#include <bits/stdc++.h>
// #include <set>
// #include <vector>
// #include <ostream>
// #include <atcoder/notall>

using namespace std;
using ll = long long;
using VI = vector<int>;
using VL = vector<ll>;
using VD = vector<double>;
using VS = vector<string>;
using VB = vector<bool>;
using VVB = vector<vector<bool>>;
using VVI = vector<VI>;
using VVL = vector<VL>;
using VVD = vector<VD>;
using PII = std::pair<int, int>;
using VPII = std::vector<std::pair<int, int>>;
using PLL = std::pair<ll, ll>;
using VPLL = std::vector<std::pair<ll, ll>>;
using TI3 = std::tuple<int, int, int>;
using TI4 = std::tuple<int, int, int, int>;
using TL3 = std::tuple<ll, ll, ll>;
using TL4 = std::tuple<ll, ll, ll, ll>;

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
#define rep3(i, s, n, d) for (int i = (s); i < (int)(n); i += (d))
#define allpt(v) (v).begin(), (v).end()
#define allpt_c(v) (v).cbegin(), (v).cend()
#define allpt_r(v) (v).rbegin(), (v).rend()
#define allpt_cr(v) (v).crbegin(), (v).crend()

const int mod1 = 1e9 + 7, mod2 = 998244353, mod3 = 1e9 + 9;
const int mod = mod2;
const ll inf = 1e18;

const string wsp = " ";
const string tb = "\t";
const string rt = "\n";
const string alphabets = "abcdefghijklmnopqrstuvwxyz";

template <typename T>
void show1dvec(const vector<T> &v) {
    if (v.size() == 0) return;
    int n = v.size() - 1;
    rep(i, n) cout << v[i] << wsp;
    cout << v[n] << rt;
    return;
}

template <typename T>
void show2dvec(const vector<vector<T>> &v) {
    int n = v.size();
    rep(i, n) show1dvec(v[i]);
}

template <typename T>
void range_sort(vector<T> &arr, int l, int r) {
    sort(arr.begin() + l, arr.begin() + r);
}

template <typename T, typename S>
void show1dpair(const vector<pair<T, S>> &v) {
    int n = v.size();
    rep(i, n) cout << v[i].first << wsp << v[i].second << rt;
    return;
}

template <typename T, typename S>
void pairzip(const vector<pair<T, S>> &v, vector<T> &t, vector<T> &s) {
    int n = v.size();
    rep(i, n) {
        t.push_back(v[i].first);
        s.push_back(v[i].second);
    }
    return;
}

template <typename T>
void maxvec(vector<T> &v) {
    T s = v[0];
    int n = v.size();
    rep(i, n - 1) {
        if (s > v[i + 1]) {
            v[i + 1] = s;
        }
        s = v[i + 1];
    }
}

template <typename T, typename S>
bool myfind(T t, S s) {
    return find(t.cbegin(), t.cend(), s) != t.cend();
}

bool check(int y, int x, int h, int w) {
    return 0 <= y && y < h && 0 <= x && x < w;
}

bool iskadomatsu(int a, int b, int c) {
    return (a != b && b != c && c != a) &&
           ((a > b && b < c) || (a < b && b > c));
}

double euc_dist(PII a, PII b) {
    return sqrt(pow(a.first - b.first, 2) + pow(a.second - b.second, 2));
}

VS split(string s, char c) {
    VS ret;
    string part;
    s += c;
    rep(i, s.length()) {
        if (s[i] == c) {
            if (part != "") ret.emplace_back(part);
            part = "";
        } else if (s[i] != c) {
            part += s[i];
        }
    }
    return ret;
}

template <typename T, typename S, typename R>
ll pow_mod(T p, S q, R mod = 1ll) {
    ll ret = 1, r = p;
    while (q) {
        if (q % 2) ret *= r, ret %= mod;
        r = (r * r) % mod, q /= 2;
    }
    return ret % mod;
}

template <typename T, typename S>
ll pow_no_mod(T p, S q) {
    ll ret = 1, r = p;
    while (q) {
        if (q % 2) ret *= r;
        r = (r * r), q /= 2;
    }
    return ret;
}

void make_frac_tables(VL &frac_list, VL &frac_inv_list) {
    rep(i, frac_list.size() - 1) {
        frac_list[i + 1] *= frac_list[i] * (i + 1);
        frac_list[i + 1] %= mod;
        frac_inv_list[i + 1] *= frac_inv_list[i] * pow_mod(i + 1, mod - 2, mod);
        frac_inv_list[i + 1] %= mod;
    }
}

pair<VL, VL> make_frac_tables(int n) {
    VL frac_list(n + 1, 1), frac_inv_list(n + 1, 1);
    rep(i, n) {
        frac_list[i + 1] *= frac_list[i] * (i + 1);
        frac_list[i + 1] %= mod;
        frac_inv_list[i + 1] *= frac_inv_list[i] * pow_mod(i + 1, mod - 2, mod);
        frac_inv_list[i + 1] %= mod;
    }
    return make_pair(frac_list, frac_inv_list);
}

