#include <bits/stdc++.h>

using namespace std;

const double PI = 3.141592653589;
#define fastio ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pb push_back
#define mp make_pair
#define int long long
#define ll long long
#define ll long long
#define all(c) (c).begin(),(c).end()
#define M 1000000007
#define INF LLONG_MAX
#define pr(...) dbs(#__VA_ARGS__, __VA_ARGS__)
template <class T> void dbs(string str, T t) {cerr << str << " : " << t << "\n";}
template <class T, class... S> void dbs(string str, T t, S... s) {int idx = str.find(','); cerr << str.substr(0, idx) << " : " << t << ", "; dbs(str.substr(idx + 1), s...);}
template <class S, class T>ostream& operator <<(ostream& os, const pair<S, T>& p) {return os << "(" << p.first << ", " << p.second << ")";}
template <class T>ostream& operator <<(ostream& os, const vector<T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class T>ostream& operator <<(ostream& os, const set<T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class S, class T>ostream& operator <<(ostream& os, const map<S, T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class T> void prc(T a, T b) {cerr << "["; for (T i = a; i != b; ++i) {if (i != a) cerr << ", "; cerr << *i;} cerr << "]\n";}
// Use pr(a,b,c,d,e) or cerr<<anything or prc(v.begin(),v.end()) or prc(v,v+n)
//  
const int N = 2e5 + 5;
int n;
vector<int> tree[N];
vector<bool> vis(N, false);
int W[N];
int ans[N];

/*
 * 1 based index, define N (max length of array possible)
 * Point update, increment of a[i] by b
 */
struct ST{
    int sum;
    ST(int _sum = 0) : sum(_sum) {}
};

ST operator + (const ST &A, const ST &B) {
	/**Merging Logic**/
  /*
   * for example for range sum query return (ST(A.sum + B.sum));
   */
    return (ST(max(A.sum, B.sum)));
}

struct segtree {
    vector<ST> tree;
    vector<int> A;
    segtree(int n = N) {
        tree.resize(4 * n);
        A.resize(n);
    }

    void build(int node, int start, int end) {
        if(start == end) {
            tree[node] = ST(A[start]);
        }
        else {
            int mid = (start + end) >> 1;
            build(2 * node, start, mid);
            build(2 * node + 1, mid+1, end);
            tree[node] = tree[2 * node] + tree[2 * node + 1];
        }
    }

    void update(int node, int start, int end, int idx, ll val) {
        if(start == end) {
            tree[node].sum = val; // ^^
        }
        else {
            int mid = (start + end) >> 1;
            if(idx <= mid) update(2 * node, start, mid, idx, val);
            else update(2 * node + 1, mid + 1, end, idx, val);
            tree[node] = tree[2 * node] + tree[2 * node + 1];
        }
    }

    ST query(int node, int start, int end, int l, int r) {
        if(start >= l && end <= r) return tree[node];
        int mid = (start + end) >> 1;
        if(mid >= r) return query(2 * node, start, mid, l, r);
        if(mid < l) return query(2 * node + 1, mid + 1, end, l, r);
        ST P1 = query(2 * node, start, mid, l, r);
        ST P2 = query(2 * node + 1, mid + 1, end, l, r);
        return P1 + P2;
    }
};

segtree st;


void dfs(int node)
{
	for(int i:tree[node])
	{
		if(!vis[i])
		{
			vis[i] = true;
            ans[i] = max(1 + st.query(1, 1, N-1, 1, W[i]-1).sum, st.query(1, 1, N-1, 1, N).sum);
			int z = st.query(1, 1, N-1, W[i], W[i]).sum;
			st.update(1, 1, N-1, W[i], ans[i]);
			dfs(i);
			st.update(1, 1, N-1, W[i], z);
		}
	}
}


int32_t main()
{
    fastio;
    //freopen("file.in", "r", stdin);
    //freopen("file.out", "w", stdout);
    cin >> n;
    vector<pair<int, int>> weights(n);
    st.A.assign(N, 0);
    st.build(1, 0, N-1);
    for(int i=0;i<n;i++)
    {
    	cin >> weights[i].first;
    	weights[i].second = i+1;
    }
    sort(all(weights));
    int curr = 2, last = -1;
    for(int i=0;i<n;i++)
    {
    	int id = weights[i].second;
    	if(last == weights[i].first)
    		W[id] = curr-1;
    	else
    	{
    		W[id] = curr;
    		last = weights[i].first;
    		curr++;
    	}
    }
    for(int i=1;i<n;i++)
    {
    	int a, b;
    	cin >> a >> b;
    	tree[a].pb(b);
    	tree[b].pb(a);
    }
    vis[1] = 1;
    ans[1] = 1;
    st.update(1, 1, N-1, W[1], 1);
    dfs(1);
    for(int i=1;i<=n;i++)
    {
    	cout << ans[i] << "\n";
    }
    // prc(W, W+n+1);
    return 0;
}

