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

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define whole(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bit(n) (1LL<<(n))
#define F first
#define S second
// functions
template <typename T> void unique(T& c){c.erase(std::unique(c.begin(), c.end()), c.end());}
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << "(" << p.first << ", " << p.second << ")"; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20);}
} fast_io_;

template <class Monoid>
class SegmentTree{
  public:
    int n;
    using T = typename Monoid::value_type;
    vector<T> val;
    T identity;

    SegmentTree(){}
    SegmentTree(int n_, vector<T> v=vector<T>()){
      n = 1;
      while(n < n_)n *= 2;
      identity = Monoid::identity;
      val.assign(2*n-1, identity);

      for(size_t i = 0; i < v.size(); i++){
        val[i+n-1] = v[i];
      }
      for(int i = n - 2; i >= 0; i--){
        val[i] = Monoid::operation(val[2*i+1], val[2*i+2]);
      }
    }
    void update(int k, const T &t){
      k = k + n - 1;
      val[k] = t;
      while(k > 0){
        k = (k - 1) / 2;
        val[k] = Monoid::operation(val[2*k+1], val[2*k+2]);
      }
    }
    T query(int a, int b, int k, int l, int r){
      if(r <= a || b <= l)return identity;
      if(a <= l && r <= b)return val[k];
      T lv = query(a, b, 2*k+1, l, (l+r)/2);
      T rv = query(a, b, 2*k+2, (l+r)/2, r);
      return Monoid::operation(lv, rv);
    }
    T query(int a, int b){
      return query(a, b, 0, 0, n);
    }
    T get(int i){
      return val[i+n-1];
    }
};

template <typename T>
class RMQ{
  public:
    const static T identity;
    using value_type = T;

    RMQ(){}
    static T operation(T &l, T &r){
      return max(l, r);
    }
};

template <typename T>
const T RMQ<T>::identity = 0;


ll a[200010];
vector<int> edges[200010], child[200010];
SegmentTree<RMQ<int>> seg;

void dfs(int i, int p = -1){
  for(auto e: edges[i]){
    if(e == p)continue;
    child[i].pb(e);
    dfs(e, i);
  }
}

int dp[200010], res[200010];
map<ll, int> nex;
vector<int> e;
int n;

void dfs2(int i){
  dp[i] = seg.query(0, nex[a[i]]);
  dp[i]++;
  seg.update(e[i], dp[i]);
  res[i] = seg.query(0, n);
  for(auto c: child[i]){
    dfs2(c);
  }
  seg.update(e[i], 0);
}

int main(int argc, char const* argv[])
{
  cin >> n;
  rep(i, n)cin >> a[i];
  rep(i, n - 1){
    int u, v; cin >> u >> v; u--; v--;
    edges[u].pb(v);
    edges[v].pb(u);
  }
  dfs(0);
  seg = SegmentTree<RMQ<int>>(n);
  vector<int> tr(n); rep(i, n)tr[i] = i;
  sort(whole(tr), [&](int i, int j){
    if(a[i] != a[j])return a[i] < a[j];
    return i < j;
  });
  e.resize(n); rep(i, n)e[tr[i]] = i;
  rep(i, n){
    if(nex.find(a[i]) == nex.end())nex[a[i]] = e[i];
    else nex[a[i]] = min(nex[a[i]], e[i]);
  }
  dfs2(0);
  rep(i, n)cout << res[i] << endl;
  return 0;
}


Measured memory_bytes: 57740