#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC push_options
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define endl ('\n')
#define MOD 1000000007LL
//#define MOD 998244353LL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
#define rep(i,n) for(lint i=0;i<lint(n);++i)
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrep(i,n) for(lint i=lint(n)-1;i>=0;--i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
auto call=[](auto f,auto... args){return f(f,args...);};

lint n;
vec a;
mat v;
template<typename T>
class pvector{
    struct node;
    using np=node*;
    struct node{
        T data;
        np ch[16];
        node(){
            for(int i=0;i<16;i++)ch[i]=nullptr;
        }
    };
    np root=nullptr;
    np set(int idx,T val,np t){
        np res=t?new node(*t):new node();
        if(idx==0)res->data=val;
        else res->ch[idx&15]=set(idx>>4,val,res->ch[idx&15]);        
        return res;
    }
    T get(int idx,np t){
        if(!t)return T();
        return idx?get(idx>>4,t->ch[idx&15]):t->data;
    }
    public:
    pvector(){}
    pvector(np t):root(t){}
    pvector set(int idx,T val){
        return pvector(set(idx,val,root));
    }
    T get(int idx){
        return get(idx,root);
    }
};

lint bs(lint mn,lint mx,auto func){
    mn--;
    mx++;
	while(mx-mn>1){
		lint mid=(mn+mx)/2;
		if(!func(mid))mx=mid;
		else mn=mid;
	}
    return mn;
}
vector<pvector<lint>>dp;
vector<lint>sz;
void dfs(lint n,lint p){
    if(n==0){
        dp[n]=dp[n].set(0,a[0]);
        sz[n]=1;
    }else if(dp[p].get(sz[p]-1)<a[n]){
        dp[n]=dp[p].set(sz[p],a[n]);
        sz[n]=sz[p]+1;
    }else{
        dp[n]=dp[p].set(bs(0,sz[p]-1,[&](lint x){return a[n]>dp[p].get(x);})+1,a[n]);
        sz[n]=sz[p];
    }
    for(auto e:v[n]){
        if(e==p)continue;
        dfs(e,n);
    }
}
vec ans;
int main(){
    cin>>n;
    a.resize(n);
    rep(i,n)cin>>a[i];
    v.resize(n);
    rep(i,n-1){
        lint s,t;
        cin>>s>>t;
        s--;t--;
        v[s].emplace_back(t);
        v[t].emplace_back(s);
    }
    ans.resize(n,0);
    dp.resize(n);
    sz.resize(n,0);
    dfs(0,-1);
    rep(i,n){
        cout<<sz[i]<<endl;
    }
    // rep(i,n){
    //     rep(j,sz[i]){
    //         cout<<dp[i].get(j)<<" ";
    //     }
    //     cout<<endl;
    // }
}

Measured memory_bytes: 149724