#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define ld long double
#define forn(low,high,i) for(i = low; i < high; i++)
#define forrev(high,low,i) for(i = high; i >= low; i--)
#define all(v) v.begin(),v.end()
#define decimal_digits cout << fixed << setprecision(15);

string to_string(string s) { return '"' + s + '"';}
string to_string(char s) { return string(1, s);}
string to_string(const char* s) { return to_string((string) s);}
string to_string(bool b) { return (b ? "true" : "false");}
template <typename A> string to_string(A);
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 f = 1; string r = "{"; for (const auto &x : v) {if (!f)r += ", "; f = 0; r += to_string(x);} return r + "}";}
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 pr(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

#define GOOGLE 0
#define MULTIPLE_TC 0

const int inf = 1e9;
const long long INF = 1e18;
const int mod = 1e9 + 7;
const int bit32 = log2(inf) + 3;
const int bit64 = log2(INF) + 3;

inline int add(long long a, long long b){a += b; if(a >= mod) a -= mod; return a;}
inline int sub(long long a, long long b){a -= b; if(a < 0) a += mod; return a;}
inline int mul(long long a, long long b){a %= mod; b %= mod; return (int)((long long) a * b % mod);}
inline int modexpo(long long a, long long b){int res = 1; while(b > 0){ if(b & 1) res = mul(res, a); a = mul(a, a); b /= 2;} return res;}
inline int divide(long long a, long long b){return mul(a, modexpo(b, mod - 2));}
inline int inv(long long a){return modexpo(a, mod - 2);}

clock_t time_p = clock();

void ktj(){
  time_p = clock() - time_p;
  cerr << "Time elapsed : " << (float)(time_p)/CLOCKS_PER_SEC << "\n";
}

void pre(){ // Reset each global variable (esp. for graphs)
  
}

const int N = 2e5 + 5;
vector<int> g[N];
int a[N], ans[N];

int t[4*N], lim, cnt[N];

void update(int v, int L, int R, int pos, int val){
  if(L == R){
    t[v] = val; return;
  }
  int mid = (L + R) >> 1;
  if(pos <= mid)
    update(2*v, L, mid, pos, val);
  else
    update(2*v + 1, mid + 1, R, pos, val);
  t[v] = max(t[2*v], t[2*v + 1]);
}

int query(int v, int L, int R, int l, int r){
  if(L > r or R < l or R < L)
    return 0;
  if(l <= L and R <= r)
    return t[v];
  int mid = (L + R) >> 1;
  return max(query(2*v, L, mid, l, r), query(2*v + 1, mid + 1, R, l, r));
}

void dfs(int u, int p, int level){

  int prev = query(1, 1, lim, a[u], a[u]);
  int q = query(1, 1, lim, 1, a[u] - 1);
  ans[u] = max(ans[u], prev);
  ans[u] = max(ans[u], ans[p]);
  ans[u] = max(ans[u], q + 1);

  update(1, 1, lim, a[u], q + 1);

  for(auto v : g[u]){
    if(v != p){
      dfs(v, u, level + 1);
    }
  }

  update(1, 1, lim, a[u], prev);
}

void solve(){
  int n, i, j, k;
  cin >> n; set<int> s;
  for(i = 1; i <= n; i++){
    cin >> a[i];
    s.insert(a[i]);
  }
  map<int, int> compress;
  i = 1;
  for(auto p : s){
    compress[p] = i++;
  }
  lim = i - 1;
  for(i = 1; i <= n; i++){
    a[i] = compress[a[i]];
  }
  for(i = 1; i < n; i++){
    int u, v; cin >> u >> v;
    g[u].push_back(v); g[v].push_back(u);
  }

  dfs(1, 0, 1);
  for(i = 1; i <= n; i++){
    cout << ans[i] << '\n';
  }
}

int32_t main(){
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);cout.tie(NULL); 

  pre();

  int t = 1, T;

  if(MULTIPLE_TC)
    cin >> t;

  for(T = 1; T <= t; T++){
    if(GOOGLE)
      cout << "Case #" << T << ": ";
    solve();
  }

  ktj();
}


Measured memory_bytes: 46548