#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

class HeavyLightDecomposition {
    void dfs_sz(int v){
        for (auto &&u : G[v]) {
            if(u == par[v]) continue;
            par[u] = v; dep[u] = dep[v] + 1;
            dfs_sz(u);
            sub_size[v] += sub_size[u];
            if(sub_size[u] > sub_size[G[v][0]]) swap(u, G[v][0]);
        }
    }

    void dfs_hld(int v, int c, int &pos){
        id[v] = pos++;
        id_inv[id[v]]= v;
        tree_id[v] = c;
        for (auto &&u : G[v]) {
            if(u == par[v]) continue;
            head[u] = (u == G[v][0] ? head[v] : u);
            dfs_hld(u, c, pos);
        }
    }

public:
    int n;
    vector<vector<int>> G;
    vector<int> par, dep, sub_size, id, id_inv, tree_id, head;
    explicit HeavyLightDecomposition(int n) : n(n), G(n), par(n), dep(n), sub_size(n, 1),
    id(n), id_inv(n), tree_id(n), head(n){}
    explicit HeavyLightDecomposition(vector<vector<int>> &G) :
    G(G), n(G.size()), par(n), dep(n) , sub_size(n, 1), id(n), id_inv(n), tree_id(n), head(n) {}

    void add_edge(int u, int v){
        G[u].emplace_back(v);
        G[v].emplace_back(u);
    }

    void build(vector<int> roots = {0}){
        int c = 0, pos = 0;
        for (auto &&i : roots) {
            dfs_sz(i);
            head[i] = i;
            dfs_hld(i, c++, pos);
        }
    }

    int lca(int u, int v){
        while(true){
            if(id[u] > id[v]) swap(u, v);
            if(head[u] == head[v]) return u;
            v = par[head[v]];
        }
    }

    int distance(int u, int v){
        return dep[u] + dep[v] - 2*dep[lca(u, v)];
    }


    template<typename F>
    void query(int u, int v, const F &f){
        while(true){
            if(id[u] > id[v]) swap(u, v);
            f(max(id[head[v]], id[u]), id[v]+1);
            if(head[u] == head[v]) break;
            v = par[head[v]];
        }
    }

    template<typename F>
    void query_edge(int u, int v, const F &f){
        while(true){
            if(id[u] > id[v]) swap(u, v);
            f(max(id[head[v]], id[u]), id[v]+1);
            if(head[u] == head[v]) {
                if(u == v) break;
                f(id[u], id[v]+1);
            }else {
                v = par[head[v]];
            }
        }
    }

    template<typename T, typename Q, typename F>
    T query(int u, int v, const T &e, const Q &q, const F &f){
        T l = e, r = e;
        while(true){
            if(id[u] > id[v]) swap(u, v), swap(l, r);
            l = f(l, q(max(id[head[v]], id[u]), id[v]+1));
            if(head[u] != head[v]) v = par[head[v]];
            else break;
        }
        return f(l, r);
    }

};

template <class M>
struct SegmentTree{
    using T = typename M::T;
    int sz;
    vector<T> seg;
    explicit SegmentTree(int n) {
        sz = 1;
        while(sz < n) sz <<= 1;
        seg.assign(2*sz, M::e());
    }

    void set(int k, const T &x){ seg[k + sz] = x; }

    void build(){
        for (int i = sz-1; i > 0; --i) seg[i] = M::f(seg[2*i], seg[2*i+1]);
    }

    void update(int k, const T &x){
        k += sz;
        seg[k] = x;
        while (k >>= 1) seg[k] = M::f(seg[2*k], seg[2*k+1]);
    }

    T query(int a, int b){
        T l = M::e(), r = M::e();
        for(a += sz, b += sz; a < b; a >>=1, b>>=1){
            if(a & 1) l = M::f(l, seg[a++]);
            if(b & 1) r = M::f(seg[--b], r);
        }
        return M::f(l, r);
    }

    template<typename C>
    int find(int t, C &c, T &val, int k, int l, int r){
        if(r-l == 1){
            val = f(val, seg[k]);
            return c(val) ? k-sz : -1;
        }
        int m = (l+r) >> 1;
        if(m <= t) return find(t, c, val, (k << 1) | 1, m, r);
        if(t <= l && !c(val = f(val, seg[k]))) return -1;
        int lv = find(t, c, val, (k << 1) | 0 , l, m);
        if(~lv) return lv;
        return find(t, c, val, (k << 1) | 1, m, r);
    }

    template<typename C>
    int find(int t, C &c){
        T val = M::e();
        return find(t, c, val, 1, 0, sz);
    }
    T operator[](const int &k) const { return seg[k + sz]; }
};


struct Monoid{
    using T = int;
    static T f(T a, T b) { return max(a, b); }
    static T e() { return -INF<int>; }
};


int main() {
    int n;
    cin >> n;
    vector<int> v(n);
    vector<int> z;
    for (int i = 0; i < n; ++i) {
        int x;
        scanf("%d", &x);
        v[i] = x;
        z.emplace_back(x);
    }
    sort(z.begin(), z.end());
    z.erase(unique(z.begin(), z.end()), z.end());
    HeavyLightDecomposition G(n);
    for (int i = 0; i < n-1; ++i) {
        int a, b;
        scanf("%d %d", &a, &b);
        a--; b--;
        G.add_edge(a, b);
    }
    G.build();
    vector<vector<int>> ver(z.size());
    for (int i = 0; i < n; ++i) {
        ver[lower_bound(z.begin(),z.end(), v[i]) - z.begin()].emplace_back(i);
    }
    SegmentTree<Monoid> seg(n);
    stack<pair<int, int>> S;
    for (int a = 0; a < z.size(); ++a) {
        for (auto &&i : ver[a]) {
            int res = 0;
            auto f = [&](int x, int y){ res = max(res, seg.query(x, y)); };
            G.query(0, i, f);
            S.emplace(G.id[i], res+1);
        }
        while(!S.empty()){
            auto [a, b] = S.top(); S.pop();
            seg.update(a, b);
        }
    }
    for (int i = 0; i < n; ++i) {
        int ans = 0;
        auto f = [&](int x, int y){ ans = max(ans, seg.query(x, y)); };
        G.query(0, i, f);
        printf("%d\n", ans);
    }
    return 0;
}

Measured memory_bytes: 43872