#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
template<class A, class B> ostream& operator <<(ostream& out, const pair<A, B> &p) {
    return out << "(" << p.first << ", " << p.second << ")";
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
  out << "["; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
  out << "["; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
  return out;
}
template<class T> inline void YES(T condition) { 
    if(condition) cout << "YES" << endl;
    else cout << "NO" << endl;
}
template<class T> inline void Yes(T condition) {
    if(condition) cout << "Yes" << endl;
    else cout << "No" << endl;
}
template<class T> T gcd(T a, T b) {
    if(a && b) { return gcd(min(a, b), max(a, b) % min(a, b)); }
    else { return a; }
}
template<class T> T lcm(T a, T b){
    return a / gcd(a, b) * b;
}
const int MOD = 2019;
long long qpow(long long a, long long b) {
    if (b == 0) return 1;
    long long res = 1;
    while (b) {
        if (b & 1) res = (res * a) % MOD;
        a = (a * a) % MOD;
        b >>= 1;
    }
    return res;
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;
    vector<int> w(n + 1);
    vector<vector<int>> nei(n + 1);
    for (int i = 1; i <= n; i++) cin >> w[i];
    for (int j = 1; j < n; j++) {
        int u, v;
        cin >> u >> v;
        nei[u].push_back(v);
        nei[v].push_back(u);
    }
    vector<int> seen(n + 1, 0);
    seen[1] = 1;
    vector<int> res(n + 1, 0);
    res[1] = 1;
    vector<int> inc = {w[1]};
    function<void(int)> dfs = [&](int x) {
        for (auto& y: nei[x]) {
            if (seen[y]) continue;
            seen[y] = 1;
            int wy = w[y];
            if (wy > inc.back()) {
                inc.push_back(wy);
                res[y] = (int)inc.size();
                dfs(y);
                inc.pop_back();
            } else {
                int l = 0, r = inc.size() - 1;
                while (l < r) {
                    int mid = (l + r) >> 1;
                    if (wy <= inc[mid]) r = mid; 
                    else l = mid + 1;
                }
                int tmp = inc[r];
                inc[r] = wy;
                res[y] = (int)inc.size();
                dfs(y);
                inc[r] = tmp;
            }
        }
    };
    dfs(1);
    for (int i = 1; i <= n; i++) cout << res[i] << '\n';

    return 0;
}


Measured memory_bytes: 30856