#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("sse4.2")

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <sstream>
#include <deque>
#include <queue>
#include <complex>
#include <random>
#include <cassert>
#include <chrono>

using namespace std;

#define FAST ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define FIXED cout << fixed << setprecision(12)
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define graph vector<vector<int>>
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define f first
#define s second
#define hashmap unordered_map
#define hashset unordered_set
#define eps 1e-9
#define mod 1000000007
#define inf 3000000000000000007ll
#define sz(a) signed(a.size())
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

#ifdef DEBUG
    mt19937 gen(857204);
#else
    mt19937 gen(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif

#ifdef DEBUG
    template<class T> T to_dbg(T x) { return x; }
    template<class T, class U> string to_dbg(pair<T, U> p) {
        stringstream ss;
        ss << '{' << p.f << ',' << p.s << '}';
        return ss.str();
    }
    string to_dbg(string s) { return "\"" + s + "\""; }
    template<class T> string to_dbg(vector<T> a) {
        stringstream ss;
        ss << '{';
        if (sz(a)) ss << to_dbg(a[0]);
        for (int i = 1; i < sz(a); ++i)
            ss << "," << to_dbg(a[i]);
        ss << '}';
        return ss.str();
    }
    template<class T>
    void dbgout(T x) { cout << to_dbg(x) << endl; }
    template<class T, class... U>
    void dbgout(T t, U... u) {
        cout << to_dbg(t) << ", ";
        dbgout(u...);
    }
    #define dbg(...) cout << "[" << #__VA_ARGS__ << "] = ", dbgout(__VA_ARGS__);
#else
    #define dbg(...) 0
#endif

template<class T, class U> inline void checkmin(T &x, U y) { if (y < x) x = y; }
template<class T, class U> inline void checkmax(T &x, U y) { if (y > x) x = y; }
template<class T, class U> inline bool ifmax(T &x, U y) { if (y > x) return x = y, true; return false; }
template<class T, class U> inline bool ifmin(T &x, U y) { if (y < x) return x = y, true; return false; }
template<class T> inline void sort(T &a) { sort(all(a)); }
template<class T> inline void rsort(T &a) { sort(rall(a)); }
template<class T> inline void reverse(T &a) { reverse(all(a)); }
template<class T, class U> inline istream& operator>>(istream& str, pair<T, U> &p) { return str >> p.f >> p.s; }
template<class T> inline istream& operator>>(istream& str, vector<T> &a) { for (auto &i : a) str >> i; return str; }
template<class T> inline T sorted(T a) { sort(a); return a; }

vector<int> a, asc, ans;
int ptr = 0;
graph G;

void recsolve(int v, int p = -1) {
    int ind = lower_bound(all(asc), a[v]) - asc.begin();
    int was = asc[ind];
    asc[ind] = a[v];
    while (asc[ptr] < mod) ++ptr;
    while (ptr > 0 && asc[ptr - 1] == mod) --ptr;
    ans[v] = ptr;
    for (auto i : G[v])
        if (i != p)
            recsolve(i, v);
    asc[ind] = was;
}

signed main() {
    FAST; FIXED;
    int n;
    cin >> n;
    a = vector<int>(n);
    cin >> a;
    G = graph(n);
    for (int i = 1; i < n; ++i) {
        int u, v;
        cin >> u >> v;
        --u, --v;
        G[u].pb(v);
        G[v].pb(u);
    }
    ans = vector<int>(n);
    asc = vector<int>(n + 1, mod);
    recsolve(0);
    for (auto i : ans) cout << i << '\n';
    #ifdef DEBUG
        cerr << "Runtime is: " << clock() * 1.0 / CLOCKS_PER_SEC << endl;
    #endif
    return 0;
}

Measured memory_bytes: 30836