#pragma region kyopro_template
#include <bits/stdc++.h>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define each(x, v) for (auto &x : v)
#define all(v) (v).begin(), (v).end()
#define sz(v) ((int)(v).size())
#define mem(a, val) memset(a, val, sizeof(a))
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define inc(...)    \
  char __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
using namespace std;
void solve();
using ll = long long;
template <class T = ll>
using V = vector<T>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vd = V<double>;
using vs = V<string>;
using vvl = vector<vector<long long>>;
using P = pair<long long, long long>;
using vp = vector<P>;
using pii = pair<int, int>;
using vpi = vector<pair<int, int>>;
constexpr int inf = 1001001001;
constexpr long long infLL = (1LL << 61) - 1;
template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}
template <typename T, typename U>
ll ceil(T a, U b) {
  return (a + b - 1) / b;
}
constexpr ll TEN(int n) {
  ll ret = 1, x = 10;
  while (n) {
    if (n & 1) ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U>
void out(const T &t, const U &... u) {
  cout << t;
  if (sizeof...(u)) cout << " ";
  out(u...);
}
template <typename T>
void die(T x) {
  out(x);
  exit(0);
}

#ifdef NyaanDebug
#include "NyaanDebug.h"
#define trc(...)                   \
  do {                             \
    cerr << #__VA_ARGS__ << " = "; \
    dbg_out(__VA_ARGS__);          \
  } while (0)
#define trca(v, N)       \
  do {                   \
    cerr << #v << " = "; \
    array_out(v, N);     \
  } while (0)
#define trcc(v)                             \
  do {                                      \
    cerr << #v << " = {";                   \
    each(x, v) { cerr << " " << x << ","; } \
    cerr << "}" << endl;                    \
  } while (0)
#else
#define trc(...)
#define trca(...)
#define trcc(...)
int main() { solve(); }
#endif

/*struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;*/

inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); }
inline int lsb(unsigned long long a) { return __builtin_ctzll(a); }
inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); }
template <typename T>
inline int getbit(T a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void setbit(T &a, int i) {
  a |= (1LL << i);
}
template <typename T>
inline void delbit(T &a, int i) {
  a &= ~(1LL << i);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
vector<T> mkrui(const vector<T> &v) {
  vector<T> ret(v.size() + 1);
  for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}
template <typename T = int>
vector<T> mkiota(int N) {
  vector<T> ret(N);
  iota(begin(ret), end(ret), 0);
  return ret;
}

#pragma endregion

constexpr int MOD = 998244353;

template <typename T, typename F, int NODES = 4194304>
struct PersistentSegmentTree {
  using ll = long long;

  struct Node {
    T data;
    Node *l, *r;
    Node() {}
    Node(const T &_data) : data(_data), l(nullptr), r(nullptr) {}
  };

  Node *pool;
  int pid;
  ll N;
  const F &f;
  const T ID;
  Node *nil;
  vector<Node *> roots;

  PersistentSegmentTree(const vector<T> &v, const F &_f, const T &_ID)
      : pid(0), f(_f), ID(_ID), nil(nullptr) {
    pool = new Node[NODES];
    nil = my_new(ID);
    nil->l = nil->r = nil;
    roots.reserve(262144);
    roots.push_back(build(v));
  }

  PersistentSegmentTree(const ll &_N, const F &_f, const T &_ID)
      : pid(0), N(_N), f(_f), ID(_ID), nil(nullptr) {
    pool = new Node[NODES];
    nil = my_new(ID);
    nil->l = nil->r = nil;
    roots.reserve(262144);
    roots.push_back(nil);
  }

  Node *my_new(const T &data) {
    pool[pid].data = data;
    pool[pid].l = pool[pid].r = nil;
    return &(pool[pid++]);
  }

  Node *build(const vector<T> &v) {
    N = (ll)v.size();
    assert(N > 0);
    return build(0, (ll)v.size(), v);
  }

  Node *merge(Node *l, Node *r) {
    Node *t = my_new(f(l->data, r->data));
    t->l = l, t->r = r;
    return t;
  }

