/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author
 */

// doot diddly donger cuckerino Hahahahahah
// Created by White Knife on 15/04/20.
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#pragma GCC target("popcnt")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;
using namespace __gnu_cxx;
using namespace std;

// @formatter:off
#define F               first
#define S               second
#define all(x)          (x).begin(), (x).end()
#define sz(x)           (long long) (x).size()
#define sim             template<typename T
#define ris             return *this
#define dor             > debug & operator <<
#define eni(x)          sim > typename enable_if<sizeof dud<T>(0) x 1, debug&>::type operator<<(T i)
sim> struct rge { T b, e; };
sim> rge<T> range(T i, T j) { return rge<T>{i, j}; }
sim> auto dud(T *x) -> decltype(cerr << *x, 0);
sim> char dud(...);
struct debug {
#ifdef LOCAL
  ~debug() { cerr << endl; }
  eni(!=) { cerr << boolalpha << i; ris; }
  eni(==) { ris << range(all(i)); }
  sim, typename U dor(pair<U, T> d) { ris << "(" << d.first << ", " << d.second << ")"; }
  sim dor(rge<T> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; }
#else
  sim dor(const T&) { ris; }
#endif
};
#define pr(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vb = vector<bool>;

using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vpii = vector<pii>;
using vpll = vector<pll>;
template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

const ld PI = acos(-1);

template <typename T> T gcd(T x, T y) { return (y == 0) ? x : gcd(y, x % y); }
template<typename T> inline T mini(T& x, T y) { return x = min(x, y); }
template<typename T> inline T maxi(T& x, T y) { return x = max(x, y); }
template <typename T> T rand(T x, T y) { return rand() % (y - x + 1) + x; }
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
// @formatter:on

//
// Created by White Knife on 14/04/20.
//

//
// Created by White Knife on 14/04/20.
//

#include <vector>
using std::vector;

template <typename T>
class graph {
public:
  struct edge {
    int from;
    int to;
    T cost;
  };
  
  std::vector<edge> edges;
  std::vector<std::vector<int>> g;
  int n;
  int max_cost;
  
  graph(int _n) : n(_n) {
    g.resize(n);
  }

  virtual int add(int from, int to, T cost) = 0;
  
//  void add_directed(int from, int to, T cost = 1) {
//    g[from].push_back({from, to, cost});
//    max_cost = max(max_cost, cost);
//  }
};

//template <typename T>
//int graph<T>::add(int from, int to, T cost){
//    add_directed(from, to, cost);
//    add_directed(to, from, cost);
//}

template <typename T>
class forest : public graph<T> {
public:
  using graph<T>::edges;
  using graph<T>::g;
  using graph<T>::n;

  forest(int _n) : graph<T>(_n) {}

  int add(int from, int to, T cost = 1) {
    assert(0 <= from && from < n && 0 <= to && to < n);
    int id = (int) edges.size();
    assert(id < n - 1);
    g[from].push_back(id);
    g[to].push_back(id);
    edges.push_back({from, to, cost});
    return id;
  }
};

class FLISOnTree {
public:
  
  void solve(std::istream &cin, std::ostream &cout) {
    int n;
    cin >> n;
    vi a(n);
    vi ans(n);
    vi seq;
    for (int i = 0; i < n; ++i) cin >> a[i];
    
    vector<vector<int>> g(n);
    
    for (int i = 0; i < n - 1; ++i) {
      int u, v;
      cin >> u >> v;
      u--, v--;
      g[u].push_back(v);
      g[v].push_back(u);
//      forest.add(u, v);
    }
    vector<bool> vis(n, false);
    function<void(int, int)> dfs = [&](int ver, int par) {
      assert(ver < n and ver >= 0);
      debug() << pr(seq);
      int pos = lower_bound(all(seq), a[ver]) - seq.begin();
      int was = pos == sz(seq) ? -1 : seq[pos];
      if (pos < sz(seq)) {
        seq[pos] = a[ver];
      } else {
        seq.push_back(a[ver]);
      }
      ans[ver] = sz(seq);
      for (auto p: g[ver]) {
        if (p == par) continue;
        dfs(p, ver);
      }
      if (was == -1) {
        seq.pop_back();
      } else {
        seq[pos] = was;
      }
    };
    
    dfs(0, -1);
    for (int i = 0; i < n; ++i) {
      cout << ans[i] << '\n';
    }
  }
};

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
	FLISOnTree solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}


Measured memory_bytes: 32968