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

#define rep(i,s,n) for (int i = (int)s; i < (int)n; i++)
#define ll long long
#define ld long double
#define pb push_back
#define eb emplace_back
#define All(x) x.begin(), x.end()
#define Range(x, i, j) x.begin() + i, x.begin() + j
#define lbidx(x, y) lower_bound(x.begin(), x.end(), y) - x.begin()
#define ubidx(x, y) upper_bound(x.begin(), x.end(), y) - x.begin()
#define llbidx(x, y, z) lower_bound(x.begin(), x.end(), z) - lower_bound(x.begin(), x.end(), y) // 二要素間の距離
#define deg2rad(deg) ((((double)deg)/((double)360)*2*M_PI))
#define rad2deg(rad) ((((double)rad)/(double)2/M_PI)*(double)360)
#define Find(set, element) set.find(element) != set.end()
#define Decimal(x) printf("%.10f\n", x) // 小数点を10桁まで表示
// debug用
#define PrintVec(x) for (auto elementPrintVec: x) { cout << elementPrintVec << " "; } cout << "\n";
#define debug(x) cerr << #x << ": " << (x) << "\n";
#define endl "\n"
// gcj print用
#define Case(x) printf("Case #%d: ", x);

typedef pair<int, int> PI;
typedef pair<ll, ll> PLL;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef vector<vector<vector<int>>> vvvl;
typedef vector<PI> vpi;
typedef vector<vector<PI>> vvpi;
typedef vector<vector<vector<PI>>> vvvpi;
typedef vector<PLL> vpl;
typedef vector<vector<PLL>> vvpl;
typedef vector<vector<vector<PLL>>> vvvpl;

int POWINT(int x, int n) {
  int ret = 1;
  while (n > 0) {
    if (n & 1) ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
};

ll POWLL(ll x, int n) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1) ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
};

template<class T>
inline bool chmax(T &a, T b) {
  if(a < b) {
    a = b;
    return true;
  }
  return false;
};

template<class T>
inline bool chmin(T &a, T b) {
  if(a > b) {
    a = b;
    return true;
  }
  return false;
};

void print() {
  cout << endl;
}

template <class T>
void print(vector<T> &vec) {
  for (auto& a : vec) {
    cout << a;
    if (&a != &vec.back()) cout << " ";
  }
  cout << endl;
}

template <class T>
void print(vector<T> &vec, ll k){
   ll n = vec.size();
   k = min(k, n);
   rep(i, 0, k-1) cout << vec[i] << " ";
   cout << vec[k-1] << endl;
}

template <class T>
void print(vector<vector<T>> &df) {
  for (auto& vec : df) {
    print(vec);
  }
}

template<class T, class U>
void print(pair<T,U> &p){
  cout << p.first << " " << p.second << "\n";
}

const int MAX_N = 200005;
const int INF = 1e9+7;

vi a(MAX_N), ans(MAX_N);
vi graph[MAX_N];
vi dp(MAX_N, INF);


void dfs(int u, int p=-1) {
  int i = lbidx(dp, a[u]);
  int old = dp[i];
  dp[i] = a[u];
  ans[u] = lbidx(dp, INF) - 1; // dp[0] = -INF分を引く
  // if (p != -1) ans[v] = max(ans[v], ans[p])
  for (int v: graph[u]) {
    if (v == p) continue;
    dfs(v, u);
  }
  dp[i] = old;
};

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

  int n; cin >> n;
  rep(i, 0, n) cin >> a[i];
  rep(i, 0, n-1) {
    int u, v;
    cin >> u >> v;
    u--; v--;
    graph[v].pb(u);
    graph[u].pb(v);
  }

  dp[0] = -INF;
  dfs(0);

  rep(i, 0, n) {
    cout << ans[i] << endl;
  }

  return 0;
};


Measured memory_bytes: 27892