#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using i64 = long long;
#define var auto

using graph = vector<vector<int>>;
template <class F>
void one_third_centroid_decomposition(graph &g, F f) {
    int n = g.size();
    assert(n >= 1);
    vector<int> size(n), xy(n), count(n), sort(n);
    using buf_node = pair<graph, graph>;
    vector<unique_ptr<buf_node>> buf;
    auto get_buf = [&](int depth) -> buf_node& {
        while (depth >= buf.size())
            buf.push_back(make_unique<buf_node>(graph(n), graph(n)));
        return *buf[depth];
    };
    auto dc = [&](auto &dc, int n, int v, graph &g, int depth) -> void {
        if (n <= 2) return;
        int s = -1;
        auto sz = [&](auto &sz, int v, int p) -> void {
            size[v] = 1;
            int mx = 0;
            for (int e : g[v]) {
                if (e != p) {
                    sz(sz, e, v);
                    size[v] += size[e];
                    mx = max(mx, size[e]);
                }
            }
            mx = max(mx, n - size[v]);
            if (mx * 2 <= n)
                s = v;
        };
        sz(sz, v, -1);
        int maxsz = 0;
        for (int e : g[s]) {
            if (size[e] > size[s])
                size[e] = n - size[s];
            count[size[e]]++;
            maxsz = max(maxsz, size[e] + 1);
        }
        for (int i = 1; i < maxsz; i++)
            count[i] += count[i - 1];
        for (int e : g[s])
            sort[--count[size[e]]] = e;
        fill(count.begin(), count.begin() + maxsz, 0);
        int xs = 0, ys = 0;
        for (int i = g[s].size(); i-- > 0;) {
            if (xs < ys)
                xy[sort[i]] = 0, xs += size[sort[i]];
            else
                xy[sort[i]] = 1, ys += size[sort[i]];
        }
        auto &[x, y] = get_buf(depth);
        x[s].clear();
        y[s].clear();
        auto build = [&](auto &build, int v, int p, auto &t) -> void {
            t[v] = g[v];
            for (int e : g[v]) {
                if (e != p) build(build, e, v, t);
            }
        };
        for (int e : g[s]) {
            auto &t = xy[e] ? y : x;
            t[s].push_back(e);
            build(build, e, s, t);
        }
        f(s, x, y);
        dc(dc, xs + 1, s, x, depth + 1);
        dc(dc, ys + 1, s, y, depth + 1);
    };
    dc(dc, n, 0, g, 0);
}

int main() {
    cin.tie(0)->sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    vector<vector<int>> edges(n);
    for (int i = 0; i < n - 1; i ++) {
        int u, v;
        cin >> u >> v;
        u--, v--;
        edges[u].push_back(v);
        edges[v].push_back(u);
    }
    vector<int> ans(n);
    auto f = [&](int s, auto &x, auto &y) {
        vector<int> table;
        auto dfs1 = [&](auto self, int node, int parent, int depth) -> void {
            while (table.size() <= depth) table.push_back(0);
            table[depth] = min(table[depth], -a[node]);
            for (int child : x[node]) {
                if (child == parent) continue;
                self(self, child, node, depth + 1);
            }
        };
        dfs1(dfs1, s, s, 0);
        int m = table.size();
        for (int i = m - 2; i >= 0; i--) {
            table[i] = min(table[i], table[i + 1]);
        }
        auto dfs2 = [&](auto self, int node, int parent, int depth) -> void {
            int pos = upper_bound(table.begin(), table.end(), -a[node]) - table.begin();
            if (pos >= 1) {
                ans[node] = max(ans[node], depth + pos - 1);
            }
            for (int child : y[node]) {
                if (child == parent) continue;
                self(self, child, node, depth + 1);
            }
        };
        dfs2(dfs2, s, s, 0);
    };
    one_third_centroid_decomposition(edges, [&](int s, auto &x, auto &y) {
        f(s, x, y);
        f(s, y, x);
    });
    for (int i = 0; i < n; i++) {
        cout << ans[i] << " \n"[i+1==n];
    }
}