#include<bits/stdc++.h>
using namespace std;

template<typename T>
bool chmax(T &a, const T &b){
    if (a >= b) return false;
    a = b;
    return true;
}

void input(int &x){
    char c;
    x = 0;
    while ((c = getchar_unlocked() ^ 48) < 10){
        x *= 10;
        x += c;
    }
}

template<class E>
struct csr {
    csr (int n_ = 0, int m_ = -1) : n(n_), m(m_) {
        if (m >= 0){
            es.reserve(m);
            start.reserve(m);
        }
        if (m == 0){
            build();
        }
    }
    int add(int idx, E elem){
        int eid = start.size();
        es.emplace_back(elem);
        start.emplace_back(idx);
        if (eid+1 == m) build();
        return eid;
    }
    void build(){
        if (m == -2) return ;
        m = start.size();
        std::vector<E> nes(m);
        std::vector<int> nstart(n+2,0);
        for (int i = 0; i < m; i++) nstart[start[i]+2]++;
        for (int i = 1; i < n; i++) nstart[i+2] += nstart[i+1];
        for (int i = 0; i < m; i++) nes[nstart[start[i]+1]++] = es[i];
        swap(es,nes);
        swap(start,nstart);
        m = -2;
    }
    const auto operator[](int idx) const {
        assert(m == -2);
        return std::ranges::subrange(es.begin()+start[idx],es.begin()+start[idx+1]);
    }
  private:
    int n, m;
    std::vector<E> es;
    std::vector<int> start;
};

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int n; input(n);
    vector<int> a(n);
    for (auto &x : a) input(x);
    csr<int> g(n,(n-1)*2);
    for (int i = 0; i < n-1; i++){
        int u, v; input(u), input(v); u--, v--;
        g.add(u,v);
        g.add(v,u);
    }
    vector<int> ids(n); iota(ids.begin(),ids.end(),0);
    sort(ids.begin(),ids.end(),[&](int l, int r){
        return a[l] > a[r];
    });
    vector<int> dmax(n,0);
    vector<int> from(n,-1);
    auto dfs_update = [&](auto sfs, int v, int f) -> void {
        for (int u : g[v]){
            if (u == f) continue;
            dmax[u] = dmax[v]+1;
            from[u] = v;
            sfs(sfs,u,v);
        }
    };
    dfs_update(dfs_update,ids[0],-1);
    int dmax_v = max_element(dmax.begin(),dmax.end()) - dmax.begin();
    vector<int> dmax2(n,0);
    auto dfs_2 = [&](auto sfs, int v, int f) -> void {
        for (int u : g[v]){
            if (u == f) continue;
            dmax2[u] = dmax2[v]+1;
            sfs(sfs,u,v);
        }
    };
    dfs_2(dfs_2,dmax_v,-1);
    int diam = *max_element(dmax2.begin(),dmax2.end());
    assert(diam <= 10000);
    auto dfs = [&](auto sfs, int v, int f, int d) -> void {
        int u = from[v];
        if (u == f) return ;
        assert(u != -1);
        if (chmax(dmax[u],d+1)){
            from[u] = v;
            dfs_update(dfs_update,u,v);
        }
        else {
            sfs(sfs,u,v,d+1);
        }
    };
    vector<int> ans(n);
    for (int l = 0, r = 0; l < n; l = r){
        while (r < n && a[ids[r]] == a[ids[l]]){
            if (r != 0){
                dfs(dfs,ids[r],-1,0);
            }
            r++;
        }
        for (int i = l; i < r; i++){
            ans[ids[i]] = dmax[ids[i]];
        }
    }
    for (int i = 0; i < n; i++){
        if (i != 0) cout << ' ';
        cout << ans[i];
    }
    cout << '\n';
}