#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <complex>
#include <cmath>
#include <cstring>
#include <deque>
#include <functional>
#include <map>
#include <initializer_list>
#include <iostream>
#include <random>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>

 
template <typename S, typename T> inline bool chmin(S& a, const T b){ if(b < a){ a = b; return true; } return false; }
template <typename S, typename T> inline bool chmax(S& a, const T b){ if(a < b){ a = b; return true; } return false; }
template <typename T> inline bool bitUP(const T state, const unsigned int k) { return (state >> k) & 1; }

inline bool isIn(int x, int y, int H, int W){ return 0 <= x and x < H and 0 <= y and y < W; }
inline auto isInTheGrid(const int H, const int W){
    return std::bind(isIn, std::placeholders::_1, std::placeholders::_2, H, W);
}


namespace MyInputAndOutput{
    // 入力関係 (cin)
    class user_input{
    private:
        static constexpr unsigned int sizeOfAscii = 128;
        bool isBlankChar[sizeOfAscii];
            /*  < definition of getchar >
                reference
                MacOS   : https://developer.apple.com/library/archive/documentation/System/Conceptual/ManPages_iPhoneOS/man3/getchar.3.html
                Windows : https://docs.microsoft.com/en-us/cpp/c-runtime-library/reference/getchar-nolock-getwchar-nolock?view=vs-2019
                Linux   : https://linux.die.net/man/3/unlocked_stdio 
                Ubuntu  : http://manpages.ubuntu.com/manpages/trusty/man3/getchar_unlocked.3posix.html
            */
            #if defined(__APPLE__)
                #define DAGGER_GETCHAR_UNLOCKED_DAGGER getchar_unlocked
            #elif defined(_WIN32) || defined(_WIN64)
                #define DAGGER_GETCHAR_UNLOCKED_DAGGER _getchar_nolock
            #elif defined(__linux) 
                #if _POSIX_C_SOURCE >= 1 || _XOPEN_SOURCE || _POSIX_SOURCE || _BSD_SOURCE || _SVID_SOURCE
                    #define DAGGER_GETCHAR_UNLOCKED_DAGGER getchar_unlocked
                #else
                    #define DAGGER_GETCHAR_UNLOCKED_DAGGER getchar
                #endif
            #else
                #define DAGGER_GETCHAR_UNLOCKED_DAGGER getchar
            #endif
        // 符号あり整数を getchar で読み込んで構成する (もし, 0 ~ 9 以外の文字が含まれると困る)
        template <typename Tp>
        inline void charToInteger(Tp& val) const {
            val = 0; int c; while(true){
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
                if(c == EOF) return;
                if('-' or (not isBlankChar[c])) break;
            }
            if(c == '-'){
                while(true){
                    c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
                    if(c < '0' or c > '9') break;
                    val = 10 * val + c - '0';
                } val = -val;
            }
            else{
                if(c < '0' or c > '9') return;
                do{
                    val = 10 * val + c - '0';
                    c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
                } while('0' <= c and c <= '9');
            }
        }
        // 符号なし整数を getchar で読み込んで構成する (もし, 符号付きだとバグる)
        template <typename Tp>
        inline void charToUnsignedInteger(Tp& val) const {
            val = 0; int c; while(true){
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
                if(c == EOF) return;
                if(not isBlankChar[c]) break;
            }
            if(c < '0' or c > '9') return;
            do{
                val = 10 * val + c - '0';
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
            } while(not (c == EOF or isBlankChar[c]));
        }
    public:
        constexpr user_input(void) : isBlankChar(){
            for(unsigned int i = 0; i < sizeOfAscii; ++i) isBlankChar[i] = false;
            isBlankChar[int('\n')] = true; isBlankChar[int('\t')] = true; 
            isBlankChar[int(' ')]  = true; isBlankChar[int('\v')] = true;
        }
        inline const user_input& operator >> (int& int_arg) const {
            charToInteger<int>(int_arg); return *this;
        }
        inline const user_input& operator >> (long long int& llint_arg) const {
            charToInteger<long long int>(llint_arg); return *this;
        }
        inline const user_input& operator >> (unsigned int& uint_arg) const {
            charToUnsignedInteger<unsigned int>(uint_arg); return *this;
        }
        inline const user_input& operator >> (unsigned long long int& ullint_arg) const {
            charToUnsignedInteger<unsigned long long int>(ullint_arg); return *this;
        }
        inline const user_input& operator >> (unsigned long& ulint_arg) const {
            charToUnsignedInteger<unsigned long>(ulint_arg); return *this;
        }
        inline const user_input& operator >> (float& float_arg) const {
            scanf("%f", &float_arg); return *this;
        }
        inline const user_input& operator >> (double& double_arg) const {
            scanf("%lf", &double_arg); return *this;
        }
        inline const user_input& operator >> (long double& ldouble_arg) const {
            scanf("%Lf", &ldouble_arg); return *this;
        }
        inline const user_input& operator >> (char* str_arg) const {
            //scanf("%s", str_arg); 
            char* str = str_arg;
            int c; while(true){ 
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
                if(c == EOF) return *this;
                if(not isBlankChar[c]) break;
            }
            do{
                *(str++) = c;
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
            } while(c != EOF and (not isBlankChar[c]) );
            return *this;
        }
        inline const user_input& operator >> (char& char_arg) const {
            do{
                if((char_arg = DAGGER_GETCHAR_UNLOCKED_DAGGER()) == EOF) return *this;
            } while(isBlankChar[int(char_arg)]);
            return *this;
        }
        inline const user_input& operator >> (std::string& str_arg) const {
            str_arg.erase();
            int c; while(true){ 
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
                if(c == EOF) return *this;
                if(not isBlankChar[c]) break;
            }
            constexpr unsigned int buffer_size = 128; 
            char buffer_input[buffer_size]; unsigned int buffer_length = 0;
            do{
                buffer_input[buffer_length++] = c;
                if(buffer_length == buffer_size){
                    buffer_length = 0; str_arg.append(buffer_input, buffer_size);
                }
                c = DAGGER_GETCHAR_UNLOCKED_DAGGER();
            } while(c != EOF and (not isBlankChar[c]) );
            str_arg.append(buffer_input, buffer_length);
            return *this;
        }
        template <typename S, typename T>
        inline const user_input& operator >>(std::pair<S, T>& pair_arg) const{
            (*this) >> pair_arg.first >> pair_arg.second; return *this;
        }
        template <typename T>
        inline const user_input& operator >>(std::vector<T>& vec) const {
            for(T& ele : vec) (*this) >> ele; 
            return *this;
        }
        // getchar の define の解除
        #undef DAGGER_GETCHAR_UNLOCKED_DAGGER
    }; constexpr user_input cin;

