#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
using namespace std;
// using namespace __gnu_pbds;
#define ff              first
#define ss              second
#define pb(x)           push_back(x)
#define mp              make_pair
#define sz(x)           (int)x.size()
#define mem(x ,y)       memset(x , y , sizeof x )
#define all(a )         a.begin() , a.end()
#define endl            "\n"
#define pii             pair<int,int> 
#define clr(x)          x.clear()
#define sl(x )          scanf("%I64d" ,&x)
#define si(x )          scanf("%d" ,&x)
#define forn(i ,x,n )   for(int i = x ; i <= n ; i++ )
#define ford(i ,x,n )   for(int i = x ; i >= n ; i-- )
#define rep(i,n )       for(int i= 0; i<n ; i++ ) 
#define repi(i,n )      for(int i= 1; i<=n ; i++ ) 
#define repit(i, c)     for( __typeof((c).begin()) i = (c).begin(); i != (c).end();++i )
#define dbg(args...)    do {   cerr << #args << ' ' ;  print(args); } while(0); cerr<< endl ;
typedef long long ll  ;
ll mod =  1e9+7, mod2 = 998244353 ; 
typedef unsigned long long  ull ;
int setbit(int n, int pos  ) { return n = n|(1<< pos) ; }
int resetbit(int n,int pos ) {  return n =  n & ~(1<<pos ); }
bool checkbit(int  n,int pos ) { return (bool ) (n&(1<<pos))  ; }
template<typename T> void print(const T& v) {    cerr << v << ' ' ;}
template<typename T>T add(T x, T y, T mod = mod ){ x%= mod ;  y%= mod ;   return (x+y)%mod ;  }
template<typename T>T sub(T x, T y, T mod = mod ){ return ((x-y)%mod+mod )%mod;  }
template<typename T>T mul(T x, T y, T mod = mod ){ x %= mod ; y %= mod ; return (x*y)%mod  ;  }
template<typename T1,typename... T2> void print( const T1& first, const T2&... rest ){ print(first); print(rest...) ;}
template<typename T> void dbg_a(T a[] ,int n=10 ) {cerr << "[ "; for(int i=0;i <= n ; i++ )cerr<<a[i]<<' ' ; cerr<< " ]" <<  endl; } 
template<typename F,typename S>ostream& operator<<( ostream& os, const pair< F, S > & p ){return os << "[ " << p.first << ", " << p.second << " ]";}
template<typename T>ostream &operator<<(ostream & os, const vector< T > &v ){os << "[ "; for(int i=0; i<sz(v) ; i++ )  os << v[i] << ' ' ; return os << " ]\n" ; } 
template<typename T>ostream &operator<<(ostream & os,const map< T ,T> &Map ){os << "[ "; repit(it , Map ) os << "[" <<(*it).ff << ' ' << (*it).ss << "] "    ; return os << "]\n" ; } 
template<typename T>ostream &operator<<(ostream & os, const set< T > &Set  ){os << "[ "; repit(it , Set ) os <<  *it  << ' ' ; return os << " ]\n" ; }  
template<typename T>ostream &operator<<(ostream & os, const multiset< T > &Set) {os << "[ "; repit(it , Set )os <<  *it  << ' ' ; return os << " ]\n" ; }  
template<class T> string to_str(T t){stringstream ss; ss<<t; return ss.str();} 
// typedef tree<  int    ,     // change type 
//               null_type, 
//               less_equal  < int  >  ,  // change type ..    
//               rb_tree_tag,
//               tree_order_statistics_node_update> ordered_set;
template < typename T > 
#define  int  ll   
T  bigmod(T x, T k ,T mod = mod) {
    if(k == 0 ) return (T)1; 
    if(k&1  ) { 
        return ( (x%mod)*bigmod(x,k-1, mod )%mod )%mod ; 
    } else { 
        T ret = bigmod(x,k/2  , mod ) ; 
        ret %= mod ;             
        return (ret*ret )%mod; 
    } 
}
template < typename T > 
T  invmod( T x , T m) {  
    return bigmod(x,m-2 , m) ;   

}  


const ll inf  =     1e18 ; //  0xc0  ; //0x3f ; // 
const int maxn  = (int) 1e6 + 123 ;
//////////////////////////////////////////////

int  a[maxn ] , dp[maxn ] ,res[maxn  ]   ;  
vector<int >g[maxn ]  ; 
void func(int u ,int len  ,int  p) {

    if(len==0)  dp[len++] = a[u]  ; 
    res[u] = len ; 
    int  x=  len ; 


    rep(i, sz(g[u])  ) {
        int v = g[u][i] , id , val , f = 0; if(v==p) continue ; 
        //  upd 
        len = x ; 

        if( a[v ]>dp[len-1]) {

            dp[len++]=a[v]  ;     

        }else {
            id = lower_bound(dp, dp+len  ,  a[v] ) - dp ;


            f=1 , val = dp[id ]  ;
            dp[id ] = a[v ] ; 


        }

        func(v, len ,  u ) ; 

        if(f) dp[id ]=val  ; 
        //  change   upd ... 
    }   
}
void solve() { 
    int x,y,z, ans=0 , q, k , n , m     ;


    cin >> n ; 
    forn(i ,1, n ) cin >> a[i]  ; 

    rep(_,n-1 )   {
        cin >>x >> y ; 
        g[x].pb(y);
        g[y].pb(x) ; 
    }
    func(1,0 ,-1   ) ; 
  
    forn(i ,1,n  ) cout << res[i] <<  endl  ;   



}          
signed main() {         
     
    ios :: sync_with_stdio(false);  cin.tie(0);   cout.tie(0) ;     
        // clock_t st = clock()  ; cout << fixed << setprecision(12) ;
    int  c = 0 ,t = 1 ; 

    // cin>>t  ; 
    while(t--) {
        solve() ;  
    }
    // cerr << "Execution time : " << (double  )  (clock()-st )/CLOCKS_PER_SEC << endl ;
    // 12m426476 _)___ ///5

    return 0 ;    
}       





 

Measured memory_bytes: 53680