#pragma GCC optimize ("O3")
#include <iostream>
#include <iomanip>
#include <istream>
#include <ostream>
#include <sstream>
#include <iterator>
#include <vector>
#include <algorithm>
#include <queue>
#include <deque>
#include <list>
#include <stack>
#include <map>
#include <unordered_map>
#include <set>
#include <bitset>
#include <utility>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <ctime>
#include <cctype>
#include <cstdlib>
#define IINF 100000000
#define INF 300000000000000000
#define MOD 1000000007
#define mod 1000000007
#define INT_MAX_ 2147483647
#define REP(i, a, n) for (ll i = a; i < (ll)(n); i++)
#define REPE(i, a, n) for (ll i = a; i <= (ll)(n); i++)
#define rep(i,n)for (ll i = 0; i < (ll)(n); i++)
#define Endl endl
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define eb emplace_back
#define mmax(x,y)(x>y?x:y)
#define mmin(x,y)(x<y?x:y)
#define chmax(x,y) x=mmax(x,y)
#define chmin(x,y) x=mmin(x,y)
#define all(x) (x).begin(),(x).end()
#define siz(x) (ll)(x).size()
#define PI acos(-1.0)
#define me memset
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
typedef pair<int,int>Pin;
typedef pair<ll,ll>Pll;
template<class T> using V=vector<T>;
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
long long GCD(long long a, long long b) {return b?GCD(b,a%b):a;}
long long LCM(long long a, long long b) {return a/GCD(a,b)*b;}
int dx[5]={-1,0,1,0,0};
int dy[5]={0,-1,0,1,0};
int ddx[8]={-1,0,1,0,1,1,-1,-1};
int ddy[8]={0,-1,0,1,1,-1,1,-1};
ll cmp1(pair<ll,ll>a,pair<ll,ll> b){
        if(a.se!=b.se)
        return a.se<b.se;
        else
        return a.fi<b.fi;
}
//----------------------------------------------------------------------
V<ll>G[200020];
vector<ll>c;
bool color[200020];
vector<ll>ans;
V<ll>a;
ll dp[200001];
/*ll getLIS()
{
    ll k=c.size();
    fill(dp, dp + k, INF);
    for (int i=0; i<k; ++i) {
        *lower_bound(dp, dp+k, c[i]) = c[i];
    }
    return lower_bound(dp, dp+k, INF) - dp;
}*/
void dfs(ll now, ll from){
    if(color[now])return;
    color[now]=1;

    ll pos = lower_bound(all(c),a[now])-c.begin();
    int abc=0;
    if(pos==c.size()){
        abc=-1;
        c.pb(a[now]);
    }
    else{
        abc=c[pos];
        c[pos]=a[now];
    }

    ans[now]=c.size();

    for(ll i=0;i<G[now].size();i++){
        if(G[now][i]==from)continue;
        dfs(G[now][i],now);
    }
    if(abc==-1)
        c.pop_back();
    else
        c[pos]=abc;
}
//----------------------------------------------------------------------
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    //-------------------------------  
    //ll begin_time=clock();
    //-------------------------------
    ll n;cin>>n;
    ans.resize(n);
    a.resize(n);
    for(ll i=0;i<n;i++)cin>>a[i];
    for(ll i=0;i<n-1;i++){
        ll u,v;cin>>u>>v;
        u--;v--;
        G[u].pb(v);
        G[v].pb(u);
    }
    dfs(0,0);
    for(ll i=0;i<n;i++){
        cout<<ans[i]<<endl;
    }
    //-------------------------------  
    //ll end_time=clock();cout<<"time="<<end_time-begin_time<<"ms"<<endl;
    //-------------------------------
    return 0;
}
//----------------------------------------------------------------------





































Measured memory_bytes: 31688