#include <iostream>
#include <iomanip>
#include <algorithm>
#include <bitset>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <cmath>
#include <time.h>
#include <random>
#include <string>
#include <cassert>
#include <vector>
#include <ostream>
#include <istream>
#include <stack>
#include <deque>
#include <queue>
#include <functional>
#include <chrono>

using namespace std;

#define int long long
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define pii pair<int, int>
#define ld long double

ostream& operator << (ostream &a, const vector<int> &b) {
    for (auto k : b) cout << k << " ";
    return a;
}

#ifdef LOCAL
    #define dbg(x) cout << #x << " : " << (x) << "\n";
    const int INF = 1e18;
    // const int mod = 2600000069;
    // const int p = 10;
    // const ld PI = 3.1415926535;
#else
    #define dbg(x)
    const int INF = 1e18;
    // const int mod = 2600000069;
    // const int p = 179;
    // const ld PI = 3.1415926535;
#endif

// #pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,sse3,sse4")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("fast-math")
// #pragma GCC target("avx2")
//#pragma GCC optimize("section-anchors")
//#pragma GCC optimize("profile-values,profile-reorder-functions,tracer")
//#pragma GCC optimize("vpt")
//#pragma GCC optimize("rename-registers")
//#pragma GCC optimize("move-loop-invariants")
//#pragma GCC optimize("unswitch-loops")
//#pragma GCC optimize("function-sections")
//#pragma GCC optimize("data-sections")`  

const int MAXN = 2e5 + 10;

vector<int> g[MAXN];
int a[MAXN];
vector<int> b[MAXN];
int t[4 * MAXN];
vector<int> seq;
map<int, int> ind;
int ans[MAXN];

void update(int v, int l, int r, int pos, int val) {
    if (l + 1 == r) {
        b[pos].pb(val);
        t[v] = val;
        return;
    }
    int m = (l + r) / 2;
    if (pos < m) update(2 * v + 1, l, m, pos, val);
    else update(2 * v + 2, m, r, pos, val);
    t[v] = max(t[2 * v + 1], t[2 * v + 2]);
}

void del(int v, int l, int r, int pos) {
    if (l + 1 == r) {
        b[pos].pop_back();
        t[v] = b[pos].back();
        return;
    }
    int m = (l + r) / 2;
    if (pos < m) del(2 * v + 1, l, m, pos);
    else del(2 * v + 2, m, r, pos);
    t[v] = max(t[2 * v + 1], t[2 * v + 2]);
}

int get(int v, int l, int r, int askl, int askr) {
    if (l >= askr || r <= askl) return 0;
    if (l >= askl && r <= askr) return t[v];
    int m = (l + r) / 2;
    return max(get(2 * v + 1, l, m, askl, askr), get(2 * v + 2, m, r, askl, askr));
}

int n;

void dfs(int v, int p) {
    seq.pb(a[v]);
    update(0, 0, n, ind[a[v]], get(0, 0, n, 0, ind[a[v]]) + 1);
    ans[v] = t[0];
    for (auto u : g[v]) {
        if (u != p) {
            dfs(u, v);
        }
    }
    seq.pop_back();
    del(0, 0, n, ind[a[v]]);
}

signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cin >> n;
    vector<int> aa(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        aa[i] = a[i];
    }
    sort(all(aa));
    aa.resize(unique(all(aa)) - aa.begin());
    int sz = aa.size();
    for (int i = 0; i < sz; i++) {
        ind[aa[i]] = i;
    }
    int u, v;
    for (int i = 0; i < n - 1; i++) {
        cin >> u >> v;
        u--, v--;
        g[u].pb(v);
        g[v].pb(u);
    }
    for (int i = 0; i < MAXN; i++) {
        b[i].pb(0);
    }
    dfs(0, 0);
    for (int i = 0; i < n; i++) {
        cout << ans[i] << "\n";
    }
}
/*

*/  


Measured memory_bytes: 62880