/// __Macro's__
#include <bits/stdc++.h>
using namespace std;
#define ll                   long long
#define II                   pair<int,int>
#define III                  pair<int, II>
#define VI                   vector<int>
#define VII                  vector<II>
#define VIII                 vector<III>
#define VVI                  vector<vector<int> >
#define VVII                 vector<vector<II> >
#define fr                   first
#define sc                   second
#define mkpr                 make_pair
#define PQ                   priority_queue
#define pb                   push_back
#define eb                   emplace_back
#define all(v)               v.begin(), v.end()
#define LINE                 putc('\n', stdout)
#define SPACE                putc(' ' , stdout)
#define TAB                  putc('\t', stdout)
#define fillarr(arr, val)    fill((int*)arr, (int*)arr+(sizeof(arr)/sizeof(int)), val)
#define Log2(x)              (31^__builtin_clz(x))
#define inf64                ((ll)1e17)
#define inf                  1000000007
#define MOD                  1000000007
#define getint ReadInt()
const char IO_MODE = 3; // in-->00<--out (MSB-->LSB) | 0: Norm, 1: Fast 
inline ll ReadInt(){ll x=0,s=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';
c=getchar();}return s*x;}inline void WriteInt(ll x){char c[20];if(!x){putchar('0');return;}if(x<0)putchar('-'),x=-x;int i=0;while(x>0)
c[++i]=x%10,x/=10;while(i)putchar(c[i--]+48);}template <typename T>inline void out(T x){if(IO_MODE&1)WriteInt(x);else if(typeid(x)==typeid(int))
printf("%i", x);else printf("%lld", (ll)x);}template<typename T, typename... Args>inline void out(T x,Args...args){out(x);SPACE;out(args...);}
template <typename T>inline void in(T &x){if(IO_MODE&2) x=ReadInt();else if(typeid(x)==typeid(int))scanf("%i",&x);else if(typeid(x)==typeid(ll))
scanf("%lld",&x);}template<typename T, typename... Args>inline void in(T &x,Args&...args){in(x);in(args...);}
int tc;
///
/// ---------------------------------------------- (Debug) -----------------------------------------------
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...);
struct debug {
#ifdef LOCAL
eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i));}
sim, class b dor(pair < b, c > d) {ris << "(" << d.first << ", " << d.second << ")";}sim dor(rge<c> d) 
{*this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]";}
#else
sim dor(const c&) { ris; }
#endif
};
vector<char*>tokenizer(const char* args){char *token=new char[111];strcpy(token, args);
token=strtok(token,", ");vector<char*> v({token});while(token=strtok(NULL,", "))v.push_back(token);
return reverse(v.begin(), v.end()),v;} void debugg(vector<char*> args) { cerr << "\b\b "; }
template <typename Head, typename... Tail> void debugg(vector<char*> args, Head H, Tail... T)
{ debug() << " [" << args.back() << ": " << H << "] "; args.pop_back(); debugg(args, T...); }
#define harg(...) #__VA_ARGS__
#ifdef LOCAL
#define dbg(...) { debugg(tokenizer(harg(__VA_ARGS__, \b\t-->Line)), __VA_ARGS__, __LINE__); cerr << endl;}
#else
#define dbg(...) { }
#endif
/// ------------------------------------------------------------------------------------------------------

#ifdef LOCAL
  #define nax 1000
  #define qax 1000
#else
  #define nax 200200
  #define qax 200100
#endif

#define int long long 

int n,m;
VI adjList[nax];
int A[nax], ans[nax];
VI lis;

void dfs(int u, int par) {
  int pos = lower_bound(lis.begin(), lis.end(), A[u]) - lis.begin();
  int old=-1;

  if(pos == lis.size()) lis.pb(A[u]);
  else {
    old = lis[pos];
    lis[pos] = A[u];
  }

  ans[u] = lis.size();

  for(auto v:adjList[u])
    if(v!=par)
      dfs(v, u);

  if(old==-1) lis.pop_back();
  else {
    lis[pos] = old;
  }
}

int32_t main()
{
  in(n);
  for(int i=0 ; i<n ; i++) in(A[i]);

  for(int i=1 ; i<n ; i++){
    int u=getint-1, v=getint-1;
    adjList[u].pb(v);
    adjList[v].pb(u);
  }  

  dfs(0, 0);

  for(int i=0 ; i<n ; i++)
    out(ans[i]), LINE;   
}

Measured memory_bytes: 31864