#include <bits/stdc++.h>
#include <chrono> 
 
using namespace std;
using namespace std::chrono; 
 
// #pragma GCC target ("avx2")
// #pragma GCC optimization ("O3")
// #pragma GCC optimization ("unroll-loops")
// #pragma optimization_level 3
// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
 
#define f0r(a, b) for (long long a = 0; a < (b); ++a)
#define f1r(a, b, c) for (long long a = (b); a < (c); ++a)
#define f0rd(a, b) for (long long a = (b); a >= 0; --a)
#define f1rd(a, b, c) for (long long a = (b); a >= (c); --a)
#define ms(arr, v) memset(arr, v, sizeof(arr))
#define pb push_back
#define send {ios_base::sync_with_stdio(false);}
#define help {cin.tie(NULL); cout.tie(NULL);}
#define fix(prec) {cout << setprecision(prec) << fixed;}
#define mp make_pair
#define f first
#define s second
#define presum(p, a, n) {p[0] = a[0]; for (int i = 1; i < (n); i++) p[i] = a[i] + p[i-1];}
#define all(v) v.begin(), v.end()
#define getunique(v) {sort(all(v)); v.erase(unique(all(v)), v.end());}
#define readgraph(list, edges) for (int i = 0; i < edges; i++) {int a, b; cin >> a >> b; a--; b--; list[a].pb(b); list[b].pb(a);}
#define ai(a, n) for (int ele = 0; ele < n; ele++) cin >> a[ele];
#define ain(a, lb, rb) for (int ele = lb; ele <= rb; ele++) cin >> a[ele];
#define ao(a, n) {for (int ele = 0; ele < (n); ele++) { if (ele) cout << " "; cout << a[ele]; } cout << '\n';}
#define aout(a, lb, rb) {for (int ele = (lb); ele <= (rb); ele++) { if (ele > (lb)) cout << " "; cout << a[ele]; } cout << '\n';}
typedef long long ll;
typedef double ld;
typedef long double lld;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
 
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v);
template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) {
  cout << "["; for(int i = 0; i < v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "]";
}
template<typename A, typename B> istream& operator>>(istream& cin, pair<A, B> &p) {
  cin >> p.first;
  return cin >> p.second;
}
 
mt19937 rng(steady_clock::now().time_since_epoch().count());
// mt19937 rng(61378913);
/* usage - just do rng() */
 
void usaco(string filename) {
  // #pragma message("be careful, freopen may be wrong")
	freopen((filename + ".in").c_str(), "r", stdin);
	freopen((filename + ".out").c_str(), "w", stdout);
}
 
const lld pi = 3.14159265358979323846;
// const ll mod = 1000000007;
// const ll mod = 998244353;
// ll mod;
 
using implicit_segtree = struct implicit_segtree;
struct implicit_segtree {
  ll v, sz;
  implicit_segtree* child[2];
  ll base = 0;
 
  implicit_segtree() {
 
  }
 
  implicit_segtree(ll n) {
    v = base;
    child[0] = nullptr;
    child[1] = nullptr;
    sz = n;
  }
 
  implicit_segtree* ch(int x) {
    if (!child[x]) child[x] = new implicit_segtree(sz);
    return child[x];
  }
 
  void add(ll loc, ll val) {
    add(loc, val, 0, sz - 1);
  }
 
  ll add(ll loc, ll val, ll l, ll r) {
    if (l > loc || r < loc) return v;
    if (l == r) return v = val;
    ll m = (l + r) / 2;
    ll a = base, b = base;
    if (loc <= m) {
      a = ch(0)->add(loc, val, l, m);
      if (child[1]) b = ch(1)->v;
    } else {
      if (child[0]) a = ch(0)->v;
      b = ch(1)->add(loc, val, m + 1, r);
    }
    
    return v = max(a, b);
  }
 
  ll query(ll ql, ll qr) {
    return query(ql, qr, 0, sz - 1);
  }
 
  ll query(ll ql, ll qr, ll tl, ll tr) {
    if (qr < tl || ql > tr || tl > tr) return base;
    if (ql <= tl && tr <= qr) return v;
    ll a = base, b = base, m = (tl + tr) / 2;
    if (child[0]) a = ch(0)->query(ql, qr, tl, m);
    if (child[1]) b = ch(1)->query(ql, qr, m + 1, tr);
    return max(a, b);
  }
};
 
ll n, m, k, q, l, r, x, y, z;
ll a[1000005];
ll b[1000005];
ll c[1000005];
string s, t;
ll ans = 0;

implicit_segtree root;
vi edges[200005];

void dfs(int v, int p) {
  b[v] = 1 + root.query(0, a[v] - 1);

  ll ov = root.query(a[v], a[v]);
  if (b[v] > ov) root.add(a[v], b[v]);

  if (p != -1) b[v] = max(b[v], b[p]);
  for (int x: edges[v]) if (x != p) dfs(x, v);

  root.add(a[v], ov);
}

void solve(int tc) {
  cin >> n;
  ai(a, n);
  readgraph(edges, n - 1);

  root = implicit_segtree(2e9);

  dfs(0, -1);

  f0r(i, n) cout << b[i] << '\n';
}
 
int main() {
  send help
 
  // usaco("file");
 
  int tc;
  tc = 1;
  // cin >> tc;
  for (int t = 0; t < tc; t++) solve(t);
} 

Measured memory_bytes: 155736