#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)
#define fore(i,a) for(auto& i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
#define pcnt __builtin_popcountll

using namespace std;
using namespace atcoder;

using ll = long long;
using ld = long double;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}}
#define retval(x) {cout << #x << endl; return;}
#define cout2(x,y) cout << x << " " << y << endl;
#define coutp(p) cout << p.fi << " " << p.se << endl;
#define out cout << ans << endl;
#define outd cout << fixed << setprecision(20) << ans << endl;
#define outm cout << ans.val() << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define outdv fore(yans , ans) cout << yans.val() << "\n";
#define assertmle(x) if (!(x)) {vi v(3e8);}
#define asserttle(x) if (!(x)) {while(1){}}
#define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define coutv2(v) fore(vy , v) cout << vy << "\n";
#define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define coutvm2(v) fore(vy , v) cout << vy.val() << "\n";
using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;
using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;
using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;
using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = dynamic_modint<0>;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
#define yes {cout <<"Yes"<<endl;}
#define no {cout <<"No"<<endl;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#ifdef MY_LOCAL_DEBUG
#include "./debug/localDebug.cpp"
#define showp(p) cerr<<#p<<" = "<<p.fi<<" : "<<p.se<<endl
#define show1(a) cerr<<#a<<" = "<<a<<endl
#define show2(a,b) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<endl
#define show3(a,b,c) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<endl
#define show4(a,b,c,d) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<endl
#define show5(a,b,c,d,e) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<" : "<<#e<<" = "<<e<<endl
#define DEBUG_LINE cout << "DEBUG_LINE : " << __LINE__ << endl
#define showv(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) {cout<<#v<<endl; fore(vy , v) cout << vy << "\n";}
#define showvm(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define showvm2(v) {cout<<#v<<endl; fore(vy , v) cout << vy.val() << "\n";}
#define showmat(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg << " "; cout << endl;}}
#define showmatm(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg.val() << " "; cout << endl;}}
#else
#define showp(p)
#define show1(a)
#define show2(a,b)
#define show3(a,b,c)
#define show4(a,b,c,d)
#define show5(a,b,c,d,e)
#define DEBUG_LINE
#define showv(v)
#define showv2(v)
#define showvm(v)
#define showvm2(v)
#define showmat(v)
#define showmatm(v)
#endif
#define overload5(a,b,c,d,e,f, ...) f
#define show(...) overload5(__VA_ARGS__, show5, show4, show3, show2, show1)(__VA_ARGS__)

template<typename T>
struct LCA {
    int n, root, l;
    vector<vector<int>> to;
    vector<vector<T>> co;
    vector<int> dep;
    vector<T> costs;
    vector<vector<int>> par;
    LCA(int n):n(n),to(n),co(n),dep(n),costs(n) {
        l = 0;
        while ((1<<l) < n) ++l;
        par = vector<vector<int>>(n+1,vector<int>(l,n));
    }
    void add_edge(int a, int b, T c=1) {
        to[a].push_back(b); co[a].push_back(c);
        to[b].push_back(a); co[b].push_back(c);
    }

    // par[x][0],dep,costsを計算
    void _dfs(int v, int d=0, T c=0, int p=-1) {
        if (p != -1) par[v][0] = p;
        dep[v] = d;
        costs[v] = c;
        for (int i = 0; i < sz(to[v]); ++i) {
            int u = to[v][i];
            if (u == p) continue;
            _dfs(u, d+1, c+co[v][i], v);
        }
    }

    void init(int _root=0) {
        root = _root;
        _dfs(root);
        for (int i = 0; i < l-1; ++i) {
            for (int v = 0; v < n; ++v) {
                par[v][i+1] = par[par[v][i]][i];
            }
        }
    }
    int lca(int a,int b){
        if (dep[a] > dep[b]) swap(a,b);
        int gap = dep[b]-dep[a];
        for (int i = l-1; i >= 0; --i) {
            int len = 1<<i;
            if (gap >= len) {
                gap -= len;
                b = par[b][i];
            }
        }
        if (a == b) return a;
        for (int i = l-1; i >= 0; --i) {
            int na = par[a][i];
            int nb = par[b][i];
            if (na != nb) a = na, b = nb;
        }
        return par[a][0];
    }

    int getPar(int x,int k){
        int now = x;
        rrep(i,30){
            if ((k >> i & 1) == 1){
                now = par[now][i];
            }
        }
        return now;
    }
    int length(int a, int b) {
        int c = lca(a,b);
        return dep[a]+dep[b]-dep[c]*2;
    }
    T dist(int a, int b) {
        int c = lca(a,b);
        return costs[a]+costs[b]-costs[c]*2;
    }
};

// 初期化方法 LCA<T> g(n) : nは頂点数、Tはコストのタイプ、注) 宣言 → add_edge → init の順で呼び出す 
// add_edge(a,b,c) : a,b間にコストcの辺をはる。cは省略可(1となる)。
// init() : ダブリングにより各頂点の2^i個上の親を計算。結果はpar[v][i]に入る。
// lca(a,b) : 頂点a,bのlcaを出力。
// getPar(x,k) : 頂点xの2^k上の祖先を出力。
// length(a,b) : 頂点a,b間の辺の数を出力。
// dist(a,b) : 頂点a,b間のコストを出力。

void solve(){
    int n; cin>>n;
    vpii v(n);
    rep(i,n){
        cin>>v[i].fi;
        v[i].se = i;
    }
    sort(rrng(v));
    LCA<int> l(n);
    rep(i,n-1){
        int a,b; cin>>a>>b;
        a--; b--;
        l.add_edge(a,b,1);
    }
    l.init();
    vi ans(n);
    int r = 0;
    int x = -1,y = -1;

    auto f = [&](int np)->void{
        if (x==-1){
            x = y = np;
            return;
        }
        int d1 = l.dist(x,y);
        int d2 = l.dist(x,np);
        int d3 = l.dist(np,y);
        if (d1>=d2 && d1>=d3) return;
        if (d2 > d3){
            y = np;
        }else{
            x = np;
        }
    };
    auto getMx = [&](int tar)->int{
        return max(l.dist(x,tar), l.dist(y,tar));
    };

    rep(i,n){
        while(r<n && v[r].fi==v[i].fi){
            r++;
        }
        vi t;
        repx(j,i,r) t.pb(v[j].se);
        fore(y , t) f(y);
        fore(y , t){
            ans[y] = getMx(y);
        }
        i = r-1;
    }
    fore(y , ans) cout << y << " ";
    cout << endl;

    return;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int t = 1;
    //cin>>t;

    rep(i,t){
        solve();
    }

    return 0;
}