#include <iostream>
#include <iomanip>
#include <cassert>
#include <cstdint>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <array>
#include <deque>
#include <stack>
#include <queue>
#include <algorithm>
#include <functional>
#include <utility>
#include <cmath>
#include <numeric>
#include <sstream>

using namespace std;

#ifdef _DEBUG
#define DUMP(x) std::cerr << (#x) << " = " << (x) << "\n"
#else
#define DUMP(x)
#endif
#define REP(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define EREP(i, a, b) for (int i = (int)(a); i <= (int)(b); ++i)
#define RREP(i, a, b) for (int i = (int)(a)-1; i >= (int)(b); --i)
#define rep(i, n) REP(i, 0, n)
#define erep(i, n) EREP(i, 0, n)
#define rrep(i, n) RREP(i, n, 0)
#define ALL(r) (r).begin(), (r).end()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second

template <typename T>
ostream &operator<<(ostream &os, vector<T> &v)
{
    os << "{";
    rep(i, v.size()) os << v[i] << (i == (int)v.size() - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &p) { return (os << "(" << p.first << ", " << p.second << ")"); }
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &m)
{
    bool first = true;
    os << "{";
    for (const auto &e : m)
    {
        if (!first)
            os << ", ";
        os << "{" << e.first << ": " << e.second << "}";
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, set<T> &s)
{
    os << "{";
    bool first = true;
    for (const auto &e : s)
    {
        if (!first)
            os << ", ";
        os << e;
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
T dup(T x, T y) { return (x + y - 1) / y; };
template <typename A, size_t N, typename T>
inline void arrayFill(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); }
template <class T>
inline bool chmax(T &a, T b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmin(T &a, T b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}
struct in
{
    const size_t n = 0;
    in() = default;
    in(size_t n) : n(n){};
    template <typename T>
    operator T()
    {
        T ret;
        cin >> ret;
        return ret;
    }
    template <typename T>
    operator vector<T>()
    {
        assert(n != 0);
        vector<T> ret(n);
        for (T &x : ret)
        {
            T tmp = in();
            x = tmp;
        }
        return ret;
    }
    template <typename T, typename U>
    operator pair<T, U>()
    {
        pair<T, U> ret;
        ret.first = in();
        ret.second = in();
        return ret;
    }
};
template <typename T>
inline void out(T x) { std::cout << x << '\n'; };

using ll = int64_t;
using vint = vector<int32_t>;
using vvint = vector<vint>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vstr = vector<string>;
using pint = pair<int32_t, int32_t>;
using vpint = vector<pint>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using setint = set<int32_t>;
using qint = queue<int32_t>;
using qpint = queue<pint>;

constexpr std::int32_t INF = 1001001001;
constexpr std::int64_t LINF = 1001001001001001001;

ll a[200005];
int ans[200005];

void dfs(const vvint &g, vint &dp, int v)
{
    for (auto nv : g[v])
    {
        if (ans[nv] != -1)
            continue;

        int idx = lower_bound(ALL(dp), a[nv]) - dp.begin();
        int val = dp[idx];
        dp[idx] = a[nv];
        ans[nv] = lower_bound(ALL(dp), INF) - dp.begin();
        dfs(g, dp, nv);
        dp[idx] = val;
    }
}

void Main()
{
    arrayFill(ans, -1);
    int n = in();
    rep(i, n) cin >> a[i];
    vvint g(n);
    rep(i, n - 1)
    {
        int u = in(), v = in();
        --u, --v;
        g[u].pb(v);
        g[v].pb(u);
    }
    vint dp(n + 5, INF);
    dp[0] = a[0];
    ans[0] = 1;
    dfs(g, dp, 0);
    rep(i, n)
        out(ans[i]);
}

signed main()
{
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}


Measured memory_bytes: 31632