#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned int;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using tuplis = array<ll, 3>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const int MOD=1000000007;
const int MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.1415926535897932;
const ll dx[] = {0, 1, 0, -1, 1, 1, -1, -1};
const ll dy[] = {1, 0, -1, 0, 1, -1, 1, -1};
#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=(n);i--;)
#define rrep2(i,n) for(ll i=(n);i--;)
#define rrep3(i,a,b) for(ll i=(b);i-->(a);)
#define rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each(i,a) for(auto&& i:a)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T, class U> bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T, class U> bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; }
vector<pll> factor(ull x){ vector<pll> ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; }
map<ll,ll> factor_map(ull x){ map<ll,ll> ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; }
vector<ull> divisor(ull x){ vector<ull> ans; for(uint i = 1; ull(i) * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; }
template<class T> unordered_map<T, ll> press(vector<T>& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); unordered_map<T, ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T, ll> press_map(vector<T>& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); map<T, ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
int scan(){ return getchar(); }
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline int __lg(int __n){ return sizeof(int) * __CHAR_BIT__  - 1 - __builtin_clz(__n); }
#define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...) void(0)
#endif
int first(bool i = true){ return out(i?"first":"second"); }
int yes(bool i = true){ return out(i?"yes":"no"); }
int Yes(bool i = true){ return out(i?"Yes":"No"); }
int No(){ return out("No"); }
int YES(bool i = true){ return out(i?"YES":"NO"); }
int NO(){ return out("NO"); }
int Yay(bool i = true){ return out(i?"Yay!":":("); }
int possible(bool i = true){ return out(i?"possible":"impossible"); }
int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
void Case(ll i){ printf("Case #%lld: ", i); }


template<class T>
struct SegmentTree{
    virtual T f(const T&, const T&) const = 0;
    const T def_value;
    ll size = 1, rank = 0, expected_size;
    vector<T> data;
    SegmentTree(ll n, const T& def_value): def_value(def_value), expected_size(n){
        while(size < expected_size){
            size *= 2;
            rank++;
        }
        data.assign(size * 2, def_value);
    }
    SegmentTree(const vector<T>& v, const T& def_value): def_value(def_value), expected_size(v.size()){
        while(size < expected_size){
            size *= 2;
            rank++;
        }
        data.assign(size * 2, def_value);
        for(ll i = 0; i < v.size(); i++) data[size + i] = v[i];
        // for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
    T operator[](ll at) const {
        return data[size + at];
    }
    void update(ll at){
        while(at /= 2) data[at] = f(data[at * 2], data[at * 2 + 1]);
    }
    void set(ll at, const T& val){
        at += size;
        data[at] = val;
        update(at);
    }
    void add(ll at, const T& val){
        at += size;
        data[at] += val;
        update(at);
    }
    T get(ll l, ll r) const {
        T L = def_value, R = def_value;
        l += size; r += size;
        for(; l < r; l /= 2, r /= 2){
            if(l & 1) L = f(L, data[l++]);
            if(r & 1) R = f(data[--r], R);
        }
        return f(L, R);
    }
    template<class F> ll find_last(const F& check, ll l = 0) const { // max x  s.t. check(get(l, x)) == true
        if(l == expected_size) return expected_size;
        ll height = 0, at = l + size;
        T val = def_value;
        for(; height <= rank; height++) if(at >> height & 1){
            T val2 = f(val, data[at >> height]);
            if(check(val2)){
                at += 1 << height;
                if(at == size * 2) return expected_size;
                val = val2;
            }
            else break;
        }
        for(; height--; ){
            T val2 = f(val, data[at >> height]);
            if(check(val2)){
                at += 1 << height;
                if(at == size * 2) return expected_size;
                val = val2;
            }
        }
        return min(at - size, expected_size);
    }
    template<class F> ll find_first(const F& check, ll r) const { // min x  s.t. check(get(x, r)) == true
        if(!r) return 0;
        ll height = 0, at = r + size;
        T val = def_value;
        for(; height <= rank; height++) if(at >> height & 1){
            T val2 = f(val, data[at >> height ^ 1]);
            if(check(val2)){
                at -= 1 << height;
                if(at == size) return 0;
                val = val2;
            }
            else break;
        }
        for(; height--; ){
            T val2 = f(val, data[(at >> height) - 1]);
            if(check(val2)){
                at -= 1 << height;
                if(at == size) return 0;
                val = val2;
            }
        }
        return at - size;
    }
    void clear(){
        for(auto& i : data) i = def_value;
    }
};
template<class T>
struct RmQ : SegmentTree<T>{
    using Base = SegmentTree<T>;
    T f(const T& a, const T& b) const {return min(a, b);}
    RmQ(ll n, const T& def_value) : Base(n, def_value){}
    RmQ(const vector<T>& v, const T& def_value) : Base(v, def_value){
        for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
};
template<class T>
struct RMQ : SegmentTree<T>{
    using Base = SegmentTree<T>;
    T f(const T& a, const T& b) const {return max(a, b);}
    RMQ(ll n, const T& def_value) : Base(n, def_value){}
    RMQ(const vector<T>& v, const T& def_value) : Base(v, def_value){
        for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
};
template<class T>
struct RSQ : SegmentTree<T>{
    using Base = SegmentTree<T>;
    T f(const T& a, const T& b) const {return a + b;}
    RSQ(ll n, const T& def_value = T()) : Base(n, def_value){}
    RSQ(const vector<T>& v, const T& def_value = T()) : Base(v, def_value){
        for(ll i = Base::size; --i;) Base::data[i] = f(Base::data[i * 2], Base::data[i * 2 + 1]);
    }
};
struct UnWeightedEdge{
    ll to;
    static constexpr ll cost = 1;
    UnWeightedEdge(){}
    UnWeightedEdge(ll to): to(to){}
    operator ll() const { return to; }
};
struct UnWeightedGraph{
    using E = UnWeightedEdge;
    vector<vector<E>> g;
    UnWeightedGraph(ll n): g(n){}
    vector<E>& operator[](ll at){ return g[at]; }
    operator vector<vector<E>>&(){ return g; }
    auto begin() const { return g.cbegin(); }
    auto end() const { return g.cend(); }
    ll size() const { return g.size(); }
    const vector<E>& operator[](ll at) const { return g[at]; }
    operator const vector<vector<E>>&() const { return g; }
    void add_edge(ll a, ll b){
        g[a].emplace_back(b);
        g[b].emplace_back(a);
    }
    void add_directed_edge(ll from, ll to){
        g[from].emplace_back(to);
    }
    template<ll start_index = 1, bool directed = false> void input_graph(ll m){
        while(m--){
            ll a, b;
            scanf("%lld%lld", &a, &b);
            a -= start_index;
            b -= start_index;
            g[a].emplace_back(b);
            if(!directed) g[b].emplace_back(a);
        }
    }
    template<ll start_index = 1> void input_tree(ll n){ input_graph<start_index>(n - 1); }
};
signed main(){
    LL(n);
    VEC(ll,a,n);
    UnWeightedGraph g(n);
    g.input_tree(n);
    vec(ll,ans,n);
    press(a);
    RMQ<ll>seg(n,0);
    auto dfs=[&](ll from,ll at,const auto& f)->void{
        ll tmp=seg[a[at]];
        ll next=seg.get(0,a[at])+1;
        if(tmp<next)seg.set(a[at],next);
        ans[at]=seg.data[1];
        each(i,g[at])if(i!=from)f(at,i,f);
        seg.set(a[at],tmp);
    };
    dfs(-1,0,dfs);
    out(ans);
}


Measured memory_bytes: 47296