#pragma GCC optimize("O2")
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <compare>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numbers>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>

//#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

#ifdef DEBUG
#define dbg(x) cout << (#x) << " = " << x << '\n'
#else
#define dbg(x)
#endif

namespace R = std::ranges;
namespace V = std::views;

using namespace std;

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
//#define double ldb

template<class T>
ostream& operator<<(ostream& os, const pair<T, T> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(const T &X : arr)
    os << X << ' ';
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(const T &X : vec)
    os << X << ' ';
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(const T &x : s)
    os << x << ' ';
  return os;
}

struct fastJump {
  vector<int> p, jp, dep;

  fastJump(vector<vector<int>> g, int root = 0) : p(ssize(g)), jp(ssize(g)), dep(ssize(g)) {
    auto dfs = [&](int v, auto self) -> void {
      if (dep[p[v]] + dep[jp[jp[p[v]]]] == 2 * dep[jp[p[v]]])
        jp[v] = jp[jp[p[v]]];
      else
        jp[v] = p[v];

      for(int x : g[v]) {
        if (x == p[v]) continue;
        p[x] = v, dep[x] = dep[v] + 1;
        self(x, self);
      }
    };

    p[root] = jp[root] = root;
    dfs(root, dfs);
  }

  int jump(int v, int k) {
    k = min(k, dep[v]);
    while(k) {
      if (int d = dep[v] - dep[jp[v]]; d <= k)
        v = jp[v], k -= d;
      else
        v = p[v], k -= 1;
    }
    return v;
  }

  int lca(int u, int v) {
    if (dep[u] < dep[v])
      swap(u, v);
    u = jump(u, dep[u] - dep[v]);
    if (u == v) return u;
    while(p[u] != p[v]) {
      if (jp[u] != jp[v]) u = jp[u], v = jp[v];
      else u = p[u], v = p[v];
    }
    return p[u];
  }

  int kth(int s, int t, int k) {
    int m = lca(s, t);
    if (dep[s] + dep[t] - 2 * dep[m] < k)
      return -1;
    else if (dep[s] - dep[m] >= k)
      return jump(s, k);
    else
      return jump(t, dep[s] + dep[t] - 2 * dep[m] - k);
  }

  int dis(int u, int v) {
    return dep[u] + dep[v] - 2 * dep[lca(u, v)];
  }
};

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n; cin >> n;
  vector<int> a(n);
  for(int &x : a)
    cin >> x;
  vector<vector<int>> g(n);
  for(int i = 1; i < n; i++) {
    int u, v; cin >> u >> v;
    u--, v--;
    g[u].emplace_back(v);
    g[v].emplace_back(u);
  }

  fastJump fj(g);

  vector<int> ord(n);
  iota(ord.begin(), ord.end(), 0);
  sort(ord.begin(), ord.end(), [&](int i, int j) { return a[i] > a[j]; });

  int l = ord[0], r = ord[0], d = 0;
  vector<int> ans(n);
  for(int i = 1, p = 0; i <= n; i++) {
    if (i == n or a[ord[i]] != a[ord[i - 1]]) {
      for(int j = p; j < i; j++) {
        int x = fj.dis(ord[j], l);
        int y = fj.dis(ord[j], r);
        if (x >= y and x > d)
          r = ord[j], d = x;
        else if (x < y and y > d)
          l = ord[j], d = y;
      }
      for(int j = p; j < i; j++)
        ans[ord[j]] = max(fj.dis(l, ord[j]), fj.dis(r, ord[j]));
      p = i;
    }
  }

  cout << ans << '\n';

  return 0;
}