#include "bits/stdc++.h"
#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
#include <ext/rope>

using namespace __gnu_pbds; 
using namespace __gnu_cxx;
using namespace std;
using ll = long long;

#define eb emplace_back
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define len(v) ((int)v.size())
#define all(v) v.begin(), v.end()
#define precision(n) fixed<<setprecision(n)

#ifdef LOCAL
    #include "debug.h"
#else
    #define debug(...) 42
#endif

void io(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);    
    #ifdef LOCAL
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
    #endif
}

template<typename T> using oset = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update >;
template<typename T> using MinPriorityQueue = priority_queue <T, vector <T>, greater <T> >;
template<typename T> void done(T ans) {cout << ans << "\n"; exit(0);}


template <typename A>
istream& operator>>(istream& input,vector<A>& x) {
  for(auto& i:x)
    input>>i;
  return input;
}
 
template<typename A>
ostream& operator<<(ostream& output,vector<A>& x) {
  for(auto& i:x)
    output<<i<<' ';
  return output;
}

 

const int mod = 1e9;
const int N = 3e5 + 5;

auto seed = chrono::high_resolution_clock::now().time_since_epoch().count();
mt19937_64 mt(seed);

template <typename T>
long long myrand(T m) {
    long long mod = m;
    long long x = mt()%mod;

    return x;
}

int a[N];
vector <int> ans(N);
vector <int> adj[N];
multiset <int> s;

void dfs(int node, int parent = 0) {
    s.insert(a[node]);
    int del = -1;
    // auto it = s.upper_bound(a[node]);
    auto it = s.lower_bound(a[node]);
    
    if( ++it != s.end()) {
        del=*it;
        s.erase(it);
    }
    ans[node] = s.size();
    
    for(auto child : adj[node])
        if(child != parent) 
            dfs(child,node);
    
    if(del != -1) 
        s.insert(del);

    s.erase(s.find(a[node]));
}
vector<int> lis;
void dfs2(int node, int parent = 0) {
    auto it = lower_bound(lis.begin(), lis.end(), a[node]);
    int del = -1;
    if(it == lis.end()) {
        del = 1;
        lis.push_back(a[node]);
    }
    else {
        del = *it;
        *it = a[node];
    }

    ans[node - 1] = lis.size();
    
    for(auto child : adj[node])
        if(child != parent) 
            dfs2(child,node);

    if(del == 1)
        lis.pop_back();
    else
        *it = del;
}
void dfs3(int node, int parent = -1) {
    int k = lower_bound(lis.begin(), lis.end(), a[node]) - lis.begin();
    int x = lis[k];
    lis[k] = a[node];
    ans[node - 1] = lower_bound(lis.begin(), lis.end(), INT_MAX) - lis.begin();
    for(int v : adj[node]){
        if(v != parent){ dfs3(v, node); }
    }
    lis[k] = x;
}

int main()
{
    io();
    int n, m, q;
    cin >> n;
    for(int i = 1; i <= n; i++) 
        cin >> a[i];
    for(int i = 0 ; i < n - 1; i++) {
        int u, v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    lis.assign(n + 4, INT_MAX);
    dfs3(1);
    ans.resize(n);
    cout << ans << " ";
    // while(q--) {
    //     int x;
    //     cin >> x;
    //     cout << ans[x] << "\n";
    // }
}



Measured memory_bytes: 30584