#include <algorithm>
#include <array>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
using namespace std;
typedef long long ll;
#define REP(i,n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i,a,b) for(int i = (a); i < (int)(b); ++i)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(v) ((int)v.size())
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b; return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b; return true;
    }
    return false;
}
template<int MOD> struct Fp {
    ll val;
    constexpr Fp(ll v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        ll a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            ll t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, ll n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};
constexpr ll MOD = 1e9 + 7;
using mint = Fp<MOD>;

#define pb push_back
#define mp make_pair
#define mt make_tuple

int INF = 1e9 + 10;

vector<int> As;
vector<vector<int>> edges;
vector<int> ans;

void dfs(int v, int par, vector<int>& dp, int local_ans) {
    // cout << "v: " << (v+1) << endl;
    // cout << "dp(before):";
    // for (auto e: dp) cout << e << ","; cout << endl;

    // 蟻本と同じ方法でLIS
    auto it = lower_bound(ALL(dp), As[v]);

    // 配列変更前の値をとっておく
    auto prev_value = *it;

    *it = As[v];

    // cout << "dp(after):";
    // for (auto e: dp) cout << e << ","; cout << endl;

    chmax(local_ans, int(it - dp.begin()) + 1);
    ans[v] = local_ans;

    for(auto u: edges[v]) {
        if (u == par) continue;
        dfs(u, v, dp, local_ans);
    }

    // もとに戻す
    *it = prev_value;
}

int main(void)
{
    cin.sync_with_stdio(false);
    int N;
    cin >> N;

    As.resize(N);
    edges.resize(N);
    ans.resize(N);

    REP(n, N) cin >> As[n];

    REP(n, N - 1) {
        int u, v;
        cin >> u >> v;
        u--; v--;
        edges[u].pb(v);
        edges[v].pb(u);
    }

    vector<int> dp(N, INF);
    dfs(0, -1, dp, 0);
    for(auto a: ans) cout << a << endl;

    return 0;
}


Measured memory_bytes: 27696