ll comb(int a, int b, const VL &frac_list, const VL &frac_inv_list) {
    if (a < b) return 0;
    if (b < 0) return 0;
    ll ret = frac_list[a];
    ret *= frac_inv_list[b];
    ret %= mod;
    ret *= frac_inv_list[a - b];
    ret %= mod;
    return ret;
}

struct vec2d {
    ll x;
    ll y;
    vec2d(ll _x, ll _y) {
        x = _x;
        y = _y;
    }
    ll dot(vec2d p) { return x * p.x + y * p.y; }
    vec2d diff(vec2d p) { return vec2d(x - p.x, y - p.y); }
};

template <typename T>
class RangeMinorMaxorSumQuery  // 0-index
{
    int const intmax = 2147483647;
    int const intmin = 0;
    vector<T> sgt;
    int n;
    int k;

   public:
    RangeMinorMaxorSumQuery(int n1, int f = -1) {
        if (f == -1)
            f = intmax;
        else if (f == 0)
            f = intmin;
        int na = 1;
        int ka = 0;
        while (na < n1) {
            na *= 2;
            ka++;
        }
        for (int i = 0; i < 2 * na; i++) sgt.push_back(f);
        n = na;
        k = ka;
    }

    void update_min(int i, int x) {
        i += n;
        sgt[i] = x;
        while (i > 1) {
            i /= 2;
            sgt[i] = min(sgt[2 * i], sgt[2 * i + 1]);
        }
    }
    void update_max(int i, T x) {
        i += n;
        sgt[i] = x;
        while (i > 1) {
            i /= 2;
            sgt[i] = max(sgt[2 * i], sgt[2 * i + 1]);
        }
    }
    void update_sum(int i, T x) {
        i += n;
        sgt[i] = x;
        while (i > 1) {
            i /= 2;
            sgt[i] = sgt[2 * i] + sgt[2 * i + 1];
        }
    }

    void add_sum(int i, T x) {
        i += n;
        sgt[i] += x;
        while (i > 1) {
            i /= 2;
            sgt[i] = sgt[2 * i] + sgt[2 * i + 1];
        }
    }

    T getmin(int a, int b, int k = 1, int l = 0,
             int r = -1)  //閉区間 l <= x < r とする
    {
        if (r == -1) r = n;
        if (r <= a || b <= l) return intmax;
        if (a == l && b == r)
            return sgt[k];
        else
            return min(
                getmin(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2),
                getmin(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r));
    }
    T getmax(int a, int b, int k = 1, int l = 0,
             int r = -1)  //閉区間 l <= x < r とする
    {
        if (r == -1) r = n;
        if (r <= a || b <= l) return intmin;
        if (a == l && b == r)
            return sgt[k];
        else
            return max(
                getmax(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2),
                getmax(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r));
    }

    T getsum(int a, int b, int k = 1, int l = 0,
             int r = -1)  //閉区間 l <= x < r とする
    {
        if (r == -1) r = n;
        if (r <= a || b <= l) return intmin;
        if (a == l && b == r)
            return sgt[k];
        else
            return getsum(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2) +
                   getsum(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r);
    }

    T operator[](int i) { return sgt[i + n]; }

    void printsegtree() {
        for (int i = 0; i < 2 * n; i++) {
            cout << sgt[i] << " ";
        }
        cout << endl;
    }
};

// void djkstra(int n, vector<vec2d> point_list, const VVL cost_list,
//              const VVI &connect) {
//     const ll llm = 1e18;
//     VVL min_cost(n, VL(n, llm));
//     min_cost[0][0] = 0;

//     vector<PII> search = {make_pair(0, 0)};
//     vector<PII> new_search;
//     while (!search.empty()) {
//         for (auto [p, q] : search) {
//             for (auto r : connect[p]) {
//                 if (point_list[r]
//                             .diff(point_list[p])
//                             .dot(point_list[q].diff(point_list[p])) <= 0 &&
//                     min_cost[r][p] > cost_list[r][p] + min_cost[p][q]) {
//                     min_cost[r][p] = cost_list[r][p] + min_cost[p][q];
//                     new_search.emplace_back(make_pair(r, p));
//                 }
//             }
//         }
//         search.clear();
//         search = new_search;
//         new_search.clear();
//         // show1dvec(search);
//         // show1dvec(shortest);
//     }
//     auto ans = *min_element(allpt_c(min_cost[1]));
//     cout << ((ans == llm) ? -1 : ans) << rt;
//     // show2dvec(min_cost);
// }

struct node {
    int parent = -1;
    ll weight = 0;
    int depth = 0;
    int subtree = 0;
    VPII children;
    VPII connect;
    node(int n) {
        parent = -1;
        weight = 0;
        depth = 0;
        subtree = 0;
        children;
        connect;
    }
};

