " ";} }std::cout << std::endl;}
template <class T> void print(std::vector<std::vector<T>> &vv) { for (auto& v : vv) { print(v); }}
void debug() { std::cerr << std::endl; }
template <class Head, class... Tail> void debug(Head&& head, Tail&&... tail) { std::cerr << head; if (sizeof...(tail) != 0) {std::cerr << " ";} print(std::forward<Tail>(tail)...); }
template <class T> void debug(std::vector<T> &v) {for (auto& a : v) { std::cerr << a; if (&a != &v.back()) {std::cerr << " ";} }std::cerr << std::endl;}
template <class T> void debug(std::vector<std::vector<T>> &vv) { for (auto& v : vv) { print(v); }}
inline bool inside(long long y, long long x, long long H, long long W) {return 0 <= y and y < H and 0 <= x and x < W; }
template<class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); }
template<class T> inline double manhattan_distance(T y1, T x1, T y2, T x2) { return abs(x1 - x2) + abs(y1 - y2); }
template<typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }
bool is_bit_on(const unsigned long long bit, const unsigned int i) { return (bit >> i) & 1u; }
unsigned long long bit_set(const unsigned long long bit, const unsigned int i, const unsigned int b) {
    assert(b == 0 or b == 1);
    if (b == 0) { return bit & ~(1ull << i); }
    else        {return bit | (1ull << i); }
}

template<class T> inline std::vector<T> unique(std::vector<T> v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
    return v;
}

long long sum_of_arithmetic_progression(long long s, long long d, long long n) {
    return n * (2 * s + (n - 1) * d) / 2;
}


bool is_power_of_two(long long x) {
    return !(x & (x - 1));
}


long long gcd(long long a, long long b) {
    if (b == 0) { return a; }
    return gcd(b, a % b);
}


long long gcd(std::vector<long long> &v) {
    long long ans = v[0];
    for (int i = 1; i < (int)v.size(); ++i) {
        ans = gcd(ans, v[i]);
    }
    return ans;
}


long long lcm(long long a, long long b) {
    long long g = gcd(a, b);
    return a / g * b;
}

const int INF = 1u << 30u;
const long long LINF = 1ull << 60u;
const double EPS = 1e-9;
const long double PI = acos(-1.0);
const std::vector<int> dy2 = {0, 1}, dx2 = {1, 0};
const std::vector<int> dy4 = {0, 1, 0, -1}, dx4 = {1, 0, -1, 0};
const std::vector<int> dy8 = { 0, -1, 0, 1, 1, -1, -1, 1 }, dx8 = { 1, 0, -1, 0, 1, 1, -1, -1 };

using namespace std;

vector<LL> A;
vector<vector<int>> tree;
vector<LL> ans;

void dfs(const int u, const int parent, vector<int> &dp) {
    const int idx = lower_bound(ALL(dp), A[u]) - dp.begin();
    const int pre = dp[idx];
    dp[idx] = A[u];

    ans[u] = lower_bound(ALL(dp), INF) - dp.begin();

    FOE(v, tree[u]) {
        if (v == parent) {
            continue;
        }

        dfs(v, u, dp);
    }

    dp[idx] = pre;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    cin >> N;
    A = make_v<LL>(N);
    FOR(i, 0, N) {
        cin >> A[i];
    }

    tree = make_v<int>(N, 0);
    FOR(i, 0, N - 1) {
        int u, v;
        cin >> u >> v;
        u--; v--;
        tree[u].emplace_back(v);
        tree[v].emplace_back(u);
    }

    auto dp = make_v<int>(N + 100);
    fill_v(dp, INF);
    ans = make_v<LL>(N);

    dfs(0, -1, dp);

    FOR(u, 0, N) {
        print(ans[u]);
    }

    return 0;
}

Measured memory_bytes: 32480