#define LOCAL
#define _USE_MATH_DEFINES
#include <array>
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <iomanip>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>
#include <random>
#include <ctime>

using namespace std;

template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
  out << "(" << a.first << "," << a.second << ")";
  return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
  out << "["; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
  out << "["; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
  return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

typedef long long int64;
typedef pair<int, int> ii;
const int INF = 1 << 29;
const int MOD = 1e9 + 7;
mt19937 mrand(random_device{}());
int rnd(int x) { return mrand() % x; }

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

const int N = 2e5 + 10;
vector<int> g[N];
int a[N], dp[N];
vector<int> A;

struct Node {
  Node *left, *right;
  multiset<int> c;
  int mx;
  void pushup() {
    mx = max(left->mx, right->mx);
  }
  void pushdown(int a, int b) { }
};

Node pool[N << 1], *last;
Node* root;

Node* build(int a, int b) {
  Node* ret = last++;
  ret->mx = 0;
  if (a + 1 == b) {
    ret->c.clear();
    return ret;
  }
  int mid = (a + b) / 2;
  ret->left = build(a, mid);
  ret->right = build(mid, b);
  return ret;
}

void insert(Node* cur, int a, int b, int pos, int C) {
  if (pos >= b || pos < a) return;
  if (a + 1 == b) {
    cur->c.insert(C);
    cur->mx = cur->c.size() ? *cur->c.rbegin() : 0;
    return;
  }
  cur->pushdown(a, b);
  int mid = (a + b) / 2;
  insert(cur->left, a, mid, pos, C);
  insert(cur->right, mid, b, pos, C);
  cur->pushup();
}

void clear(Node* cur, int a, int b, int pos, int C) {
  if (pos >= b || pos < a) return;
  if (a + 1 == b) {
    auto it = cur->c.find(C);
    cur->c.erase(it);
    cur->mx = cur->c.size() ? *cur->c.rbegin() : 0;
    return;
  }
  cur->pushdown(a, b);
  int mid = (a + b) / 2;
  clear(cur->left, a, mid, pos, C);
  clear(cur->right, mid, b, pos, C);
  cur->pushup();
}

int query(Node* cur, int a, int b, int ll, int rr) {
  if (ll >= rr || a >= rr || b <= ll) return 0;
  if (a >= ll && b <= rr) {
    return cur->mx;
  }
  cur->pushdown(a, b);
  int mid = (a + b) / 2;
  int ret = 0;
  ret = max(ret, query(cur->left, a, mid, ll, rr));
  ret = max(ret, query(cur->right, mid, b, ll, rr));
  return ret;
}

void DFS(int u, int parent) {
  int best = query(root, 0, A.size(), 0, a[u]) + 1;
  insert(root, 0, A.size(), a[u], best);
  dp[u] = query(root, 0, A.size(), 0, A.size());
  // trace(u, dp[u]);
  for (auto& v : g[u]) {
    if (v == parent) continue;
    DFS(v, u);
  }
  clear(root, 0, A.size(), a[u], best);
}

int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
    A.push_back(a[i]);
  }
  sort(A.begin(), A.end());
  A.erase(unique(A.begin(), A.end()), A.end());
  for (int i = 0; i < n; ++i) {
    a[i] = lower_bound(A.begin(), A.end(), a[i]) - A.begin();
  }
  for (int i = 1; i < n; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    --x; --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  last = pool;
  root = build(0, A.size());
  // for (int i = 0; i < n; ++i) trace(i, a[i]);
  DFS(0, -1);
  for (int i = 0; i < n; ++i) {
    printf("%d\n", dp[i]);
  }
  return 0;
}


Measured memory_bytes: 64876