#include <bits/stdc++.h> // ver2.6.3
//#include <complex.h> // FFT用
//#include <boost/math/tools/minima.hpp>
//#include <boost/multiprecision/cpp_int.hpp>
//using boost::math::tools::brent_find_minima;//fmin(f,L,R,100)で最小値をmp(x,min)で取得
//using boost::multiprecision::cpp_int;//cpp_int (任意の長さのint)
#define fmin brent_find_minima
#define int long long
#define endl "\n"
#define ALL(v) (v).begin(),(v).end()
#define Vi vector<int>
#define VVi vector<Vi>
#define VVVi vector<VVi>
#define Vm vector<mint>
#define Vs vector<string>
#define Vd vector<double>
#define Pii pair<int,int>
#define Pdd pair<double,double>
#define VPii vector<Pii>
#define Tiii tuple<int,int,int>
#define VTiii vector<Tiii>
#define PQi priority_queue<int>
#define PQir priority_queue<int,vector<int>,greater<int>>
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define itos to_string
#define stoi stoll
#define FI first
#define SE second
#define cYES cout<<"YES"<<endl
#define cNO cout<<"NO"<<endl
#define cYes cout<<"Yes"<<endl
#define cNo cout<<"No"<<endl
#define cyes cout<<"yes"<<endl
#define cno cout<<"no"<<endl
#define sortr(v) sort(v,greater<>())
#define rep(i,a,b) for(int i=a;i<b;i++)
#define repeq(i,a,b) for(int i=a;i<=b;i++)
#define repreq(i,a,b) for(int i=a;i>=b;i--)
#define dem(a,b) ((a+b-1)/(b))
#define Vin(a) rep(iI,0,a.size())cin>>a[iI]
#define INF 3000000000000000000 // 3.0*10^18(MAXの1/3くらい)
#define MAX LLONG_MAX
#define PI 3.141592653589793238462
#define MOD 1000000007 // 10^9 + 7
//int MOD = 998244353; // caseに応じて変える必要がある場合はこちら
const double EPS = 1e-10;

using namespace std;

struct mint{int x;mint(int x=0):x((x%MOD+MOD)%MOD){}
mint operator-()const{return mint(-x);}
mint& operator+=(const mint a){if((x+=a.x)>=MOD)x-=MOD;return*this;}
mint& operator-=(const mint a){if((x+=MOD-a.x)>=MOD)x-=MOD;return*this;}
mint& operator*=(const mint a){(x*=a.x)%=MOD;return*this;}
mint operator+(const mint a)const{return mint(*this)+=a;}
mint operator-(const mint a)const{return mint(*this)-=a;}
mint operator*(const mint a)const{return mint(*this)*=a;}
mint pow(int t)const{if(!t)return 1;mint a=pow(t>>1);a*=a;if(t&1)a*=*this;return a;}
mint inv()const{return pow(MOD-2);}
mint& operator/=(const mint a){return*this*=a.inv();}
mint operator/(const mint a)const{return mint(*this)/=a;}};
istream& operator>>(istream& is, const mint& a) {return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) {return os << a.x;}

/* デバッグ用 */
template <typename T> // vector出力
ostream& operator<<(ostream& os,const vector<T> &V){int N=V.size();
rep(i,0,N-1){os<<V[i]<<' ';}os<<V[N-1];return os;}
template <typename T> // vector<vector>出力
ostream& operator<<(ostream& os,const vector<vector<T>> &V){
int N=V.size();rep(i,0,N-1)cout<<V[i]<<endl;cout<<V[N-1];return os;}
template <typename T,typename S> // pair出力
ostream& operator<<(ostream& os, pair<T,S> const&P){os<<P.FI<<' '<<P.SE;return os;}
template <typename T> // set出力
ostream& operator<<(ostream& os,set<T> &S){auto it=S.begin();while(it!=S.end()){
os<<*it;if(next(it,1)!=S.end())os<<' ';it++;};return os;}
template <typename T> // deque出力
ostream& operator<<(ostream& os, deque<T> &q){for(auto it=q.begin();it<q.end();it++){
os<<*it;if(it+1!=q.end())os<<" ";}return os;}