  Node *build(ll l, ll r, const vector<T> &v) {
    if (l + 1 == r) return my_new(v[l]);
    ll m = (l + r) >> 1;
    return merge(build(l, m, v), build(m, r, v));
  }

  Node *_update(ll a, const T &x, Node *n, ll l, ll r) {
    if (l + 1 == r) return my_new(x);
    ll m = (l + r) >> 1;
    if (a < m) return merge(_update(a, x, n->l, l, m), n->r);
    return merge(n->l, _update(a, x, n->r, m, r));
  }

  Node *update(Node *n, ll k, const T &x) {
    Node *root = _update(k, x, n, 0, N);
    roots.push_back(root);
    return root;
  }
  Node *update(int t, ll k, const T &x) {
    Node *root = _update(k, x, roots[t], 0, N);
    roots.push_back(root);
    return root;
  }
  Node *update(ll k, const T &x) {
    Node *root = _update(k, x, roots.back(), 0, N);
    roots.push_back(root);
    return root;
  }

  Node *_add(ll a, const T &x, Node *n, ll l, ll r) {
    if (l + 1 == r) return my_new(f(x, n->data));
    ll m = (l + r) >> 1;
    if (a < m) return merge(_add(a, x, n->l, l, m), n->r);
    return merge(n->l, _add(a, x, n->r, m, r));
  }

  Node *add(Node *n, ll k, const T &x) {
    Node *root = _add(k, x, n, 0, N);
    roots.push_back(root);
    return root;
  }
  Node *add(int t, ll k, const T &x) {
    Node *root = _add(k, x, roots[t], 0, N);
    roots.push_back(root);
    return root;
  }
  Node *add(ll k, const T &x) {
    Node *root = _add(k, x, roots.back(), 0, N);
    roots.push_back(root);
    return root;
  }

  T _query(ll a, ll b, Node *n, ll l, ll r) {
    if (n == nil) return ID;
    if (r <= a or b <= l) return ID;
    if (a <= l and r <= b) return n->data;
    ll m = (l + r) >> 1;
    return f(_query(a, b, n->l, l, m), _query(a, b, n->r, m, r));
  }

  T query(Node *n, ll a, ll b) { return _query(a, b, n, 0, N); }
  T query(int t, ll a, ll b) { return _query(a, b, roots[t], 0, N); }
  T query(ll a, ll b) { return _query(a, b, roots.back(), 0, N); }
};

template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}
  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].pb(y);
    if (!is_directed) g[y].pb(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].eb(x, y, c);
    if (!is_directed) g[y].eb(y, x, c);
  }
  return g;
}

// Depth of Rooted Tree
// unvisited nodes : d = -1
vector<int> Depth(UnweightedGraph &g, int start = 0) {
  vector<int> d(g.size(), -1);
  auto dfs = [&](auto rec, int cur, int par = -1) -> void {
    d[cur] = par == -1 ? 0 : d[par] + 1;
    each(dst, g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, cur);
    }
  };
  dfs(dfs, start);
  return d;
}

// Diameter of Tree
pair<int, int> Diameter(UnweightedGraph &g, int start = 0) {
  auto d = Depth(g, start);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(u, v);
}

void solve() {
  ini(N);
  vi a(N);
  in(a);
  auto g = graph(N);

  auto f = [](int a, int b) { return max(a, b); };
  PersistentSegmentTree<int, decltype(f),7777777> seg(inf, f, 0);
  using node = decltype(seg)::Node;

  vi ans(N);
  auto dfs = [&](auto rec, int cur, node* n, int par = -1) -> void {
    int cm = seg.query(n, 0, a[cur]) + 1;
    auto cn = seg.update(n, a[cur], cm);
    ans[cur] = seg.query(cn, 0, inf);
    trc(cur,a[cur],ans[cur]);
    each(dst, g[cur]) {
      if (dst == par) continue;
      rec(rec, dst,cn, cur);
    }
  };
  dfs(dfs, 0, seg.nil);
  each(x, ans) out(x);
}

Measured memory_bytes: 201976