//{{{
#include <bits/stdc++.h>
using namespace std;

#define putchar(x) cout << (x)
#define repeat(x) int _ = 0; _ < (x); ++_

template<typename T> constexpr auto range(T start, T stop, T step) {
    struct iterator {
        T i, step;
        bool operator!=(const iterator& other) const { return i != other.i; }
        auto& operator++() { i += step; return *this; }
        auto& operator*() { return i; }
    };
    struct iterable_wrapper {
        T start, stop, step;
        auto begin() const { return iterator{ start, step }; }
        auto end() const { return iterator{ stop, step }; }
        size_t size() const { return (stop - start) / step; }

        iterable_wrapper(T start_, T stop_, T step_): start(start_), stop(stop_), step(step_) {
            stop = step > 0 ? max(start, stop) : min(start, stop);
            stop += (step - (stop - start) % step) % step;
        }
    };
    return iterable_wrapper(start, stop, step);
};
template<typename T> constexpr auto range(T start, T stop) { return range(start, stop, T(1)); }
template<typename T> constexpr auto range(T stop) { return range(T(0), stop, T(1)); }

template<typename T, typename Iter = decltype(begin(declval<T>()))>
constexpr auto printer(T&& iterable) {
    struct iterator {
        Iter iter, ed;
        auto operator!=(const iterator& other) const {
            auto ret = (iter != other.iter);
            if(not ret) cout << '\n';
            return ret;
        }
        auto& operator++() { ++iter; if(iter != ed) cout << ' '; return *this; }
        auto& operator*() { return *iter; }
    };
    struct iterable_wrapper {
        T iterable;
        auto begin() const { return iterator{ std::begin(iterable), std::end(iterable) }; }
        auto end() const { return iterator{ std::end(iterable), std::end(iterable) }; }
    };
    return iterable_wrapper{ forward<T>(iterable) };
};

template<size_t ...Is, typename T> auto getis(const T& t) { return tie(get<Is>(t)...); }
template<class T> void setmax(T& a, const T& b) { a = max(a, b); }
template<class T> void setmin(T& a, const T& b) { a = min(a, b); }

template<typename T> struct is_const_char_arr_ref : false_type {};
template<size_t N> struct is_const_char_arr_ref<char const (&)[N]> : true_type {};
template<typename T, typename = void> struct is_container : false_type {};
template<typename T>
struct is_container<T, conditional_t<false, decltype(begin(declval<T>())), void>> : true_type {};
template<class T> using IsC = typename enable_if<is_container<T>::value and
    not is_same<T, string>::value>::type;
template<class T> using NotC = typename enable_if<not is_container<T>::value or
    is_same<T, string>::value>::type;
template<class T> inline IsC<T> print_1(const T& v);
template<class T> inline NotC<T> print_1(const T& x) { cout << x; }
template<size_t N> void print_1(const array<char, N>& x) { cout << &x[0]; };
inline void print_1(const tuple<>&) { cout << "()"; };
template<size_t L, size_t I, class T> void print_tuple(const T& t) {
    if(I != 0) cout << ", "; print_1(get<I>(t));
    if(I + 1 < L) print_tuple<L, (I + 1) % L>(t);
}
template<class ...T> inline void print_1(const tuple<T...>& x) {
    cout << "("; print_tuple<sizeof...(T), 0, tuple<T...>>(x); cout << ")";
}
inline void print_n() {}
template<class T, class ...U> inline void print_n(const T& head, const U&... tail);
template<class T, class U> inline void print_1(const pair<T, U>& p) {
    cout << "("; print_1(p.first); cout << ", "; print_1(p.second); cout << ")";
}
template<class T, class ...U> inline void print_n(const T& head, const U&... tail) {
    print_1(head); if(sizeof...(tail)) cout << " "; print_n(tail...);
}
template<class T> inline IsC<T> print_1(const T& v) {
    cout << "[";
    for(auto it = v.begin(); it != v.end(); ++it) { if(it != v.begin()) cout << ", "; print_1(*it); }
    cout << "]";
}
template<class ...T> inline void print(const T& ...args) { print_n(args...); putchar('\n'); }
inline void read() {}
template<class T, class ...U> inline void read(T& head, U&... tail) { cin >> head; read(tail...); }

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
static int fastio = [](){ ios_base::sync_with_stdio(false); cin.tie(0); cout.precision(17); return 0; }();

template<class T> void print_dbg(const string& s, T&& x) {
    if(is_const_char_arr_ref<T>::value) { print_n(x); } else { print_n(s, "=", x); }
}
#define SELECT(_1, _2, _3, _4, _5, _6, _7, _8, NAME,...) NAME
#define dbg1(a) print_dbg(#a, a); cout << endl;
#define dbg2(a, b) print_dbg(#a, a); cout << ", "; dbg1(b);
#define dbg3(a, b, c) print_dbg(#a, a); cout << ", "; dbg2(b, c);
#define dbg4(a, b, c, d) print_dbg(#a, a); cout << ", "; dbg3(b, c, d);
#define dbg5(a, b, c, d, e) print_dbg(#a, a); cout << ", "; dbg4(b, c, d, e);
#define dbg6(a, b, c, d, e, f) print_dbg(#a, a); cout << ", "; dbg5(b, c, d, e, f);
#define dbg7(a, b, c, d, e, f, g) print_dbg(#a, a); cout << ", "; dbg6(b, c, d, e, f, g);
#define dbg8(a, b, c, d, e, f, g, h) print_dbg(#a, a); cout << ", "; dbg7(b, c, d, e, f, g, h);
#define debug(...) SELECT(__VA_ARGS__, dbg8, dbg7, dbg6, dbg5, dbg4, dbg3, dbg2, dbg1)(__VA_ARGS__)
//}}}
using PII = pair<int, int>;
using LL = long long;

const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const LL LLINF = 0x3f3f3f3f3f3f3f3f;
const int MAX_N = 200005;


int n;
vector<int> G[MAX_N];
int a[MAX_N], ans[MAX_N];
int lis[MAX_N];

void dfs(int v, int p) {
    int i = lower_bound(lis, lis + n, a[v]) - lis;

    int backup = lis[i];
    lis[i] = a[v];

    int l = lower_bound(lis, lis + n, INF) - lis;
    ans[v] = l;

    for(int u : G[v]) {
        if(u != p) {
            dfs(u, v);
        }
    }

    lis[i] = backup;
}

struct Solution {
    Solution(int) {
        memset(lis, INF, sizeof(lis));

        read(n);
        for(int i : range(1, n + 1)) {
            read(a[i]);
        }
        for(repeat(n - 1)) {
            int u, v;
            read(u, v);
            G[u].push_back(v);
            G[v].push_back(u);
        }
        dfs(1, 0);
        for(int i : range(1, n + 1)) {
            print(ans[i]);
        }
    }
};

int main() {
    int T = 1;
    //cin >> T;
    for(int i = 1; i <= T; ++i) {
        ignore = Solution(i);
    }
    return 0;
}


Measured memory_bytes: 31260