#include <bits/stdc++.h>
#ifdef LOCAL_DEBUG
#define DEBUG 1
#define CERR if(DEBUG) cerr
#define MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,NAME,...) NAME
#define pr(...) CERR<<MACRO(__VA_ARGS__,pr10,pr9,pr8,pr7,pr6,pr5,pr4,pr3,pr2,pr1)(__VA_ARGS__)<<endl
#define pr1(a) (#a)<<"="<<(a)<<" "
#define pr2(a,b) pr1(a)<<pr1(b)
#define pr3(a,b,c) pr1(a)<<pr2(b,c)
#define pr4(a,b,c,d) pr1(a)<<pr3(b,c,d)
#define pr5(a,b,c,d,e) pr1(a)<<pr4(b,c,d,e)
#define pr6(a,b,c,d,e,f) pr1(a)<<pr5(b,c,d,e,f)
#define pr7(a,b,c,d,e,f,g) pr1(a)<<pr6(b,c,d,e,f,g)
#define pr8(a,b,c,d,e,f,g,h) pr1(a)<<pr7(b,c,d,e,f,g,h)
#define pr9(a,b,c,d,e,f,g,h,i) pr1(a)<<pr8(b,c,d,e,f,g,h,i)
#define pr10(a,b,c,d,e,f,g,h,i,j) pr1(a)<<pr9(b,c,d,e,f,g,h,i,j)
#define prArr(a){CERR<<(#a)<<"={";int i=0;for(auto t:(a))CERR<<(i++?", ":"")<<t;CERR<<"}"<<endl;}
#else
#define DEBUG 0
#define pr(...)
#define prArr(a)
#endif
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL<<60)+1e9; // ~ 1.15 * 1e18
const Int mod = (1e9)+7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int,Int>;
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
template<class T1, class T2> ostream& operator<<(ostream& o,pair<T1,T2> p){return o<<"("<<p.first<<","<<p.second<<")";}
template<class T1, class T2, class T3> ostream& operator<<(ostream& o,tuple<T1,T2,T3> t){return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";}
template<class T1, class T2> istream& operator>>(istream& i,pair<T1,T2> &p){return i>>p.first>>p.second;}
template<class T> ostream& operator<<(ostream& o,vector<T> a){Int i=0;for(T t:a)o<<(i++?" ":"")<<t;return o;}
template<class T> istream& operator>>(istream& i,vector<T> &a){for(T &t:a)i>>t;return i;}
//INSERT ABOVE HERE

template <typename T>
class Compress{
public:
  vector<T> X;
  bool ok;
  Compress():ok(false){};

  Int size(){assert(ok); return X.size();}
  //void add(T a){ok = false; X.push_back(a); X.push_back(a-1); X.push_back(a+1);}
  void add(T a){ok = false; X.push_back(a);};
  void add(const vector<T> a){for(T x:a) add(x);}
  //void add(const vector<T> &a){for(T x:a) add(x);}

  void build(){
    ok = true;
    sort(X.begin(),X.end());
    X.erase(unique(X.begin(),X.end()),X.end());
  }

  Int getL(T x){assert(ok); return lower_bound(X.begin(),X.end(),x) - X.begin();}
  Int getU(T x){assert(ok); return upper_bound(X.begin(),X.end(),x) - X.begin();}
};

template<typename dtype, dtype initValue/*範囲外のときに返す値*/>
class RMQ{
public:
  Int n,n_;
  vector<dtype> dat;
  Int toMax;

  //初期化
  RMQ(){n=-1;}
  RMQ(Int n_,Int toMax = 0):n_(n_),toMax(toMax){
    n=1;
    while(n<n_)n*=2;
    dat.resize(2*n-1,initValue);
  }

  inline dtype merge(dtype a,dtype b){return toMax? max(a, b):min(a, b); }

  //k番目の値をaに変更
  void update(Int k,dtype a){
    k+=n-1;
    dat[k]=a;
    while(k>0){
      k=(k-1)/2;
      dat[k]=merge(dat[k*2+1],dat[k*2+2]);
    }
  }

  dtype dfs(Int a,Int b,Int k,Int l,Int r){
    if(r<=a||b<=l)return initValue;
    if(a<=l&&r<=b)return dat[k];
    dtype vl = dfs(a,b,k*2+1,l,(l+r)/2);
    dtype vr = dfs(a,b,k*2+2,(l+r)/2,r);
    return merge(vl,vr);
  }

  //[a,b)の最小値を求める
  dtype get(Int a,Int b){
    assert(a <= b), assert(a <= n_ && b <= n_), assert(a >= 0 && a >= 0);
    return dfs(a,b,0,0,n);
  }
};


Int N;
vector<Int> A;
vector<vector<Int> > G;
vector<Int> ans;
RMQ<Int, 0>  rmq;
Compress<Int> cmp;

void dfs(Int pos, Int pre){
  Int num = cmp.getL(A[pos]);
  Int score = rmq.get(0, num) + 1;
  Int tmp = rmq.get(num, num + 1);
  if(tmp < score) rmq.update(num, score);
  ans[pos] = rmq.get(0, cmp.size());

  for(Int to:G[pos]){
    if(to == pre) continue;
    dfs(to, pos);
  }
  rmq.update(num, tmp);
}

signed main(){
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  cin>>N;
  A.resize(N);
  G.resize(N);
  cin>>A;
  for(Int i=0;i<N-1;i++){
    Int a, b;
    cin>>a>>b; a--, b--;
    G[a].push_back(b);
    G[b].push_back(a);
  }

  cmp.add(A);
  cmp.build();
  ans.resize(N);
  rmq = RMQ<Int, 0>(cmp.size(), 1);
  rmq.update(0, 0);
  dfs(0, -1);
  for(Int a:ans) cout<<a<<endl;

  return 0;
}


Measured memory_bytes: 30632