// skip until line 65
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <deque>
#include <fstream>
#include <functional>
#include <iostream>
#include <istream>
#include <iterator>
#include <sstream>
#include <list>
#include <map>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <iomanip>
using namespace std;

#define BR "\n"
#define REP(i, n) for(int (i)=0;(i)<(n);++(i))
#define ALL(cont) begin(cont),end(cont)
#define AS_MOD(a, b) ((((a) % (b) ) + (b)) % (b))
#define FEACH(it, cont) for(auto (it) = begin(cont); it!=end(cont);++it)
#define FEACHR(it, cont) for(auto (it) = rbegin(cont); it!=rend(cont);++it)
#define pb push_back
#define pob pop_back
#define fi first
#define se second
#define getll() ([](){ll s;scanf("%lld", &s);return s;})()
#define getld() ([](){ld s;scanf("%Lf", &s);return s;})()
#define prl(P) printf("%lld", P)
#define prd(P) printf("%.10Lf", P)
#define pr(P) printf(P)
#define MAX(V, T) V=max(V,T)
#define MIN(V, T) V=min(V,T)

#define DumpArray(cont, from, to) for(int __i=from;__i<to;++__i) {cout<<"(" <<__i<<": " << cont[__i]<<")";} cout<<endl;

/*
 * ***_bound(6)
 * 5 6 6 6 6 6 7 7 7
 *   ^lower    ^upper
 * void reverse(c.begin(), c.end())
 *
 * graph
 * seg tree
 * dp
 * brute force
 */
struct Comparator{
    int operator()(int l, int r) const {
        return r<l;
    }
};
struct Vec{
    double v[2];
    string to_s(){
        return "("+to_string(v[0])+","+to_string(v[1])+")";
    }
    double& operator[](int t){
        return v[t];
    }
    Vec operator+(Vec t) {
        return {v[0]+t[0],v[1]+t[1]};
    }
    Vec& operator+=(Vec t) {
        v[0]+=t[0];v[1]+=t[1];
        return *this;
    }
    Vec operator-(Vec t) {
        return {v[0]-t[0],v[1]-t[1]};
    }
    Vec& operator-=(Vec t) {
        v[0]-=t[0];v[1]-=t[1];
        return *this;
    }
    Vec operator*(double t) {
        return {v[0]*t,v[1]*t};
    }
    Vec& operator*=(double t) {
        v[0]*=t;v[1]*=t;
        return *this;
    }
    double operator*(Vec t) {
        return v[0]*t[0]+v[1]*t[1];
    }
    Vec operator-(){
        return {-v[0],-v[1]};
    }
    static Vec Z;
};
Vec Vec::Z={0,0};
//set<int, Comparator> S;

// solution below
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> P;

vector<bool> Visited;
vector<int> Ans;

int N;
vector<int> A;
vector<vector<int>> G;
stack<P> hist;
int INF=3*100000;
vector<int> DP(3*100000,INF);
void dfs(int c) {
    Visited[c]=true;
    auto it=lower_bound(ALL(DP),A[c]);
    auto dist=distance(DP.begin(),it);
    int nv=min(DP[dist],A[c]);
    hist.push({dist,DP[dist]});
    DP[dist]=nv;
    Ans[c]=distance(DP.begin(),lower_bound(ALL(DP),INF-1));
    for(int v:G[c]) {
        if (!Visited[v]) {
            dfs(v);
        }
    }
    auto p=hist.top();
    DP[p.fi]=p.se;
    hist.pop();
}
int main() {
    cin >> N;
    A.resize(N,0);
    Ans.resize(N);
    Visited.resize(N,false);
    G.resize(N);
    REP(i,N)
        cin>>A[i];
    // tood: normalize
    {
        map<int,int> Dict;
        vector<int> B=A;
        sort(ALL(B));
        Dict.insert({B[0],0});
        int c=0;
        for(int i=1;i<N;++i) {
            if (B[i]!=B[i-1])c++;
            Dict.insert({B[i],c});
        }
        REP(i,N)
            A[i]=Dict[A[i]];
    }
    REP(i,N-1) {
        int u,v;
        cin >>u >>v;--u;--v;
        G[u].pb(v);
        G[v].pb(u);
    }
    dfs(0);
    REP(i,N){
        cout<<Ans[i]<<endl;
    }
}


Measured memory_bytes: 34280