    void ends(void) {putchar('\0'); }
    void endl(void) {putchar('\n'); fflush(stdout);}
    void flush(void) {fflush(stdout);}
    constexpr char eol = '\n';

    // 出力関係 (cout)
    class user_output{
    public:
        constexpr user_output(void){}
        inline const user_output& operator << (const int int_arg) const{
            printf("%d", int_arg); return *this;
        }
        inline const user_output& operator << (const unsigned int uint_arg) const{
            printf("%u", uint_arg); return *this;
        }
        inline const user_output& operator << (const long long int llint_arg) const {
            printf("%lld", llint_arg); return *this;
        }
        inline const user_output& operator << (const unsigned long long int ullint_arg) const {
            printf("%llu", ullint_arg); return *this;
        }
        inline const user_output& operator << (const unsigned long ulint_arg) const {
            printf("%lu", ulint_arg); return *this;
        }
        inline const user_output& operator << (const float flt_arg) const {
            printf("%.16f", flt_arg); return *this;
        }
        inline const user_output& operator << (const double ld_arg) const {
            printf("%.16lf", ld_arg); return *this;
        }
        inline const user_output& operator << (const long double ld_arg) const {
            printf("%.16Lf", ld_arg); return *this;
        }
        inline const user_output& operator << (const char char_arg) const {
            putchar(char_arg); return *this;
        }
        inline const user_output& operator << (const unsigned char uchar_arg) const {
            putchar(uchar_arg); return *this;
        }
        inline const user_output& operator << (const char* str_arg) const {
            fputs(str_arg, stdout); return *this;
        }
        inline const user_output& operator << (const std::string& str_arg) const {
            fputs(str_arg.c_str(), stdout); return *this;
        }
        inline const user_output& operator << (void(* const func_arg)(void)) const {
            func_arg(); return *this;
        }
        template <typename S, typename T>
        inline const user_output& operator <<(const std::pair<S, T>& pair_arg) const{
            (*this) << pair_arg.first << ' ' << pair_arg.second; return *this;
        }
        template <typename Tp_name>
        inline const user_output& operator << (const std::vector<Tp_name>& vec) const {
            const size_t size_of_vec = vec.size();
            if(size_of_vec <= 0) return *this;
            (*this) << vec[0]; 
            for(size_t index = 1; index < size_of_vec; ++index) (*this) << ' ' << vec[index];
            return *this;
        }
    }; constexpr user_output cout;

