const int N = 400005;
const int LG = 21;
const long long MOD = 1e9 + 7;
const long long INF = 1e9;
const long long INFLL = 1e18;

#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <cmath>
#include <time.h>
#include <unordered_set>
#include <bitset>
#include <deque>

using namespace std;

#define int long long
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<ll> vi;

#define forn(i, n) for (int (i) = 0; (i) != (n); (i)++)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define popcount(x) __builtin_popcount(x)
#define popcountll(x) __builtin_popcountll(x)
#define fi first
#define se second
#define re return
#define uniq(x) sort(all(x)); (x).resize(unique(all(x)) - (x).begin())

#ifdef LOCAL
#define dbg(x) cerr << __LINE__ << " " << #x << " " << x << endl
#define ln cerr << __LINE__ << endl
#else
#define dbg(x) void(0)
#define ln void(0)
#endif // LOCAL

int cx[4] = {-1, 0, 1, 0};
int cy[4] = {0, -1, 0, 1};

ll inq(ll x, ll y)
{
    if (!y) re 1 % MOD;
    ll l = inq(x, y / 2);
    if (y % 2) re l * l % MOD * x % MOD;
    re l * l % MOD;
}

ll rev(ll x)
{
    return inq(x, MOD - 2);
}

bool __precomputed_combinatorics = 0;
vector<ll> __fact, __ufact, __rev;

void __precompute_combinatorics()
{
    __precomputed_combinatorics = 1;
    __fact.resize(N);
    __ufact.resize(N);
    __rev.resize(N);
    __rev[1] = 1;
    for (int i = 2; i < N; i++) __rev[i] = MOD - __rev[MOD % i] * (MOD / i) % MOD;
    __fact[0] = 1, __ufact[0] = 1;
    for (int i = 1; i < N; i++) __fact[i] = __fact[i - 1] * i % MOD, __ufact[i] = __ufact[i - 1] * __rev[i] % MOD;
}

ll fact(int x)
{
    if (!__precomputed_combinatorics) __precompute_combinatorics();
    return __fact[x];
}

ll cnk(int n, int k)
{
    if (!__precomputed_combinatorics) __precompute_combinatorics();
    return __fact[n] * __ufact[n - k] % MOD * __ufact[k] % MOD;
}

ll n;
ll a[N];
vector<int> graph[N];
vector<int> lis[N];
ll ans[N];

void dfs(int v, int p)
{
    int l = 0, r = N;
    while (l + 1 < r)
    {
        int m = (l + r) / 2;
        if (lis[m].size() == 0)
        {
            r = m;
            continue;
        }
        if (lis[m].back() < a[v])
        {
            l = m;
        }
        else
        {
            r = m;
        }
    }
    ans[v] = l + 1;
    int t = 0;
    if (lis[l + 1].size() == 0 || a[v] < lis[l + 1].back()) t = 1, lis[l + 1].push_back(a[v]);
    for (auto u : graph[v]) if (u != p)
    {
        dfs(u, v);
    }
    if (t) lis[l + 1].pop_back();
}

void push_dfs(int v, int p)
{
    if (p != 0) ans[v] = max(ans[v], ans[p]);
    for (auto u : graph[v]) if (u != p)
    {
        push_dfs(u, v);
    }
}

signed main()
{
    srand(time(NULL));
    #ifdef ONLINE_JUDGE
        ios_base::sync_with_stdio(false);
        cin.tie(0);
        cout.tie(0);
    #endif // ONLINE_JUDGE
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];
    for (int i = 0; i < n - 1; i++)
    {
        int v, u;
        cin >> v >> u;
        graph[v].push_back(u);
        graph[u].push_back(v);
    }
    lis[1] = {a[1]};
    dfs(1, 0);
    push_dfs(1, 0);
    for (int i = 1; i <= n; i++) cout << ans[i] << "\n";
}

/* Note:
Check constants at the beginning of the code.
N is set to 4e5 but be careful in problems with large constant factor.
Check corner cases.
No def int long long for now.
*/


Measured memory_bytes: 43944