struct graph {
    int _n;
    int root = 0;
    vector<node> nodes;
    graph(int n) {
        _n = n;
        rep(i, _n) nodes.emplace_back(node(_n));
    }
    void getconnect1() {
        int a, b;
        cin >> a >> b;
        a--, b--;
        nodes[a].connect.emplace_back(b, 0);
        nodes[b].connect.emplace_back(a, 0);
    }
    void getconnect2() {
        int a, b, c;
        cin >> a >> b >> c;
        a--, b--;
        nodes[a].connect.emplace_back(b, c);
        nodes[b].connect.emplace_back(a, c);
    }
    void showparent() {
        rep(i, _n - 1) cout << nodes[i].parent << wsp;
        cout << nodes[_n - 1].parent << rt;
    }
    void showweight() {
        rep(i, _n - 1) cout << nodes[i].weight << wsp;
        cout << nodes[_n - 1].weight << rt;
    }
    void showsubtree() {
        rep(i, _n - 1) cout << nodes[i].subtree << wsp;
        cout << nodes[_n - 1].subtree << rt;
    }
    void showdepth() {
        rep(i, _n - 1) cout << nodes[i].depth << wsp;
        cout << nodes[_n - 1].depth << rt;
    }
};

void dfs(int i, graph &tree, RangeMinorMaxorSumQuery<ll> &sgt) {
    auto before = sgt[tree.nodes[i].weight];
    // cout << i << wsp << tree.nodes[i].weight << wsp << sgt.getmax(0,
    // tree.nodes[i].weight) << rt;
    // sgt.printsegtree();
    auto after = max(sgt.getmax(0, tree.nodes[i].weight) + 1, before);
    sgt.update_max(tree.nodes[i].weight, after);
    if (i == tree.root) {
        tree.nodes[i].subtree = sgt[tree.nodes[i].weight];
    } else {
        tree.nodes[i].subtree =
            max<int>(tree.nodes[tree.nodes[i].parent].subtree,
                     sgt[tree.nodes[i].weight]);
    }

    // sgt.printsegtree();
    for (auto [j, c] : tree.nodes[i].connect)
        if (j != tree.root && tree.nodes[j].parent == -1) {
            tree.nodes[j].parent = i;
            dfs(j, tree, sgt);
        }

    sgt.update_max(tree.nodes[i].weight, before);
}

struct point {
    int x;
    int y;
    point() {
        x = 0;
        y = 0;
    }
    point(int _x, int _y) {
        x = _x;
        y = _y;
    }
    void pointinput() {
        int _x, _y;
        cin >> _x >> _y;
        x = _x;
        y = _y;
    }
    void pointinv() { swap(x, y); }
};

double pointseuc(point a, point b) {
    return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2));
}

double dist_segment_point(TL3 segment, point p) {
    double a = get<0>(segment);
    double b = get<1>(segment);
    double c = get<2>(segment);
    return abs(a * p.x + b * p.y - c) / (a * a + b * b + c * c);
}

TL3 segment_parameter(point p, point q) {
    ll a, b, c;
    a = q.y - p.y;
    b = p.x - q.x;
    c = a * p.x + b * p.y;
    TL3 ret = (TL3){a, b, c};
    // cout << a << b << c << rt;
    return ret;
}

int cross_check(TL3 segment, point p) {
    ll a = get<0>(segment);
    ll b = get<1>(segment);
    ll c = get<2>(segment);

    auto f = a * p.x + b * p.y - c;
    int ret;
    if (f > 0) ret = 1;
    if (f == 0) ret = 0;
    if (f < 0) ret = -1;
    return ret;
}

template <typename T>
void coordinate_compress(vector<T> &x, map<T, int> &zip, int &xs) {
    sort(x.begin(), x.end());
    x.erase(unique(x.begin(), x.end()), x.end());
    xs = x.size();
    for (int i = 0; i < xs; i++) zip[x[i]] = i;
}



int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    // リアクティブ問題のときはコメントアウト

#ifdef DEBUG
    cout << "DEBUG MODE" << endl;
    ifstream in("input.txt");  // for debug
    cin.rdbuf(in.rdbuf());     // for debug
#endif

    int n, w, ws;
    VI w_list{-1};
    map<int, int> w_map;
    cin >> n;
    graph tree(n);
    rep(i, n) {
        cin >> w;
        tree.nodes[i].weight = w;
        w_list.emplace_back(w);
    }

    coordinate_compress(w_list, w_map, ws);
    rep(i, n) tree.nodes[i].weight = w_map[tree.nodes[i].weight];
    RangeMinorMaxorSumQuery<ll> sgt(ws + 1, 0);

    rep(i, n - 1) tree.getconnect1();
    dfs(tree.root, tree, sgt);
    // tree.showweight();
    rep(i, n) cout << tree.nodes[i].subtree << rt;

    return 0;
}


Measured memory_bytes: 67608