#pragma GCC optimize("Ofast,unroll-loops")

#include <algorithm>
// #include <bitset>
// #include <complex>
// #include <deque>
// #include <exception>
// #include <fstream>
// #include <functional>
// #include <iomanip>
// #include <ios>
// #include <iosfwd>
#include <iostream>
// #include <istream>
// #include <iterator>
// #include <limits>
// #include <locale>
// #include <map>
// #include <new>
// #include <numeric>
// #include <ostream>
// #include <queue>
#include <set>
// #include <unordered_set>
// #include <sstream>
// #include <stack>
// #include <stdexcept>
// #include <streambuf>
// #include <string>
// #include <utility>
// #include <valarray>
#include <vector>
#include <cstring>
// #include <unordered_map>
// #include <cmath>
// #include <array>
// #include <cassert>
// #include <random>
// #include <chrono>

using namespace std;

#define          BIT(i,j)  (((i)>>(j))&1LL)
#define           MASK(i)  (1LL<<(i))
#define            ALL(x)  (x).begin(),(x).end()
#define             SZ(x)  (int)(x).size()
#define                fi  first
#define                se  second
#define               ull  ungsigned long long
#define                ll  long long
#define                ld  long double
#define                vi  vector<int>
#define               vvi  vector<vi>
#define              vvvi  vector<vvi>
#define               pii  pair<int,int>
#define              vpii  vector<pii>
#define             vvpii  vector<vpii>
#define REPDIS(i,be,en,j)  for(int i = (be); i<=(en); i+=j)
#define     REPD(i,be,en)  for(int i = (be); i>=(en); i--)
#define      REP(i,be,en)  for(int i = (be); i<=(en); i++)
#define              endl  "\n"
#define                MP  make_pair
// #define               int  ll

//-----------------------------------------------------------------------------------------------//
inline void scan(){} template<typename F, typename... R> inline void scan(F &f,R&... r){cin>>f;scan(r...);}
inline void print(){} template<typename F, typename... R> inline void print(F f,R... r){cout<<f;print(r...);}
//-----------------------------------------------------------------------------------------------//

void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
//------------------------------------------------------------------------------------------------//
const  ll   LINF = 1e18;
const int    INF = 1e9;
const int    LOG = 20;
const int   MAXN = 2e5+7;
const int      N = 1e2+3;
const int    MOD = 1e9+7;
const int   BASE = 1e5;
const  ld    EPS = 1e-9;
// const  ld     PI = acos(-1);
const int OFFSET = 1e3;
//------------------------------------------------------------------------------------------------//
template<typename T1, typename T2> bool mini(T1 &a, T2 b){if(a>b){a=b;return true;}return false;}
template<typename T1, typename T2> bool maxi(T1 &a, T2 b){if(a<b){a=b;return true;}return false;}
template<typename T> T gcd(T a, T b) { while(b) { a %= b; swap(a,b); } return a; }
template<typename T> T lcm(T a, T b) { return a/gcd(a,b)*b; }
//------------------------------------------------------------------------------------------------//

/*
----------------------------------------------------------------
    END OF TEMPLATE
----------------------------------------------------------------
*/

int BUF=100000;
int buf_readed;
int buf_index;
char buffer[100000];
 
void my_init(){
    buf_index=buf_readed=0;
}
/*****************************************/
char my_getchar(){
    char x;
    if(buf_index==buf_readed){
        buf_index=0;
        buf_readed=fread(buffer,1,BUF,stdin);
    }   
    x=buffer[buf_index];
    buf_index++;
    return x;
}
/*************************************/
int readInt(){
    int r=0;
    char c;
    while(1){
        c=my_getchar();
        if((c>='0' && c<='9')){
            r=(c-'0');
            break;
        }
    }
    while(1){
        c=my_getchar();
            if(!(c>='0' && c<='9'))
                break;
        r=r*10+(c-'0');
    }
    return r;
}
/***************************************/

vi adj[MAXN],c;
int a[MAXN],res[MAXN],del[MAXN],child[MAXN],n;
multiset<int> tam[MAXN];
int t[MAXN<<1];
vpii b;