    // その他出力関数
    template <typename Integer = unsigned long long int>
    void binary_output(const Integer value, const unsigned int length = 64){
        char out[length + 1];
        for(unsigned int i = 0, j = length - 1; i < length; ++i, --j) out[j] = ((value >> i) & 1) ? '1' : '0';
        out[length] = '\0'; puts(out);
    }
    template <typename InputType>
    void print(InputType first, InputType last, const char separate_c = ' ', const char end_c = '\n'){
        InputType it = first;
        while(true){
            MyInputAndOutput::cout << *it;
            if(++it == last){MyInputAndOutput::cout << end_c; return;}
            MyInputAndOutput::cout << separate_c;  
        }
    }
}; namespace MIO = MyInputAndOutput;

namespace MyStandardLibrary{
    // z-algorithm
    template <class T> std::vector<unsigned int> z_algorithm(const T &str) {
        const size_t n = str.size();
        std::vector<unsigned int> resOfCP(n); resOfCP[0] = n;
        int i = 1, j = 0;
        while (i < n) {
            while (i + j < n and str[j] == str[i + j]) ++j;
            resOfCP[i] = j;
            if (j == 0) { ++i; continue;}
            int k = 1;
            while (i + k < n and k + resOfCP[k] < j) resOfCP[i + k] = resOfCP[k], ++k;
            i += k; j -= k;
        }
        return resOfCP;
    }
    // 累乗を求める関数 : 指数部は非負整数
    unsigned int power(unsigned int a, unsigned long long int n, const unsigned int mod_number = 1000000007){
        unsigned int res = 1;
        while(n){
            if(n & 1) res = (unsigned long long int)(res) * a % mod_number;
            a = (unsigned long long int)(a) * a % mod_number;
            n >>= 1;
        }
        return res;
    }
    // 転倒数を求める関数 : 任意の Ai に対し, Ai ∈ [0, bound) であることを仮定している : O(Nlog{bound})
    unsigned long long int tentou(const std::vector<unsigned int>& A, const unsigned int bound){
        const unsigned int n = A.size();
        if(n <= 30){ // ある程度小さい時はナイーブの方が早い
            unsigned long long int res = 0;
            for(unsigned int i = 0; i < n; ++i) for(unsigned int j = i + 1; j < n; ++j) if(A[i] > A[j]) ++res;
            return res;
        }
        std::vector<unsigned int> fenwick(bound + 1, 0);
        unsigned long long int res = (unsigned long long int)(n) * (n - 1) >> 1;
        for(unsigned int i = 0; i < n; ++i){
            for(unsigned int x = A[i]    ; x ; x -= x & (-x)) res -= fenwick[x];
            for(unsigned int x = A[i] + 1; x <= bound; x += x & (-x)) ++fenwick[x];
        }
        return res;
    }
    // modintクラス : 法 modulous はコンパイル時定数
    template <const unsigned int  modulous> class modInt{
    private:
        static unsigned int power(unsigned int a, unsigned int n){
            unsigned int res = 1;
            while(n){
                if(n & 1) res = (unsigned long long int)(res) * a % modulous;
                a = (unsigned long long int)(a) * a % modulous;
                n >>= 1;
            }
            return res;
        }
        static unsigned int inverse(const unsigned int n_val){ return power(n_val, modulous - 2); }

