#include <stdio.h>
#include <stdlib.h>

#include <iostream>
#include <iomanip>
#include <sstream>
#include <fstream>
#include <stdint.h>
#include <string.h>

#define _USE_MATH_DEFINES
#include <math.h>

#include <vector>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <deque>
#include <string>

#include <algorithm>
#include <functional>
#include <bitset>
#include <functional>
#include <chrono>
#include <random>

#define sqr(x) (x) * (x)

typedef unsigned int u32;
typedef int i32;
typedef unsigned long long int u64;
typedef int i64;
typedef uint16_t u16;
typedef int16_t i16;
typedef uint8_t u8;
typedef int8_t i8;

using namespace std;
using namespace std::chrono;

//const i64 mod = 1000000007ll;
const i64 smod = 998244353ll;
const i64 inf = 1'000'000'000'000'000'000ll + 7;
//const i64 inf = 1'000'000'007;

const long double eps = 1e-8;

struct segtree {
    using type = i32;
    const type zero = 0;

    inline type combine(type a, type b) {
        return max(a, b);
    }

    i64 n = 0;
    vector<type> st;

    void init(i64 size) {
        n = 1;
        while (n < size) {
            n *= 2;
        }
        st.assign(n * 2, zero);
    }

    void set(i64 i, type v, i64 x, i64 lx, i64 rx) {
        if (rx - lx == 1) {
            st[x] = v;
            return;
        }

        i64 m = (lx + rx) / 2;
        if (i < m) {
            set(i, v, x * 2 + 1, lx, m);
        }
        else {
            set(i, v, x * 2 + 2, m, rx);
        }

        st[x] = combine(st[x * 2 + 1], st[x * 2 + 2]);
    }

    void set(i64 i, type v) {
        set(i, v, 0, 0, n);
    }

    type calc(i64 l, i64 r, i64 x, i64 lx, i64 rx) {
        if (lx >= r || l >= rx) {
            return zero;
        }

        if (l <= lx && rx <= r) {
            return st[x];
        }

        i64 m = (lx + rx) / 2;
        type v1 = calc(l, r, x * 2 + 1, lx, m);
        type v2 = calc(l, r, x * 2 + 2, m, rx);
        return combine(v1, v2);
    }

    type calc(i64 l, i64 r) {
        return calc(l, r, 0, 0, n);
    }
};


const i64 MAXN = 2 * 100'000 + 6;

i64 n, m;
i64 a[MAXN];
vector<i64> e[MAXN];
map<i64, i64> z;

i64 r[MAXN];

segtree st;

void dfs(i64 c, i64 p, map<i64, vector<i64>>& q) {
    i64 v = 1;

    i64 t = st.calc(0, a[c]);
    v += t;

    q[a[c]].push_back(v);
    st.set(a[c], v);


    r[c] = st.calc(0, z.size());

    for (auto n : e[c]) {
        if (n == p) {
            continue;
        }
        dfs(n, c, q);
    }

    q[a[c]].pop_back();
    st.set(a[c], q[a[c]].size() ? q[a[c]].back() : 0);

    if (q[a[c]].empty()) {
        q.erase(a[c]);
    }
}

void dict() {
    vector<i64> q;
    for (i64 i = 1; i <= n; i++) {
        q.push_back(a[i]);
    }
    sort(q.begin(), q.end());

    for (auto t : q) {
        if (z.count(t)) {
            continue;
        }
        z[t] = z.size();
    }

    for (i64 i = 1; i <= n; i++) {
        a[i] = z[a[i]];
    }
}

int main(int argc, char* argv[]) {
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout.precision(15); cout.setf(ios::fixed);

    cin >> n;

    for (i64 i = 1; i <= n; i++) {
        cin >> a[i];
    }

    for (i64 i = 1; i < n; i++) {
        i64 u, v;
        cin >> u >> v;

        e[u].push_back(v);
        e[v].push_back(u);
    }

    dict();
    st.init(z.size());

    map<i64, vector<i64>> q;
    dfs(1, 0, q);

    stringstream ss;
    for (i64 i = 1; i <= n; i++) {
        ss << r[i] << endl;
    }
    cout << ss.str();


    return 0;
}

Measured memory_bytes: 55820