#pragma target("avx")
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> P;
typedef vector<ll> V;
typedef unordered_map<ll, ll> U_MAP;
typedef priority_queue<ll> pq;
typedef priority_queue<ll, vector<ll>, greater<ll>> rpq;
constexpr ll INF = 1e9, MOD = 1e9 + 7, ohara = 1e6 + 10;
constexpr ll LINF = 1e18;

#define rep(i, n) for (ll(i) = 0; (i) < (int)(n); (i)++)
#define rrep(i, a, b) for (ll i = (a); i < (b); i++)
#define rrrep(i, a, b) for (ll i = (a); i >= (b); i--)
#define all(v) (v).begin(), (v).end()
#define Size(n) (n).size()
#define Cout(x) cout << (x) << endl
#define doublecout(a) cout << fixed << setprecision(15) << a << endl;
#define fi first
#define se second
#define m_p make_pair
#define p_b push_back
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

//------ Believe yourself as a genius!!!!!! ------

struct SegmentTree {
  int siz;
  vector<ll> node;
  SegmentTree(int n, ll init) {
    siz = 1;
    while (siz < n) siz <<= 1;
    node.assign(2 * siz, init);
  }

  void update(int k, ll x) {
    k += siz - 1;
    node[k] = x;
    while (k > 0) {
      k = (k - 1) / 2;
      node[k] = max(node[2 * k + 1], node[2 * k + 2]);
    }
  }

  ll query(int a, int b, int k = 0, int l = 0, int r = -1) {
    if (r < 0) r = siz;
    if (r <= a || b <= l) return -LINF;
    if (a <= l && r <= b) return node[k];
    ll vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
    ll vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
    return max(vl, vr);
  }
};

template <class T>
vector<ll> Zarts(const vector<T> &AR, ll CNT = 0) {
  vector<ll> RES;
  map<T, ll> MP;
  for (auto &e : AR) MP[e] = 0;
  for (auto &e : MP) e.se = CNT++;
  for (auto &e : AR) {
    RES.push_back(MP[e]);
  }
  return RES;
}

int dy[] = {1, 0, -1, 0};
int dx[] = {0, 1, 0, -1};
// int dy[]={-1,0,1,-1,1,-1,0,1};int dx[]={-1,-1,-1,0,0,1,1,1};
string alph("abcdefghijklmnopqrstuvwxyz"), s;
ll n, cnt, ans[ohara], a[ohara], b, c, d, tmp, m, h, w, x, y, sum, k, q, res;
V g[ohara];
bool vi[ohara];
multiset<ll> st;
SegmentTree tree(ohara, -LINF);
U_MAP mp;
ll be[ohara];

void dfs(ll now) {
  if (vi[now]) return;
  vi[now] = true;
  // cout << "A : " << now + 1 << "\n";
  res = tree.query(0, a[now]);
  if (res == -LINF) res = 0;
  res++;
  ans[now] = res;
  rep(i, Size(g[now])) {
    ll to = g[now][i];
    ans[now] = max(ans[now], ans[to]);
  }
  be[now] = tree.query(a[now], a[now] + 1);
  tree.update(a[now], res);
  rep(i, Size(g[now])) {
    ll to = g[now][i];
    dfs(to);
  }
  // cout << "A : " << now + 1 << "\n";
  tree.update(a[now], be[now]);
}

int main(void) {
  cin.tie(0);
  cout.tie(0);
  ios::sync_with_stdio(false);

  cin >> n;
  V aa(n + 1);
  rep(i, n) cin >> aa[i];
  auto bb = Zarts<ll>(aa);
  rep(i, n) a[i] = bb[i];
  rep(i, n - 1) {
    cin >> c >> b;
    c--;
    b--;
    g[c].p_b(b);
    g[b].p_b(c);
  }
  dfs(0LL);
  rep(i, n) Cout(ans[i]);
  return 0;
}

Measured memory_bytes: 94440