// clang-format off
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define stoi stoll
using pii = pair<int,int>;
using vi = vector<int>;
using vvi = vector<vi>;
#define all(c) begin(c), end(c)
#define rall(c) rbegin(c), rend(c)
#define fore(x, c) for(auto &&x : c)
#define rep(i, a, n) for(int i = a, i##len = (int)(n); i < i##len; ++i)
#define rrep(i, a, n) for(int i = (int)(n - 1); i >= a; --i)
#define sz(c) ((int)c.size())
#define contains(c, x) (c.find(x) != end(c))
#define inseg(l, x, r) ((l) <= (x) && (x) < (r))
#define dump(...)
#define pb push_back
#define eb emplace_back
#define _ 0
const signed INF_ = 1001001001; const long long INF = 1001001001001001001LL;
const int DX[9] = {0,1,0,-1,1,1,-1,-1,0}, DY[9] = {-1,0,1,0,-1,1,1,-1,0};
template<class T> ostream& operator<<(ostream &os, const vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++) os<<*i<<(i==end(v)-1?"":" ");return os;}
template<class T> istream& operator>>(istream &is, vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++) is>>*i;return is;}
template<class T,class U> istream& operator>>(istream &is, pair<T,U> &p) {
  is>>p.first>>p.second;return is;}
template<class T, class U> bool chmax(T &a, const U &b){return a<b?a=b,1:0;}
template<class T, class U> bool chmin(T &a, const U &b){return a>b?a=b,1:0;}
template <class T> void psum(T& c) {partial_sum(begin(c), end(c), begin(c));}
template<class T> using heap = priority_queue<T, deque<T>, greater<T>>;
struct before_main_function {
  before_main_function() {
      cin.tie(nullptr); ios::sync_with_stdio(0);
      cout << setprecision(15) << fixed;
  }
} before_main_function;
// clang-format on
//------------------8<------------------------------------8<--------------------

template <class Monoid>
class SegmentTree {
  using T = typename Monoid::T;
  int size;
  vector<T> data;
  void build() {
    for (int i = size - 1; i > 0; --i)
      data[i] = Monoid::op(data[i << 1], data[i << 1 | 1]);
  }

 public:
  SegmentTree(int n) {
    size = 1;
    while (size < n) size <<= 1;
    data.assign(size << 1, Monoid::identity());
  }
  template <class InputIt>
  SegmentTree(InputIt first, InputIt last)
      : SegmentTree(std::distance(first, last)) {
    copy(first, last, std::begin(data) + size);
    build();
  }

  // 0-indexed
  void update(int p, const T &value) {
    for (data[p += size] = value; p >>= 1;)
      data[p] = Monoid::op(data[p << 1], data[p << 1 | 1]);
  }
  // [l, r)  0-indexed
  T query(int l, int r) {
    T resl = Monoid::identity(), resr = Monoid::identity();
    for (l += size, r += size; l < r; l >>= 1, r >>= 1) {
      if (l & 1) resl = Monoid::op(resl, data[l++]);
      if (r & 1) resr = Monoid::op(data[--r], resr);
    }
    return Monoid::op(resl, resr);
  }
  // 0-indexed
  T get(int p) { return data[p + size]; }
};

struct RMQ {
  using T = int;
  static T op(T a, T b) { return max(a, b); }
  static constexpr T identity() { return 0; }
};

signed main() {
  int N;
  cin >> N;
  vi A(N), Z;
  cin >> A;
  rep(i, 0, N) { Z.pb(A[i]); }
  sort(all(Z));
  Z.erase(unique(all(Z)), end(Z));
  auto getidx = [&](int x) { return lower_bound(all(Z), x) - begin(Z); };

  vvi G(N);
  rep(i, 0, N - 1) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    G[a].pb(b);
    G[b].pb(a);
  }

  SegmentTree<RMQ> seg(N);
  vi ans(N);
  auto dfs = [&](auto &self, int v, int p) -> void {
    int idx = getidx(A[v]);
    ans[v] = seg.query(0, N);
    int tmp = seg.query(0, idx) + 1;
    chmax(ans[v], tmp);

    int pre = seg.get(idx);
    if (tmp > pre) seg.update(idx, tmp);

    for (int w : G[v]) {
      if (w == p) continue;
      self(self, w, v);
    }

    seg.update(idx, pre);
  };
  dfs(dfs, 0, -1);
  rep(i, 0, N) { cout << ans[i] << endl; }
  return (0 ^ _ ^ 0);
}



Measured memory_bytes: 37104