/* 便利関数 */
int gcd(int a,int b){return b?gcd(b,a%b):a;} // 最大公約数gcd
int lcm(int a,int b){return a/gcd(a,b)*b;} // 最小公倍数lcm
int mypow(int x, int n, int m){ // 累乗x^n(mod m) O(log(n))
if(n==0)return 1;if(n%2==0)return mypow(x*x%m,n/2,m);else return x*mypow(x,n-1,m)%m;}
int scomb(int n, int r){if(r<0||r>n)return 0;if((n-r)<r)r=n-r; // nCr
int a=1;for(int i=n;i>n-r;--i){a=a*i;}for(int i=1;i<r+1;++i){a=a/i;}return a;}
Vi vis(Vi &v){Vi S(v.size()+1);rep(i,1,S.size())S[i]+=v[i-1]+S[i-1];return S;} // 累積和
int digit(int k,int i){string s = itos(k);return s[s.size()-i]-'0';} // i桁目の数字
void press(Vi &v){v.erase(unique(ALL(v)),v.end());} // 圧縮
Vi zip(Vi b){int Z=b.size(); // 座標圧縮
Pii p[Z+10];int a=b.size();Vi l(a);for(int i=0;i<a;i++)
p[i]=mp(b[i],i);sort(p,p+a);int w=0;for(int i=0;i<a;i++)
{if(i&&p[i].first!=p[i-1].first)w++;l[p[i].second]=w;}return l;}
Vi beki2V(){Vi a(63);int q = 1;rep(i,0,63){a[i]=q;q*=2;}return a;}
Vi beki2 = beki2V(); // 2^n配列
int modiv(int a,int b){return a*mypow(b,MOD-2,MOD)%MOD;} // a÷b(MOD環境)
int SMALLER(Vi &a,int x){return lower_bound(a.begin(),a.end(),x)-a.begin();}
int orSMALLER(Vi &a,int x){return upper_bound(a.begin(),a.end(),x)-a.begin();}
int BIGGER(Vi &a,int x){return a.size()-orSMALLER(a,x);}
int orBIGGER(Vi &a,int x){return a.size()-SMALLER(a,x);}
int COUNT(Vi &a,int x) {return upper_bound(ALL(a),x)-lower_bound(ALL(a),x);}
int maxind(Vi &a){return max_element(ALL(a))-a.begin();}
int minind(Vi &a){return min_element(ALL(a))-a.begin();}
Vi stpowV(){Vi a(300005);
a[0]=1;repeq(i,1,300004)a[i]=a[i-1]*i%MOD;return a;}
//Vi stpow = stpowV(); // 階乗配列(%MOD)

/****************************** START ******************************/

int n;
Vi a;
Vi par;
Vi dep;
VVi chi;
Vi chisize;
Vi longest;
Vi ans;
Vi now;

struct TreeAna {
  
  VVi parII;
  VPii memot;
  Vi treeFI;
  
  TreeAna(int n) {
    par = Vi(n);
    dep = Vi(n);
    chi = VVi(n);
  }
  
  void set_parII(){
    int n = par.size();
    parII = VVi(n,Vi(20,-1));
    rep(i,0,n) parII[i][0] = par[i];
    rep(i,0,19){
      rep(j,0,n){
        if(parII[j][i] == -1) parII[j][i+1] = -1;
        else parII[j][i+1] = parII[parII[j][i]][i];
      }
    }
    return;
  }
  
  int lca(int u,int v) { // 頂点uと頂点vの共通の"先祖"で一番近いやつを返す
    if(dep[u] > dep[v]) swap(u,v);
    
