#define MOD_TYPE 1

#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
/*
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using multiInt = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
*/
/*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
*/
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9;
constexpr ll LINF = (ll)4e18;
constexpr ld PI = acos(-1.0);
constexpr ld EPS = 1e-11;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define Yay(n) cout << ((n) ? "Yay!" : ":(") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";

inline void init_main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(30) << setiosflags(ios::fixed);
}
template <typename T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b)
{
  return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
  fill((T *)array, (T *)(array + N), val);
}
#pragma endregion

//最長部分増加列の長さ
int LIS(vector<ll> &v, bool strict)
{
  vector<ll> lis;
  for (auto p : v)
  {
    vector<ll>::iterator itr;
    if (strict)
      itr = lower_bound(lis.begin(), lis.end(), p);
    else
      itr = upper_bound(lis.begin(), lis.end(), p);
    if (itr == lis.end())
      lis.push_back(p);
    else
      *itr = p;
  }
  return lis.size();
}

int n;
int par[200010], a[200010];
int ans[200010];
vector<int> E[200010];
void dfs(int p, vector<int> &dp)
{
  for (auto u : E[p])
  {
    if (par[p] == u)
      continue;
    par[u] = p;
    auto itr = lower_bound(all(dp), a[u]);
    int before = *itr;
    *itr = a[u];
    auto itr2 = lower_bound(all(dp), INF + 5);
    ans[u] = distance(dp.begin(), itr2);
    dfs(u, dp);
    *itr = before;
  }
}

int main()
{
  init_main();

  cin >> n;
  rep(i, n) cin >> a[i];
  rep(i, n - 1)
  {
    int u, v;
    cin >> u >> v;
    u--, v--;
    E[u].emplace_back(v);
    E[v].emplace_back(u);
  }

  vector<int> dp(n, INF + 10);
  dp[0] = a[0];
  ans[0] = 1;
  dfs(0, dp);
  rep(i, n) cout << ans[i] << "\n";
  return 0;
}


Measured memory_bytes: 31692