#pragma region Macros
#include <bits/stdc++.h>
#define SORT(x) sort((x).begin(), (x).end())
#define RSORT(x) sort((x).rbegin(), (x).rend())
#define ALL(x) (x).begin(), (x).end()
#define REV(x) reverse(ALL(x))
#define rep(i, n) for (ll i = 0; i < n; i++)
#define reps(i, m, n) for (ll i = m; i < n; i++)
#define repr(i, m, n) for (ll i = m; i >= n; i--)
#define SP << " " <<
#define INF2 1000000000000000037
#define INF  1000000007
#define lwb(x,n) distance(x.begin(),lower_bound(ALL(x),(n)))
#define upb(x,n) distance(x.begin(),upper_bound(ALL(x),(n)))
#define fora(i, ...) if(ll i = -1) for(__VA_ARGS__) if(i++, true)
#ifdef _MY_DEBUG
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0,a1,a2,a3,x,...) x
#define debug_1(x1) cout<<#x1<<": "<<x1<<endl
#define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl
#define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl
#define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl
#define de(...) CHOOSE((__VA_ARGS__,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__)
#else
#define de(...)
#endif
using namespace std;
using ll = long long;
using ld = long double;
template<class T = ll> using v = vector<T>;
template<class T = ll> using vv = vector<vector<T>>;
template<class T = ll> using vvv = vector<vector<vector<T>>>;
template<class T> bool maxi(T &a, const T &b){ if(a<b){a=b;return 1;}return 0;}
template<class T> bool mini(T &a, const T &b){ if(b<a){a=b;return 1;}return 0;}
template<class T> ll sumer(const T& a){ return accumulate(ALL(a),0LL); }
template<class T> void UNIQUE(vector<T> &a){ SORT(a);a.erase(unique(ALL(a)),a.end());}
template<class T, class U> ostream &operator<<(ostream &os, const pair<T,U> &pe) { os << pe.first << " " << pe.second; return os;}
template<class T> ostream &operator<<(ostream &os, const v<T> &ve) { rep(i,ve.size()) os<< (i?" ":"")<<ve[i]; return os;}
ll topbit(ll a) { return a==0?-1:63-__builtin_clzll(a);}
ll botbit(ll a) { return a==0?64:__builtin_ctzll(a);}
ll popcount(ll a) { return __builtin_popcountll(a);}
#define dame {cout<< retword <<"\n"; return;}
#pragma endregion
//--MODIFS---------------------------------
#pragma region Modifs
#define retword "-1"
#define MOD  1000000007
using P  = pair<ll,ll>;
using TP  = tuple<ll,ll,ll>;
#pragma endregion
//--GLOBAL---------------------------------
map<ll,ll> zip;
ll unzip[202020];
ll compress(vector<ll> &vec, bool repl=true) {
    auto ve=vec;
    UNIQUE(ve);
    rep(i,ve.size()){
        zip[ve[i]] = i;
        unzip[i] = ve[i];
    }
    if(repl) rep(i,vec.size()) vec[i]=zip[vec[i]];
    return ve.size();
}
v<> A, dp, ans;
struct edge{ll to;};
struct graph{
    ll N;
    vector<vector<edge> > G;

    graph(ll n): N(n), G(N) {}

    void ade(ll s, ll t){
        G[s].emplace_back((edge){t});
        G[t].emplace_back((edge){s}); //無向ならON
    }

    void dfs(ll v=0, ll p=-1){
        ll pos=lwb(dp,A[v]);
        ll mae=dp[pos];
        mini(dp[pos],A[v]);
        ans[v]=lwb(dp,INF-1);
        for(auto E : G[v]){
            if(E.to == p) continue;
            dfs(E.to, v);
        }
        dp[pos]=mae;
    }
};
//--MAIN-----------------------------------
void Main() {
    ll N;
    cin>>N;
    dp.resize(N+1,INF);
    ans.resize(N,0);
    A.resize(N);
    rep(i,N) cin>>A[i];
    compress(A,1);
    graph g(N);
    rep(i,N-1){
        ll a,b; cin>>a>>b; --a,--b;
        g.ade(a,b);
    }
    g.dfs();
    rep(i,N) cout<< ans[i] <<"\n";
}
//--START----------------------------------
int main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    // ll Qkai; cin>>Qkai; rep(QQ,Qkai) Main();
    Main();
}
//-----------------------------------------

Measured memory_bytes: 42388