#include <bits/stdc++.h>

using i32 = int_fast32_t;
using i64 = int_fast64_t;
using u32 = uint_fast32_t;
using u64 = uint_fast64_t;
using f64 = double;
using f80 = long double;

#define FOR(v, a, b) for(i64 v = (a); v < (b); ++v)
#define FORE(v, a, b) for(i64 v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(i64 v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))

#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...) ((void)0)
#endif

using namespace std;

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}
template <typename T> void pout(const T &value){std::cout << value << "\n";}
template <typename T, typename ...Args> void pout(const T &value, const Args&... args){std::cout << value << " ";pout(args...);}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}
template <typename T> auto make_vector(int n, int m, const T &value){return vector<vector<T>>(n, vector<T>(m, value));}


struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(12);
    cerr << fixed << setprecision(12);
  }
}init;


template <typename Cost = int> class Edge{
public:
  int from,to;
  Cost cost;
  Edge() {}
  Edge(int to, Cost cost): to(to), cost(cost){}
  Edge(int from, int to, Cost cost): from(from), to(to), cost(cost){}

  Edge rev() const {return Edge(to,from,cost);}
  
  friend std::ostream& operator<<(std::ostream &os, const Edge &e){
    os << "(FROM: " << e.from << "," << "TO: " << e.to << "," << "COST: " << e.cost << ")";
    return os;
  }
};

template <typename T> using Graph = std::vector<std::vector<Edge<T>>>;
template <typename T> using Tree = std::vector<std::vector<Edge<T>>>;

template <typename C, typename T> void add_edge(C &g, int from, int to, T w){
  g[from].emplace_back(from, to, w);
}

template <typename C, typename T> void add_undirected(C &g, int a, int b, T w){
  add_edge(g, a, b, w);
  add_edge(g, b, a, w);
}



template <typename F>
struct FixPoint : F{
  explicit constexpr FixPoint(F &&f) noexcept : F(std::forward<F>(f)){}

  template <typename... Args>
  constexpr decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
static inline constexpr decltype(auto) make_fix_point(F &&f){
  return FixPoint<F>(std::forward<F>(f));
}


template <typename Container, typename T = typename Container::value_type>
int lis(const Container &xs){
  std::vector<T> dp;
  dp.reserve(xs.size());
  
  for(auto x : xs){
    if(dp.empty() or dp.back() < x){
      dp.push_back(x);
    }else{
      dp[std::lower_bound(dp.begin(),dp.end(),x)-dp.begin()] = x;
    }
  }

  return dp.size();
}


int main(){
  int N;

  while(cin >> N){
    vector<int> a(N); cin >> a;

    Tree<int> tree(N);
    REP(i,N-1){
      int u, v; cin >> u >> v;
      --u, --v;
      add_undirected(tree, u, v, 1);
    }

    vector<vector<int>> dp;
    vector<int> memo;
    vector<int> ans(N);

    auto f =
      make_fix_point([&](auto &&f, int cur, int par) -> void{
                       int check = -1;
                       
                       if(dp.empty() or dp.back().back() < a[cur]){
                         dp.push_back({a[cur]});
                         memo.push_back(a[cur]);
                       }else{
                         int i = lower_bound(ALL(memo), a[cur]) - memo.begin();
                         dp[i].push_back(a[cur]);
                         memo[i] = a[cur];
                         check = i;
                       }


                       ans[cur] = dp.size();

                       for(auto &e : tree[cur]){
                         if(e.to == par) continue;
                         f(e.to, cur);
                       }

                       if(check == -1){
                         dp.pop_back();
                         memo.pop_back();
                       }else{
                         dp[check].pop_back();
                         memo[check] = dp[check].back();
                       }
                     });
    

    f(0, -1);
    

    join(cout, ALL(ans), "\n");
  }

  return 0;
}


Measured memory_bytes: 36820