#include <algorithm>
#include <functional>
#include <iostream>
#include <iomanip>
#include <vector>
#include <map>
#include <set>
#include <unordered_set>
#include <queue>
#include <numeric>
#include <bitset>
#include <cmath>

using namespace std;
using ll = long long;
using ull = unsigned long long;
// const ll mod =  998244353 ;
const ll mod =  1000000007 ;
const ll inf = 1e18;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};


#define REP(i, n) for (ll i = 0; i < (n); ++i)
#define REP_FROM(i, j, n) for (ll i = (j); i < (n); ++i)
#define REP_REV(i, n) for (ll i = n-1; i >= 0; --i)
#define REP_FROM_REV(i, j, n) for (ll i = n-1; i >= j; --i)
#define all(x) (x).begin(),(x).end()
#define sz(x) ll(x.size())

template<typename T> void print_vec(vector<T> a) {int n = a.size();REP(i, n) {cout >> a[i]; if(i!=n-1) cout << " "; else cout << endl;}}
ll power(ll base, ll exponent){ if(exponent % 2){ return power(base, exponent - 1) * base % mod; }else if(exponent){ ll root_ans = power(base, exponent / 2); return root_ans * root_ans % mod; }else{ return 1; }}
ll inverse(ll x){ return power(x, mod - 2);}
ll gcd(ll a, ll b) {if(a < b) gcd(b, a);ll r;while(r=a%b) {a=b;b=r;}return b;}
template<typename T> ll sum(T begin, T end) {return accumulate(begin, end, 0ll);}
struct combination{ vector<ll> fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } ll C(int p, int q) const{ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } };

using Pair = pair<ll, ll>;

template <ll Modulus> struct ModInt {
    ll a;
    constexpr ModInt(const ll x = 0) noexcept  : a((x%mod+mod) % mod){}
    constexpr ll &value() noexcept {return a;}
    constexpr const ll &value() const noexcept {return a;}
    constexpr ModInt operator+(const ModInt x) const noexcept {
      return ModInt(*this) += x;
    }
    constexpr ModInt operator-(const ModInt x) const noexcept {
      return ModInt(*this) -= x;
    }
    constexpr ModInt operator*(const ModInt x) const noexcept {
      return ModInt(*this) *= x;
    }
    constexpr ModInt operator/(const ModInt x) const noexcept {
      return ModInt(*this) /= x;
    }
    constexpr ModInt &operator+=(const ModInt x) noexcept {
      a += x.a;
      if (a >= Modulus) {
        a -= Modulus;
      }
      return *this;
    }
    constexpr ModInt &operator-=(const ModInt x) noexcept {
      if (a < x.a) {
        a += Modulus;
      }
      a -= x.a;
      return *this;
    }
    constexpr ModInt &operator*=(const ModInt x) noexcept {
      a = a * x.a % Modulus;
      return *this;
    }
    constexpr ModInt &operator/=(ModInt x) noexcept {
      ll exp = Modulus - 2;
      while (exp) {
        if (exp % 2) {
          *this *= x;
        }
        x *= x;
        exp /= 2;
      }
      return *this;
    }
    constexpr  ModInt operator-() noexcept {
      return ModInt(-a);
    }
    friend ostream& operator<<(ostream& os, const ModInt& m){
      os << m.a;
      return os;
    }
};
using mint = ModInt<mod>;

vector<ll> a, ans, dp;
vector<vector<int>> g;

void dfs(int i) {
  auto index = lower_bound(all(dp), a[i]);
  ll old = *index;
  *index = a[i];
  ans[i] = upper_bound(all(dp), inf-1) - dp.begin();
  REP(j, sz(g[i])) {
    if(ans[g[i][j]] >= 0) continue;
    dfs(g[i][j]);
  }
  *index = old;
}

signed main() {
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  ll n;
  cin >> n;
  a.resize(n);
  dp.resize(n, inf);
  ans.resize(n, -1);
  g.resize(n);
  REP(i, n) cin >> a[i];
  REP(i, n-1) {
    int x, y;
    cin >> x >> y;
    x--;y--;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  dfs(0);
  REP_FROM(i, 0, n) {
    cout << ans[i] << endl;
  }
  return 0;
}


Measured memory_bytes: 27460