bool DBG = false;
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
// #pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
//#include <boost/multiprecision/cpp_dec_float.hpp>
//#include <boost/multiprecision/cpp_int.hpp>
using namespace std;
using ll = long long;
using ld = long double;
//using i128 = __int128_t;
//using bint = boost::multiprecision::cpp_int
//using d1024 = boost::multiprecision::number<mp::cpp_dec_float<1024>>;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define IFOR(i,a,b) for(int i=(b-1);i>=(a);--i)
#define RPT(i,a,b) for(int i=(a);i<((a)+(b));++i)
#define IRPT(i,a,b) for(int i=((a)+(b)-1);i>=(a);--i)
#define ALL(x) x.begin(),x.end()
#define RALL(x) x.rbegin(),x.rend()
#define fs first
#define sd second
#define couts(x) cout << (x) << (" ")
#define coutn(x) cout << (x) << ("\n")
#define ncouts(x) numout(x),outst[outst_N++] = ' '
#define ncoutn(x) numout(x),outst[outst_N++] = '\n'
#define scouts(x) strout(x),outst[outst_N++] = ' '
#define scoutn(x) strout(x),outst[outst_N++] = '\n'
#define dcouts(x) if(DBG) couts(x)
#define dcoutn(x) if(DBG) coutn(x)
#define endl "\n"
#define psb push_back
#define ppb pop_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define LBIT(x,a) (((x)>>(a))&1LL)
#define IBIT(x,a) (((x)>>(a))&1)
#define BCOUNT(x) (__builtin_popcount(x))
template<typename T> std::istream &operator>>(std::istream &is, std::vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T1, typename T2> std::istream &operator>>(std::istream &is, std::pair<T1,T2> &p){is >> p.first >> p.second; return is; }
template<typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> std::ostream &operator<<(std::ostream &os, const std::deque<T> &vec){ os << "deque["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> std::ostream &operator<<(std::ostream &os, const std::set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> std::ostream &operator<<(std::ostream &os, const std::unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> std::ostream &operator<<(std::ostream &os, const std::multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> std::ostream &operator<<(std::ostream &os, const std::unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> std::ostream &operator<<(std::ostream &os, const std::map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> std::ostream &operator<<(std::ostream &os, const std::unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }

template<class T> using V = vector<T>;
template<class T> using V2 = V<V<T>>;
template<class T> using V3 = V<V2<T>>;
template<class T> using V4 = V<V3<T>>;

constexpr ll LINF = 1LL << 55;
constexpr int IINF = 1 << 28;
constexpr ll mod = 1'000'000'007;


char outst[100'000'000]; int outst_N = 0;
char outst_tmp[200];
template<class NUM >
void numout(NUM n){
  if(n<0) { n*=-1; outst[outst_N++] = '-';}
  int cnt = 0;
  while(n>0){
    outst_tmp[cnt++] = '0' + (n % 10);
    n /= 10;
  }
  IFOR(i,0,cnt){
    outst[outst_N++] = outst_tmp[i];
  }
}
void strout(std::string s){
  for(auto x: s){
    outst[outst_N++] = x;
  }
}




int n;
V<ll> a;
V2<int> g;
V<int> ans;
V<ll> dp;
using PIL = pair< int, ll>;


PIL dfs(int s, int par = -1){
  PIL ret;
  ret.fs = lb(ALL(dp), a[s]) - dp.begin();
  ret.sd = dp[ ret.fs ];
  dp[ ret.fs ] = a[s];
  ans[s] = lb(ALL(dp), LINF) - dp.begin();
  //couts("F");couts(s); couts(par);coutn(dp);
  for(auto x: g[s]){
    if(x==par) continue;
    auto p = dfs(x, s);
    dp[ p.fs ] = p.sd;
  }
  //couts("S");couts(s); couts(par);coutn(dp);
  return ret;
}


void solve(){
  cin >> n;
  a = V<ll>(n);
  g = V2<int>(n);
  ans = V<int>(n);
  dp = V<ll>(n, LINF);
  cin >> a;
  FOR(_,0,n-1){
    int u, v; cin >> u >> v;
    --u, --v;
    g[u].eb(v);
    g[v].eb(u);
  }
  dfs(0);
  for(auto x:ans) coutn(x);
}

int main(void){
  std::cout << std::fixed << std::setprecision(20);
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
  //printf("%s", outst);
  return 0;
}



Measured memory_bytes: 29484