//https://atcoder.jp/contests/abc165/tasks/abc165_f?lang=en
#include <bits/stdc++.h>
using namespace std;

#define el '\n'
#define pb push_back
#define sp ' '
#define all(x) (x).begin(), (x).end()
#define mset(x, y) memset(x, y, sizeof(x))
#define ff first
#define ss second

// clang-format off
bool chmin(int& a, int b){ return b < a ? a = b, true : false; }
bool chmax(int& a, int b){ return b > a ? a = b, true : false; }
bool chmin(long long& a, long long b){ return b < a ? a = b, true : false; }
bool chmax(long long& a, long long b){ return b > a ? a = b, true : false; }
#ifndef ONLINE_JUDGE
template <typename T, size_t N> int SIZE(const T (&t)[N]){ return N; } template<typename T> int SIZE(const T &t){ return t.size(); } string to_string(const string s, int x1=0, int x2=1e9){ return '"' + ((x1 < (int)s.size()) ? s.substr(x1, x2-x1+1) : "") + '"'; } string to_string(const char* s) { return to_string((string) s); } string to_string(const bool b) { return (b ? "true" : "false"); } string to_string(const char c){ return string({c}); } template<size_t N> string to_string(const bitset<N> &b, int x1=0, int x2=1e9){ string t = ""; for(int __iii__ = min(x1,SIZE(b)),  __jjj__ = min(x2, SIZE(b)-1); __iii__ <= __jjj__; ++__iii__){ t += b[__iii__] + '0'; } return '"' + t + '"'; } template <typename A, typename... C> string to_string(const A (&v), int x1=0, int x2=1e9, C... coords); int l_v_l_v_l = 0, t_a_b_s = 0; template <typename A, typename B> string to_string(const pair<A, B> &p) { l_v_l_v_l++; string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; l_v_l_v_l--; return res; } template <typename A, typename... C> string to_string(const A (&v), int x1, int x2, C... coords) { int rnk = rank<A>::value; string tab(t_a_b_s, ' '); string res = ""; bool first = true; if(l_v_l_v_l == 0) res += el; res += tab + "["; x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v)); auto l = begin(v); advance(l, x1); auto r = l; advance(r, (x2-x1) + (x2 < SIZE(v))); for (auto e = l; e != r; e = next(e)) { if (!first) { res += ", "; } first = false; l_v_l_v_l++; if(e != l){ if(rnk > 1) { res += el; t_a_b_s = l_v_l_v_l; }; } else{ t_a_b_s = 0; } res += to_string(*e, coords...); l_v_l_v_l--; } res += "]"; if(l_v_l_v_l == 0) res += el; return res; } void dbgm(){;} template<typename Heads, typename... Tails> void dbgm(Heads H, Tails... T){ cout << to_string(H) << " | "; dbgm(T...); } 
#define dbg(...) cout << "[" << #__VA_ARGS__ << "]: "; cout << to_string(__VA_ARGS__) << endl
#define dbgm(...) cout << "[" << #__VA_ARGS__ << "]: "; dbgm(__VA_ARGS__); cout << endl
#else
#define dbg(...) ;
#define dbgm(...) ;
#endif
// clang-format on

typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<pii, pii> ppi;
typedef pair<ll, ll> pll;
typedef pair<int, ll> pil;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pii> vpii;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<vpii> vvpii;
typedef vector<vpll> vvpll;

const int inf = 1e09 + 5e3;
const ll linf = 2e18 + 5e3;
const int mod = 1e9 + 7;
const int mxn = 3e5 + 30;

int n;
vvi adj;
int a[mxn], sz[mxn], ans[mxn], t[4 * mxn], q = 2;

int query(ll v, int tl, int tr, int l, int r)
{
    // dbgm(v, tl, tr, l, r);
    if (l > r)
        return 0;
    if (l == tl && r == tr)
    {
        return t[v];
    }
    int tm = (tl + tr) / 2;
    return max(query(v * 2, tl, tm, l, min(r, tm)), query(v * 2 + 1, tm + 1, tr, max(l, tm + 1), r));
}

void update(ll v, int tl, int tr, int pos, int new_val)
{
    if (tl == tr)
    {
        t[v] = new_val;
    }
    else
    {
        ll tm = (tl + tr) / 2;
        if (pos <= tm)
            update(v * 2, tl, tm, pos, new_val);
        else
            update(v * 2 + 1, tm + 1, tr, pos, new_val);
        t[v] = max(t[v * 2], t[v * 2 + 1]);
    }
}

void dfs(int v, int p)
{
    // dbgm(v, p, a[v]);
    int my_best = query(1, 0, q, 0, a[v] - 1) + 1;
    // dbg("Here1");
    int prev = query(1, 0, q, a[v], a[v]);
    // dbg("here2");
    update(1, 0, q, a[v], my_best);
    ans[v] = t[1];
    for (auto u : adj[v])
        if (u != p)
            dfs(u, v);
    update(1, 0, q, a[v], prev);
}

int main()
{
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);

    mset(ans, -1);
    mset(t, 0);
    cin >> n;
    adj.assign(n, vi());
    int temp, temp2;
    map<int, vi> ma;
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
        ma[a[i]].pb(i);
    }

    for (auto it = ma.begin(); it != ma.end(); q++, it++)
    {
        for (auto blah : it->ss)
            a[blah] = q;
    }

    for (int i = 1; i < n; i++)
    {
        cin >> temp >> temp2;
        temp--, temp2--;
        adj[temp].pb(temp2);
        adj[temp2].pb(temp);
    }
    // build(1, 0, n - 1);
    // dbg(t, 0, 4 * n);
    dfs(0, 0);

    for (int i = 0; i < n; i++)
    {
        cout << ans[i] << el;
    }
}


Measured memory_bytes: 52160