#pragma region header
#include <bits/stdc++.h>
#define int long long
#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)
#define mp make_pair
#define mt make_tuple
#define rep1(i, n) for (decltype(+n) i = 0; i < (n); i++)
#define rrep1(i, n) for (auto i = n - 1; i > static_cast<decltype(i)>(-1); i--)
#define rep2(i, a, b) for (auto i = (a); i < (b); i++)
#define rrep2(i, a, b) for (auto i = b - 1; i >= a; i--)
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define rep(...) GET_MACRO(__VA_ARGS__, rep2, rep1) (__VA_ARGS__)
#define rrep(...) GET_MACRO(__VA_ARGS__, rrep2, rrep1) (__VA_ARGS__)
#define each(i, a) for (auto &&i : (a))
using namespace std;

using ld = long double;
using vi = vector<int>;
using vvi = vector<vi>;
using vs = vector<string>;
using vvs = vector<vs>;
using vd = vector<ld>;
using vvd = vector<vd>;
using vb = vector<bool>;
using vvb = vector<vb>;
using pii = pair<int, int>;
using vp = vector<pii>;
using vvp = vector<vp>;
using mii = map<int, int>;
using vm = vector<mii>;
using vvm = vector<vm>;
template <class T>
using less_queue = priority_queue<T>;
template <class T>
using greater_queue = priority_queue<T, vector<T>, greater<T>>;

constexpr int INF = 1e18;

template <class T>
void SORT(T &a) { stable_sort(all(a)); }
template <class T>
void RSORT(T &a) { stable_sort(rall(a)); }
template <class T>
void rev(T &a) { reverse(rall(a)); }
template <class T>
void uniq(T &a) { a.erase(unique(all(a)), end(a)); }
template <class T>
auto min_of(T a) { return *min_element(all(a)); }
template <class T>
auto max_of(T a) { return *max_element(all(a)); }
template <class T>
int sum_of(T a) { return accumulate(all(a), 0ll); }
template <class T, class U>
auto sum_of(T a, U init) { return accumulate(all(a), init); }
template <class T, class U>
int count_of(T a, U i) { return count(all(a), i); }
template <class T, class U>
int lower_index(T a, U i) { return lower_bound(all(a), i) - cbegin(a); } // use member func for set
template <class T, class U>
int upper_index(T a, U i) { return upper_bound(all(a), i) - cbegin(a); }
template <class T, class U>
bool binary(T a, U i) { return binary_search(all(a), i); }
template <class T, class U>
bool has(T a, U i) { return find(all(a), i) != end(a); }
template <class T>
int sz(T a) { return a.size(); };

template <class T>
void COUT(T x) { cout << x << endl; }
template <class T, class U>
void COUT(T x, U y) { cout << x << ' ' << y << endl; }
template <class T, class U, class V>
void COUT(T x, U y, V z) { cout << x << ' ' << y << ' ' << z << endl; }
template <class T>
void CSP(T x) { cout << x << ' '; }
template <class T>
void CVEC(T v) {
  int c = v.size() - 1;
  for (size_t i = 0; i < c; i++) cout << v[i] << ' ';
  if (c > -1) cout << v[c];
  cout << endl;
}

template <class T>
bool amin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool amax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

int ceil_div(int x, int y) { return (x - 1) / y + 1; }

#pragma endregion header

// no MOD


void solve(int N, vi a, vi u, vi v) {
  vvi adj(N);
  rep(i, N - 1) {
    adj[u[i]].push_back(v[i]);
    adj[v[i]].push_back(u[i]);
  }
  vb used(N);
  vi lis(N + 1, INF);
  lis[0] = 0;
  vi ans(N);
  function<void(int)> dfs = [&](int i) {
    used[i] = true;
    int l = lower_bound(all(lis), a[i]) - begin(lis);
    int tmp = lis[l];
    lis[l] = a[i];
    ans[i] = lower_bound(all(lis), INF) - begin(lis) - 1;
    each(next, adj[i])if(!used[next])dfs(next);
    lis[l] = tmp;
  };
  dfs(0);
  each(x, ans)COUT(x);
}


#pragma region main
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout << fixed << setprecision(15);

  int N;
  cin >> N;
  vi a(N);
  for(int i = 0 ; i < N ; i++){
    cin >> a[i];
  }
  vi u(N-1);
  vi v(N-1);
  for(int i = 0 ; i < N-1 ; i++){
    cin >> u[i];
    cin >> v[i];
    u[i]--;
    v[i]--;
  }
  solve(N, move(a), move(u), move(v));
}
#pragma endregion main


Measured memory_bytes: 36140