/*
     ॐ त्र्यम्बकं यजामहे सुगन्धिं पुष्टिवर्धनम् |
     उर्वारुकमिव बन्धनान्मृत्योर्मुक्षीय माऽमृतात् ||
*/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define int            long long int
#define F              first
#define S              second
#define pb             push_back
#define si             set <int>
#define vi             vector <int>
#define pii            pair <int, int>
#define vpi            vector <pii>
#define vpp            vector <pair<int, pii>>
#define mii            map <int, int>
#define mpi            map <pii, int>
#define spi            set <pii>
#define endl           "\n"
#define sz(x)          ((int) x.size())
#define all(p)         p.begin(), p.end()
#define double         long double
#define que_max        priority_queue <int>
#define que_min        priority_queue <int, vi, greater<int>>
#define bug(...)       __f (#__VA_ARGS__, __VA_ARGS__)
#define print(a)       for(auto x : a) cout << x << " "; cout << endl
#define print1(a)      for(auto x : a) cout << x.F << " " << x.S << endl
#define print2(a,x,y)  for(int i = x; i < y; i++) cout<< a[i]<< " "; cout << endl

inline int power(int a, int b)
{
     int x = 1;
     while (b)
     {
          if (b & 1) x *= a;
          a *= a;
          b >>= 1;
     }
     return x;
}

typedef tree<pii, null_type, less<pii>, rb_tree_tag, tree_order_statistics_node_update> Set;

template <typename Arg1>
void __f (const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << endl; }
template <typename Arg1, typename... Args>
void __f (const char* names, Arg1&& arg1, Args&&... args)
{
     const char* comma = strchr (names + 1, ',');
     cout.write (names, comma - names) << " : " << arg1 << " | "; __f (comma + 1, args...);
}

const int N = 200005;
int a[N], n, m, k;

struct info
{
     int x;
     info () : x(0) {};
};
struct SegTree
{
     int N;
     vector<info> st;

     void init(int n)
     {
          N = n;
          st.resize(4 * N + 5);
     }

     void merge(info &cur, info &l, info &r)
     {
          cur.x = max(l.x , r.x);
     }
     info Query(int node, int L, int R, int i, int j)
     {
          if (j < L || i > R)
               return info();
          if (i <= L && R <= j)
               return st[node];
          int M = (L + R) / 2;
          info left = Query(node * 2, L, M, i, j);
          info right = Query(node * 2 + 1, M + 1, R, i, j);
          info cur;
          merge(cur, left, right);
          return cur;
     }

     void Update(int node, int L, int R, int pos, int val)
     {
          if (L == R)
          {
               st[node].x = val;
               return;
          }
          int M = (L + R) / 2;
          if (pos <= M)
               Update(node * 2, L, M, pos, val);
          else
               Update(node * 2 + 1, M + 1, R, pos, val);

          merge(st[node], st[node * 2], st[node * 2 + 1]);
     }

     info query(int l, int r) { return Query(1, 1, N, l, r); }

     void update(int pos, int val) { Update(1, 1, N, pos, val); }

} seg;

vi g[N];
int ans[N];

void dfs(int i, int p)
{
     int x = seg.query(1, a[i] - 1).x;
     int cur = seg.query(a[i], a[i]).x;

     // bug(i, x, cur);

     seg.update(a[i], x + 1);
     ans[i] = seg.query(1, n).x;

     for (auto x : g[i])
     {
          if (x != p)
          {
               dfs(x, i);
          }
     }
     seg.update(a[i], cur);
}
void init(int edge)
{
     for (int i = 0; i < edge; i++)
     {
          int x, y; cin >> x >> y;
          g[x].pb(y);
          g[y].pb(x);
     }
}

void solve()
{
     cin >> n;
     mii mp;
     for (int i = 1; i <= n; i++)
     {
          cin >> a[i];
          mp[a[i]];
     }
     int cnt = 0;
     for (auto &x : mp)
          x.S = ++cnt;

     for (int i = 1; i <= n; i++)
          a[i] = mp[a[i]];

     seg.init(n);
     init(n - 1);

     dfs(1, 0);
     for (int i = 1; i <= n; i++)
          cout << ans[i] << endl;

}

int32_t main()
{
     ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

     cout << setprecision(9) << fixed;
     clock_t z = clock();
     solve();
     cerr << "Run Time : " << ((double)(clock() - z) / CLOCKS_PER_SEC);

     return 0;
}

Measured memory_bytes: 51520