#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) REP(i,0,n)
#define REP(i,s,e) for(int i=(s); i<(int)(e); i++)
#define repr(i, n) REPR(i, n, 0)
#define REPR(i, s, e) for(int i=(int)(s-1); i>=(int)(e); i--)
#define pb push_back
#define all(r) r.begin(),r.end()
#define rall(r) r.rbegin(),r.rend()
#define fi first
#define se second

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const ll INF = 1e18;
const ll MOD = 1e9 + 7;
const double EPS = 1e-8;

template<typename T> T chmax(T& a, const T& b){return a = (a > b ? a : b);}
template<typename T> T chmin(T& a, const T& b){return a = (a < b ? a : b);}

// #define DEBUG_MODE
#ifdef DEBUG_MODE
#define dump(x) cout << #x << " : " << x << " "
#define dumpL(x) cout << #x << " : " << x << '\n'
#define LINE cout << "line : " << __LINE__ << " "
#define LINEL cout << "line : " << __LINE__ << '\n'
#define dumpV(v) cout << #v << " : ["; for(auto& t : v) cout << t << ", "; cout<<"]" << " "
#define dumpVL(v) cout << #v << " : ["; for(auto& t : v) cout << t << ", "; cout<<"]" << endl
#define STOP assert(false)
#else
#define dump(x) 
#define dumpL(x) 
#define LINE 
#define LINEL 
#define dumpV(v) 
#define dumpVL(v) 
#define STOP assert(false)
#endif
#define mp make_pair
 
namespace std {
template<class S, class T>
ostream &operator <<(ostream& out, const pair<S, T>& a) {
    out << '(' << a.fi << ", " << a.se << ')';
    return out;
}
}

using ull = unsigned long long;


constexpr ll initVal = -(1LL<<31)-1;     //TODO: fix type and value
constexpr ll initLazy = (1LL<<60)-1;    //TODO: fix type and value
template <typename T>
struct Node {
    T val;
    T lazy;
    ull l, r;
    Node<T>* l_node = nullptr;
    Node<T>* r_node = nullptr;
    Node(ull l, ull r, const T& val = initVal) : l(l), r(r), val(val), lazy(initLazy) {}
    T getVal() {
        return (lazy != initLazy ? lazy : val); //TODO: fix
    }
    T f1(const T& a, const T& b) {
        return max(a, b);               //TODO: fix
    }
    T f2(const T& a, const T& b) {
        return b;                       //TODO: fix
    }
    void push() {
        if(r - l > 1) {
            auto m = (l+r)/2;
            {
                if(l_node == nullptr) l_node = new Node(l, m);
                if(lazy != initLazy) l_node->lazy = f2(l_node->lazy, this->lazy);
            }
            {
                if(r_node == nullptr) r_node = new Node(m, r);
                if(lazy != initLazy) r_node->lazy = f2(r_node->lazy, this->lazy); 
            }
        }
        val = getVal();
        lazy = initLazy;
    }
    void fix() {
        if(r - l == 1) return;
        val = f1(l_node->getVal(), r_node->getVal());
    }
    T query(ull qL, ull qR) {
        if(qR <= l || r <= qL) return initVal;
        if(qL <= l && r <= qR) return getVal();
        if(r - l == 1)  return getVal();

        push();
        T l_val = l_node->query(qL, qR), r_val = r_node->query(qL, qR);
        return f1(l_val, r_val);
    }
    void update(ull uL, ull uR, const T& uVal) {
        if(uR <= l || r <= uL) return;
        if(uL <= l && r <= uR) lazy = f2(lazy, uVal);
        else {
            push();
            l_node->update(uL, uR, uVal);
            r_node->update(uL, uR, uVal);
            fix();
        }
    }
};

template <typename T>
struct DynamicLazySegTree {
    Node<T> root;
    DynamicLazySegTree(ull l, ull r, const T& val) : root(l, r, val) {}
    T query(ull l, ull r) {
        return root.query(l, r);
    }
    void update(ull l, ull r, const T& val) {
        root.update(l, r, val);
    }
};

template<typename T>
void zaatu(const vector<T>& v, map<T, ll>& mv, vector<T>& rv) {
    for(auto&& i: v) mv[i] = 0;
    rv.resize(mv.size());
    int cnt = 0;
    for(auto& p : mv) {
        rv[cnt] = p.fi;
        p.se = cnt++;
    }
}

int main(){
    int n;
    cin >> n;
    vi a(n);
    rep(i, n) cin >> a[i];
    map<int, ll> ma;
    vi ra;
    ma[0] = 0;
    zaatu(a, ma, ra);
    vector<vi> es(n);
    rep(i, n-1) {
        int a, b;
        cin >> a >> b;
        --a;
        --b;
        es[a].pb(b);
        es[b].pb(a);
    }
    DynamicLazySegTree<ll> seg(0, ma.size()+10, 0);
    rep(i, ma.size()+1) seg.update(i, i+1, 0);
    vi ans(n);
    function<void(int, int)> calc = [&](int cur, int par) {
        int i = ma[a[cur]];
        auto pre = seg.query(i, i+1);
        seg.update(i, i+1, max(seg.query(0, i)+1, pre));
        dump(cur+1);dump(a[cur]);dump(i);dump(pre);dumpL(seg.query(i, i+1));
        ans[cur] = seg.query(0, ma.size()+1);
        for(auto&& to: es[cur]) if(to != par) calc(to, cur);
        seg.update(i, i+1, pre);
    };
    calc(0, -1);
    rep(i, n) {
        cout << ans[i] << '\n';
    }
    return 0;
}

Measured memory_bytes: 71188