#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
 #define int long long

#define all(X) (X).begin(), (X).end()
#define reset(X) memset(X, 0, sizeof(X))
#define mp(a, b) make_pair(a, b)
#define pb push_back
#define endl '\n'
#define fi first
#define se second

 
 
using namespace __gnu_pbds;
using namespace std;
 const int mod=1e9+7;
 // const int mod=998244353;
 // const int mod=1e9+9;
const int INF=4e18+10;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
 
#define read(n) int n; cin>>n;
#define readv(x, n) vector<int> x(n); for(auto &i:x) cin>>i; 
int multiply(int a, int b, int in_mod){return (a*b)%in_mod;} 
int mult_identity(int a){return 1;}


auto power(auto a, int b, int in_mod)
{
    auto prod=mult_identity(a);
    auto mult=a%in_mod;
    while(b!=0)
    {
        if(b%2)
        {
            prod=multiply(prod,mult, in_mod);

        }
        mult=multiply(mult, mult,in_mod);
        b/=2;
    }
    return prod;
}
int mod_inv(int q, int in_mod)
{

    return power(q, in_mod-2,in_mod);
}

const int MAXN=2e5+100;
vector<int> adj[MAXN];
vector<int> a(MAXN);
vector<int> d(MAXN, INF);
vector<int> ans(MAXN);
multiset<int> best;
void dfs(int root, int parent)
{

    //add the node to the queue
    int ind = upper_bound(all(d), a[root])-d.begin();
    int old_val = d[ind];
    int flag=false;
    if(d[ind-1]<a[root] && a[root]< d[ind])
    {
        d[ind]=a[root];
        flag=true;
        best.insert(ind);
    }
    for(auto i:adj[root])
    {
        if(i!=parent)
        {
            dfs(i, root);
        }
    }
    //restore the value

    int index = lower_bound(all(d), INF) - d.begin();
    index -=1;
 
    ans[root]=*((best.rbegin()))-1;

    if(flag)
    best.erase(best.find(ind));


    d[ind]=old_val;
    //happy now hopefully the right answer

}

void solve()
{
    int n;
    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].pb(v);
        adj[v].pb(u);
    }
    d[0]=-INF;
    adj[0].pb(1);
    best.insert(0);
    dfs(0, 0);
    for(int i=1;i<=n;i++)
        cout<<ans[i]<<" ";

}

 
 
signed main()
 
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);  
    cout.tie(NULL);
    #ifndef ONLINE_JUDGE
        if(fopen("INPUT.txt","r"))
        {
            freopen ("INPUT.txt" , "r" , stdin);
            freopen ("OUTPUT.txt" , "w" , stdout);
        }
    #endif
    auto clk=clock(); 
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    // -------------------------------------Code starts here---------------------------------------------------------------------     
 
    int t=1;
    // cin>>t;
    for(int test=1;test<=t;test++)
    {
        // cout<<"Case #"<<test<<": ";
        solve();
        // cout<<endl;
 
    }
 
    // -------------------------------------Code ends here------------------------------------------------------------------
 
 
    clk = clock() - clk;
    cerr << fixed << setprecision(6) << "Time: " << ((double)clk)/CLOCKS_PER_SEC << "\n";
    return 0;
 }


Measured memory_bytes: 37712