#include <iostream>
#include <vector>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <cstdio>
#include <bitset>
#include <queue>
#include <deque>
#include <algorithm>
#include <numeric>
#include <cassert>
#include <functional>
#include <stack>
#include <cmath>
#include <string>

using namespace std;

#define REP(i, N) for (int i = 0; i < (int)N; i++)
#define FOR(i, a, b) for (int i = a; i < (int)b; i++)
#define ALL(x) (x).begin(), (x).end()
#define INF (1 << 30)
#define LLINF (1LL << 62)
#define DEBUG(...) debug(__LINE__, ":" __VA_ARGS__)

constexpr int MOD = 1000000007;
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;

inline int popcount(ll x) { return __builtin_popcountll(x); }
inline int div2num(ll x) { return __builtin_ctzll(x); }
inline bool bit(ll x, int b) { return (x >> b) & 1; }

template <class T>
string to_string(T s);
template <class S, class T>
string to_string(pair<S, T> p);
string to_string(string s) { return s; }
string to_string(const char s[]) { return to_string(string(s)); }

template <class T>
string to_string(T v) {
  if (v.empty()) return "{}";
  string ret = "{";
  for (auto x : v) ret += to_string(x) + ",";
  ret.back() = '}';
  return ret;
}

template <class S, class T>
string to_string(pair<S, T> p) {
  return "{" + to_string(p.first) + ":" + to_string(p.second) + "}";
}
void debug() { cerr << endl; }

template <class Head, class... Tail>
void debug(Head head, Tail... tail) {
  cerr << to_string(head) << " ";
  debug(tail...);
}

struct IO {
#ifdef _WIN32
  inline char getchar_unlocked() { return getchar(); }
  inline void putchar_unlocked(char c) { putchar(c); }
#endif
  std::string separator = " ";
  template <class T>
  inline void read(T& x) {
    char c;
    do {
      c = getchar_unlocked();
    } while (c != '-' && (c < '0' || '9' < c));
    bool minus = 0;
    if (c == '-') {
      minus = 1;
      c = getchar_unlocked();
    }
    x = 0;
    while ('0' <= c && c <= '9') {
      x *= 10;
      x += c - '0';
      c = getchar_unlocked();
    }
    if (minus) x = -x;
  }
  inline void read(std::string& x) {
    char c;
    do {
      c = getchar_unlocked();
    } while (c == ' ' || c == '\n');
    x.clear();
    do {
      x += c;
      c = getchar_unlocked();
    } while (c != ' ' && c != '\n' && c != EOF);
  }
  template <class T>
  inline void read(std::vector<T>& v) {
    for (auto& x : v) read(x);
  }
  template <class S, class T>
  inline void read(std::pair<S, T>& p) {
    read(p.first);
    read(p.second);
  }
  template <class Head, class... Tail>
  inline void read(Head& head, Tail&... tail) {
    read(head);
    read(tail...);
  }
  template <class T>
  inline void write(T x) {
    char buf[32];
    int p = 0;
    if (x < 0) {
      x = -x;
      putchar_unlocked('-');
    }
    if (x == 0) putchar_unlocked('0');
    while (x > 0) {
      buf[p++] = (x % 10) + '0';
      x /= 10;
    }
    while (p) {
      putchar_unlocked(buf[--p]);
    }
  }
  inline void write(std::string x) {
    for (char c : x) putchar_unlocked(c);
  }
  inline void write(const char s[]) {
    for (int i = 0; s[i] != 0; ++i) putchar_unlocked(s[i]);
  }
  template <class T>
  inline void write(std::vector<T> v) {
    if (v.empty()) return;
    for (auto itr = v.begin(); itr + 1 != v.end(); ++itr) {
      write(*itr);
      write(separator);
    }
    write(v.back());
  }
  template <class Head, class... Tail>
  inline void write(Head head, Tail... tail) {
    write(head);
    write(separator);
    write(tail...);
  }
  template <class Head, class... Tail>
  inline void writeln(Head head, Tail... tail) {
    write(head, tail...);
    write("\n");
  }
  void set_separator(std::string s) { separator = s; }
} io;

int main() {
  int N;
  io.read(N);
  vector<int> a(N);
  io.read(a);
  vector<vector<int>> G(N);
  REP(i, N - 1) {
    int u, v;
    io.read(u, v);
    G[u - 1].push_back(v - 1);
    G[v - 1].push_back(u - 1);
  }
  vector<int> ans(N);
  vector<int> lis;
  function<void(int, int)> dfs = [&](int u, int p) {
    auto it = lower_bound(ALL(lis), a[u]);
    if (it == lis.end()) {
      lis.emplace_back(a[u]);
      ans[u] = lis.size();
      for (int v : G[u])
        if (v != p) dfs(v, u);
      lis.pop_back();
    } else {
      int d = it - lis.begin();
      int pr = lis[d];
      lis[d] = a[u];
      ans[u] = lis.size();
      for (int v : G[u])
        if (v != p) dfs(v, u);
      lis[d] = pr;
    }
  };
  dfs(0, -1);
  REP(i, N) io.writeln(ans[i]);
  return 0;
}

Measured memory_bytes: 35764