    for(int i=19;i>=0;i--) {
      if(((dep[v]-dep[u])>>i)&1) v = parII[v][i];
    }
    if(u==v) return u;
    for(int i=19;i>=0;i--) {
      if(parII[u][i] != parII[v][i]){
        u = parII[u][i];
        v = parII[v][i];
      }
    }
    return parII[u][0];
  }
  
  void connect(int a,int b) {
    memot.pb(mp(a,b));
    memot.pb(mp(b,a));
    return;
  }
  
  void preset() {
    sort(ALL(memot));
    rep(i,0,memot.size()) treeFI.pb(memot[i].FI);
    return;
  }
  
  void make(int root) {
    int st,en,now;
    int n = par.size();
    par = Vi(n,-2);
    dep = par;
    chi = VVi(n,Vi(0));
    par[root] = -1;
    dep[root] = 0;
    queue<int> next;
    next.push(root);
    while(!next.empty()){
      now = next.front();
      next.pop();
      st = lower_bound(ALL(treeFI), now)-treeFI.begin();
      en = upper_bound(ALL(treeFI), now)-treeFI.begin();
      rep(i,st,en){
        if(par[memot[i].SE]!=-2) continue;
        next.push(memot[i].SE);
        chi[now].pb(memot[i].SE);
        par[memot[i].SE] = now;
        dep[memot[i].SE] = dep[now]+1;
      }
    }
  }
  
  void makechisize() {
    int n = par.size();
    chisize = Vi(n,0);
    Vi chinasi(0);
    rep(i,0,n) if(chi[i].size()==0) chinasi.pb(i);
    
    VVi dev(n+5);
    rep(i,0,n) {
      dev[dep[i]].pb(i);
    }
    repreq(i,n+3,0){
      rep(j,0,dev[i].size()){
        if(par[dev[i][j]]==-1) continue;
        chisize[par[dev[i][j]]] += chisize[dev[i][j]]+1;
      }
    }
    return;
  }
  
  void makelongest() {
    int n = par.size();
    longest = Vi(n,-1);
    Vi chinasi(0);
    rep(i,0,n) {if(chi[i].size()==0) chinasi.pb(i);}
    rep(i,0,chinasi.size()){
      int now = chinasi[i];
      int ct = 0;
      while(1) {
        if(longest[now] >= ct) break;
        else {
          longest[now] = ct;
          ct++;
          if(par[now] == -1) break;
          now = par[now];
        }
      }
    }
    return;
  }
  
  /* 使い方 */
  /*
  TreeAna tree(n) // 宣言 nは頂点数
  tree.connect(a,b) // 頂点aとbをつなぐ(0-index)
  tree.preset() // 頂点をつなぎ終わったら必ずこれをする！！！！！！！
  tree.make(k) // 頂点kを根としてpar,dep,chiを作り上げる
  tree.makechisize(); // 頂点が持つ子の総数の配列 Vi chisize を作り上げる
  tree.makelongest(); // 頂点から何回下にいけるかのヤツ(Vi longest)を作り上げる
  tree.set_parII() // lcaを使う前に必ずこれをする！！！！！！！
  tree.lca(a,b) // 頂点aとbの共通の"先祖"で一番近い"頂点"を返す
  */
  
};

void f(int K) {
  int pre,neu;
  int tmp = SMALLER(now,a[K]);
  pre = now[tmp];
  now[tmp] = a[K];
  ans[K] = SMALLER(now,INF);
  rep(i,0,chi[K].size()){
    f(chi[K][i]);
  }
  now[tmp] = pre;
  return;
}


signed main() {
  cin.tie(0);cout.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(12);
  cin >> n;
  a.resize(n);
  ans.resize(n);
  Vin(a);
  rep(i,0,n+10) now.pb(INF);
  TreeAna tree(n);
  int qw,er;
  rep(i,0,n-1){
    cin >> qw >> er;
    qw--,er--;
    tree.connect(qw,er);
  }
  tree.preset();
  tree.make(0);
  
  f(0);
  
  rep(i,0,n) cout << ans[i] << endl;
  return 0;
}

Measured memory_bytes: 39720