#include <bits/stdc++.h>
using namespace std;
#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
using ll = long long;
using ld = long double;
#define int ll
#define double ld
#define VARNAME(v) #v
using P = pair<int,int>;
constexpr  int MOD = 1000000007;
//constexpr  int MOD = 998244353;
constexpr ll INF = 1e16;
#pragma region tmp
constexpr double EPS = 1e-10;
constexpr double PI = 3.141592653589793;
const string endn = "\n";
const string abc="abcdefghijklmnopqrstuvwxyz";
const string ABC="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
template<class T1, class T2>ostream &operator<<(ostream &out, const pair<T1, T2> &o){out << "(" << o.first << ", " << o.second << ")";return out;}
template<class T> ostream &operator<<(ostream &out, const vector<T> &o){for(auto itr=o.begin();itr != o.end();itr++)out << *itr << (itr+1 != o.end() ? " " : "");return out;}
template<class T> ostream &operator<<(ostream &out, const deque<T> &o){for(auto itr=o.begin();itr != o.end();itr++)out << *itr << (itr+1 != o.end() ? " " : "");return out;}
template<class T> ostream &operator<<(ostream &out, const set<T> &o){out << "{";for(auto itr=o.begin();itr != o.end();itr++)out << *itr << (next(itr,1) != o.end() ? "," : "");out << "}";return out;}
template<class T> ostream &operator<<(ostream &out, const multiset<T> &o){out << "{";for(auto itr=o.begin();itr != o.end();itr++)out << *itr << (next(itr,1) != o.end() ? "," : "");out << "}";return out;}
template<class T, class U> ostream &operator<<(ostream &out, const map<T, U> &o){out << "{";for(auto itr=o.begin();itr != o.end();itr++)out << *itr << (next(itr,1) != o.end() ? " " : "");out << "}";return out;}
template<class T, class U> ostream &operator<<(ostream &out, const multimap<T, U> &o){out << "{";for(auto itr=o.begin();itr != o.end();itr++)out << *itr << (next(itr,1) != o.end() ? " " : "");out << "}";return out;}
template<class T> ostream &operator<<(ostream &out, queue<T> o){while(!o.empty())out << o.front() << (o.size() > 0 ? " " : ""),o.pop();return out;}
template<class T, class U> ostream &operator<<(ostream &out, priority_queue<T, vector<T>, U> o){while(!o.empty())out << o.top() << (o.size() > 0 ? " " : ""),o.pop();return out;}
template<class T> ostream &operator<<(ostream &out, stack<T> o){while(!o.empty())out << o.top() << (o.size() > 0 ? " " : ""),o.pop();return out;}
template<class T> inline bool chmin(T& a, T b){if(a>b){a = b;return 1;}return 0;}
template<class T> inline bool chmax(T& a, T b){if(a<b){a = b;return 1;}return 0;}
template<class T> inline bool chmin(T& a, initializer_list<T> b){T c = min(b);if(a>c){a = c;return 1;}return 0;}
template<class T> inline bool chmax(T& a, initializer_list<T> b){T c = max(b);if(a<c){a = c;return 1;}return 0;}
inline int mrep(int& a, int M=MOD){a%=M;return a=(a<0 ? a+M : a);}
inline int add(int& a, int b, int M=MOD){return a=(mrep(a,M)+mrep(b,M))%M;}
inline int mul(int& a, int b, int M=MOD){return a=(mrep(a,M)*mrep(b,M))%M;}
inline int add(int& a, initializer_list<int> b, int M=MOD){return a=(mrep(a,M)+accumulate(b.begin(), b.end(), (int)0, [&M](int acc, int i){return (acc+mrep(i,M))%M;}))%M;}
inline int mul(int& a, initializer_list<int> b, int M=MOD){return a=(mrep(a,M)*accumulate(b.begin(), b.end(), (int)1, [&M](int acc, int i){return (acc*mrep(i,M))%M;}))%M;}
inline int modpow(int b, int e, int M=MOD){int ret=1;while(e > 0){if(e%2)mul(ret,b,M);mul(b,b,M);e /= 2;};return ret;}
inline int modinv(int a, int M=MOD){int b=M,u=1,v=0;while(b){int t=a/b;a-=t*b;swap(a,b);u-=t*v;swap(u,v);}return mrep(u,M);}
template<class T> inline void print(T a){cout << a << endl;}
template<class T> inline void print(vector<T> a, int n){chmin(n,int(a.size()));rep(i,n)cout << a[i] << (i != n-1 ? " " : "\n");}
template<class T, size_t SIZE> inline void print(T (&a)[SIZE], int n=SIZE){chmin(n,int(SIZE));rep(i,n)cout << a[i] << (i != n-1 ? " ":"\n");}
#pragma #endregion tmp

int n, sz;
vector<int> g[210000];
vector<int> ans, seg, a, b;

void update(int i, int x){
  i += (sz-1);
  seg[i] = x;
  while(i > 0){
    i = (i-1)/2;seg[i] = max(seg[2*i+1], seg[2*i+2]);
  }
}

int get(int a, int b, int k=0, int l=0, int r=-1){
  if(r < 0)r = sz;
  if(a <= l && r <= b)return seg[k];
  if(r <= a || b <= l)return 0;
  int vl = get(a,b,2*k+1,l,(l+r)/2),
      vr = get(a,b,2*k+2,(l+r)/2,r);
  return max(vl, vr);
}

void dfs(int x, int p){
  ans[x] = get(0,n);
  for(auto to : g[x]){
    if(to == p)continue;
    int m = get(0,a[to])+1, org = get(a[to], a[to]+1);
    chmax(m, org);
    update(a[to], m);
    dfs(to, x);
    update(a[to], org);
  }
}
signed main(){
  cin>>n;a.resize(n);b.resize(n);rep(i,n)cin>>a[i], b[i] = a[i];
  rep(i,n-1){
    int uu,vv;cin>>uu>>vv;uu--;vv--;
    g[uu].push_back(vv);
    g[vv].push_back(uu);
  }
  sz = 1;
  while(sz < n)sz *= 2;
  ans.resize(n);
  seg.resize(2*sz-1, 0);
  sort(b.begin(), b.end());
  b.erase(unique(b.begin(), b.end()), b.end());
  rep(i,n)a[i] = distance(b.begin(),lower_bound(b.begin(), b.end(), a[i]));
  update(a[0], 1);
  dfs(0, -1);
  rep(i,n)cout << ans[i] << endl;
}





Measured memory_bytes: 34468