        static unsigned int inverse_euclidean(unsigned int a){
            unsigned int b = modulous; long long int u = 1, v = 0;
            while(b){
                const unsigned int t = a / b;
                std::swap(a -= t * b, b);
                std::swap(u -= t * v, v);
            }
            return (u < 0) ? u + modulous : u;
        }
    public:
        unsigned int val;
        constexpr modInt(void):val(){}
        template <typename Integer> constexpr modInt(const Integer n_val):val(){
            if(n_val < 0){ const unsigned int tmp_val = (-n_val) % modulous; val = (tmp_val) ? modulous - tmp_val : 0; }
            else{ val = n_val % modulous; }
        }
        constexpr modInt& operator += (const modInt& other){ if((val += other.val) >= modulous) val -= modulous; return *this; }
        constexpr modInt& operator -= (const modInt& other){ if(val < other.val) val += modulous - other.val; else val -= other.val; return *this; }
        constexpr modInt& operator *= (const modInt& other){ val = static_cast<unsigned long long int>(val) * other.val % modulous; return *this; }
        constexpr modInt& operator /= (const modInt& other){ val = static_cast<unsigned long long int>(val) * inverse_euclidean(other.val) % modulous; return *this; }
        constexpr modInt  operator +  (const modInt& other) const { return modInt(*this) += other; }
        constexpr modInt  operator -  (const modInt& other) const { return modInt(*this) -= other; }
        constexpr modInt  operator *  (const modInt& other) const { return modInt(*this) *= other; }
        constexpr modInt  operator /  (const modInt& other) const { return modInt(*this) /= other; }
        constexpr modInt& operator ++ (void){ if(++val == modulous) val = 0; return *this; }
        constexpr modInt& operator -- (void){ if(!(val--)) val = modulous - 1; return *this; }
        constexpr bool    operator == (const modInt& other) const { return val == other.val; }
        constexpr bool    operator != (const modInt& other) const { return val != other.val; }
        constexpr modInt  operator -  (void) const { return modInt(val ? modulous - val : 0); }
        friend std::ostream& operator << (std::ostream& os, const modInt& modint_val){
            os << modint_val.val; return os;
        }
    };
    // BIT
    template <class Integer> class BinaryIndexedTree{
    private:
        const unsigned int n;
        std::vector<Integer> data;
    public:
        // コンストラクタ
        BinaryIndexedTree(const unsigned int n, const Integer init_val = Integer()):n(n){ data.assign(n + 1, init_val); }
        // @ A[i] に val を加える (0-indexed)
        inline Integer add(unsigned int idx, const Integer& val){ for(++idx; idx <= n; idx += idx & (~idx)) data[idx] += val; }
        // @ 和 ∑_[0, idx) Ai を計算する (0-indexed)
        Integer sum(unsigned int idx) const {
            if(!idx) return Integer();
            Integer res = Integer(); while(idx){ res += data[idx]; idx -= idx & (~idx); }
            return res;
        }

    };
}; namespace MSL = MyStandardLibrary;

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

// グリッド上の縦横移動 
constexpr std::array<std::pair<int, int>, 4> dxdy = {
    { {1, 0}, {-1, 0}, {0, 1}, {0, -1} }
};

// 型エイリアス
using unint = unsigned int;
using lli = long long int;
using ulli = unsigned long long int;
using pii = std::pair<int, int>;

#define REP(i, n) for(unsigned int i = 0; i < n; ++i)
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

using MIO::cin; using MIO::cout; using MIO::eol;


constexpr int INF = 1'000'000'334;
int n;
std::vector<int> A;
std::vector<std::vector<int>> edge;
std::vector<int> LIS;
std::vector<int> depth;
std::vector<int> Res;

void dfs(int v){
    int idx, val;{
        int ok = 0, ng = n + 1;
        while(ng - ok > 1){
            const int mid = (ok + ng) >> 1;
            if(LIS[mid] >= A[v]) ng = mid; else ok = mid;
        }
        idx = ng; val = LIS[ng];
    }
    LIS[idx] = A[v];
    {
        int ok = 0, ng = n + 1;
        while(ng - ok > 1){
            const int mid = (ok + ng) >> 1;
            if(LIS[mid] == INF) ng = mid; else ok = mid;
        }
        Res[v] = ok;
    } 

    for(const int u : edge[v]){
        if(depth[u] == INF){ 
            depth[u] = depth[v] + 1; dfs(u);
        }
    }
    LIS[idx] = val;
}

int main(void){
    cin >> n;
    A.resize(n); for(int i = 0; i < n; ++i) cin >> A[i];
    edge.assign(n, std::vector<int>(0));
    for(int i = 1; i < n; ++i){
        int u, v; cin >> u >> v; --u; --v;
        edge[u].emplace_back(v); edge[v].emplace_back(u);
        //cout << u << ' ' << v << '\n';
    }

    LIS.assign(n + 2, INF); LIS[0] = 0;
    depth.assign(n, INF); depth[0] = 0;
    Res.resize(n);
    dfs(0); //dfs(1); dfs(2);
    for(int i = 0; i < n; ++i) cout << Res[i] << '\n';





    return 0;
}


Measured memory_bytes: 28804