void build() {  // build the tree
  for (int i = n - 1; i > 0; --i) t[i] = max(t[i<<1],t[i<<1|1]);
}

int query(int l, int r) {
    int res = -INF;
    for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
        if (l&1) maxi(res,t[l++]);
        if (r&1) maxi(res,t[--r]);
    }
    return res;
}

void modify(int p, int value) {  // set value at position p
    for (t[p += n] = value; p > 1; p >>= 1) t[p>>1] = max(t[p],t[p^1]);
}

void seg_update(int pos, int val){
    tam[pos].insert(val);
    modify(pos,*tam[pos].rbegin());
}

void seg_rem(int pos, int val){
    tam[pos].erase(tam[pos].find(val));
    if(SZ(tam[pos])>0) modify(pos,*tam[pos].rbegin());
    else modify(pos,-INF);
}

int dfs1(int u, int par){
    child[u] = 1;
    for(int &v:adj[u]){
        if(del[v] || v==par) continue;
        child[u] += dfs1(v,u);
    }
    return child[u];
}

int dfs2(int u, int par, int siz){
    for(int &v:adj[u]){
        if(v==par || del[v]) continue;
        if(child[v]*2>siz) return dfs2(v,u,siz);
    }
    return u;
}

void update(int u, int par, int dis){
    c.emplace_back(u);
    seg_update(a[u],dis);
    for(int &v:adj[u]){
        if(del[v] || v==par) continue;
        update(v,u,dis+1);
    }
}

void solve(int u, int par, int dis){
    b.emplace_back(u,dis);
    seg_rem(a[u],dis);
    for(int &v:adj[u]){
        if(del[v] || v==par) continue;
        solve(v,u,dis+1);
    }
}

void calc(int u){
    int siz = dfs1(u,-1);
    u = dfs2(u,-1,siz);
    del[u] = 1;
    update(u,-1,0);
    maxi(res[u],query(a[u],n));
    for(int &v:adj[u]){
        if(del[v]) continue;
        while(SZ(b)) b.pop_back();
        solve(v,u,1);
        for(auto &&[x,dis]:b) maxi(res[x],dis+query(a[x],n));
        for(auto &&[x,dis]:b) seg_update(a[x],dis);
    }
    for(int &x:c){
        if(SZ(tam[a[x]])>0){
            tam[a[x]].clear();
            seg_update(a[x],-INF);
        }
    }
    while(SZ(c)) c.pop_back();
    for(int &v:adj[u]){
        if(del[v]) continue;
        calc(v);
    }
}

void solve(){
    n = readInt();
    vi compress;
    for(int i = 0; i<n; ++i){
        a[i] = readInt();
        compress.emplace_back(a[i]);
    }
    sort(ALL(compress));
    compress.resize(unique(ALL(compress))-compress.begin());
    for(int i = 0; i<n; ++i){
        a[i] = lower_bound(ALL(compress),a[i])-compress.begin();
        // cerr << a[i] << " ";
    }
    for(int i = 1; i<n; ++i){
        int u = readInt(),v = readInt();
        --u; --v;
        adj[u].emplace_back(v);
        adj[v].emplace_back(u);
    }
    for(int i = 0; i<=2*n; i++) t[i] = -INF;
    calc(0);
    for(int i = 0; i<n; ++i) cout << res[i] << ' ';
}

signed main(){
    ios::sync_with_stdio(false);
    cout.tie(0);
    #define task "test"
    if(fopen(task".inp","r")){
        freopen(task".inp","r",stdin);
        freopen(task".out","w",stdout);
    }
    #define task1 "nothing"
    if(fopen(task1".inp","r")){
        freopen(task1".inp","r",stdin);
        freopen(task1".out","w",stdout);
    }

    int test = 1;

    while(test--){
        solve();
    }
    cerr << "\nTime elapsed: " << 1000*clock()/CLOCKS_PER_SEC << "ms\n";
    return 0;
}

/**  /\_/\
 *  (= ._.)
 *  / >TL \>AC
**/