#include <iostream>
#include <map>
#include <set>
#include <algorithm>
#include <vector>
#include <sstream>
#include <string>
#include <functional>
#include <queue>
#include <deque>
#include <stack>
#include <limits>
#include <unordered_map>
#include <unordered_set>
#include <math.h>
#include <fstream>
#include <iterator>
#include <random>
#include <chrono>
 
 
#define forr(i,start,count) for (int i = (start); i < (start)+(count); ++i)
#define set_map_includes(set, elt) (set.find((elt)) != set.end())
#define readint(i) int i; cin >> i
#define readll(i) ll i; cin >> i
#define readdouble(i) double i; cin >> i
#define readstring(s) string s; cin >> s

typedef long long ll;
 
using namespace std;


template<class T>
class depth_first_search_iterator {
  public:
    stack<pair<T,T>> todo;
    function<bool(T)> notvisited;
    function<void(T)> mark_visited;
    function<set<T>(T)> neighbors;

    depth_first_search_iterator() {}

    depth_first_search_iterator(T start, function<bool(T)> notv, function<void(T)> mark_v, function<set<T>(T)> neigh) :
      notvisited(notv), mark_visited(mark_v), neighbors(neigh), end_(false), current(start), prev(start) {
          todo.push(make_pair(start, start)); operator++();
    }

    void operator++() {
        end_ = true;
        while (!todo.empty()) {
            current = todo.top().first; prev = todo.top().second; todo.pop();
            if (notvisited(current)) {
                mark_visited(current);
                for (const T x : neighbors(current)) {  todo.push(make_pair(x, current));   }
                end_ = false;
                break;
            }
        }
    }

    T operator*() {     return current;    }

    T previous() {  return prev;  }

    bool end() {  return end_;  }

  private:
    T current; // contains current node
    T prev;    // contains previous node
    bool end_;
};

template<class T>
class breadth_first_search_iterator {
  public:
    queue<pair<T,T>> todo;
    function<bool(T)> notvisited;
    function<void(T)> mark_visited;
    function<set<T>(T)> neighbors;

    breadth_first_search_iterator() {}

    breadth_first_search_iterator(T start, function<bool(T)> notv, function<void(T)> mark_v, function<set<T>(T)> neigh) :
      notvisited(notv), mark_visited(mark_v), neighbors(neigh), end_(false), current(start), prev(start) {
          todo.push(make_pair(start, start)); operator++();
    }

    void operator++() {
        end_ = true;
        while (!todo.empty()) {
            current = todo.front().first; prev = todo.front().second; todo.pop();
            if (notvisited(current)) {
                mark_visited(current);
                for (const T x : neighbors(current)) {  todo.push(make_pair(x, current));   }
                end_ = false;
                break;
            }
        }
    }

    T operator*() {     return current;    }

    T previous() {  return prev;  }

    bool end() {  return end_;  }

  private:
    T current;   // current node
    T prev;      // previous node
    bool end_;
};


template<class T>
class DirectedGraph {
    // allows only single connection between two vertices
    public:
      vector<T> vertices;
      vector<set<int>> neighbors;
      depth_first_search_iterator<int> dfs_iterator;
      breadth_first_search_iterator<int> bfs_iterator;
      vector<bool> visited;

      DirectedGraph() {}

      DirectedGraph(int n) {  for (int i = 0; i < n; ++i) {  AddVertex(0);  }   }

      bool EdgeExists(int i_from, int j_to) {
          return (neighbors[i_from].find(j_to) != neighbors[i_from].end());
      }

      void AddVertex(T val) {
          vertices.push_back(val);
          neighbors.push_back(set<int>());      }

      void AddEdge(int i_from, int j_to) {
          if (!EdgeExists(i_from, j_to)) {     neighbors[i_from].insert(j_to);      }
      }

      T& operator[](int i) {      return vertices[i];      }

      void RemoveEdge(int i_from, int j_to) {
          if (EdgeExists(i_from, j_to)) {
          neighbors[i_from].erase(find(neighbors[i_from].begin(), neighbors[i_from].end(), j_to));      } }

      DirectedGraph<T> Transpose() {
          DirectedGraph<T> ret;
          for (auto x : vertices) {  ret.AddVertex(x);   }
          for (int i_from = 0; i_from < vertices.size(); ++i_from) {
              for (int j_to : neighbors[i_from]) {
                  ret.AddEdge(j_to, i_from);
              }
          }
          return ret;      }

      int vertices_count() {   return vertices.size();  }

      void dfs_init(int start) {
          visited = vector<bool>(vertices.size(), false);
          dfs_iterator = depth_first_search_iterator<int>(start, [this](int x){ return !visited[x]; }, [this](int x) { visited[x] = true;  },
            [this](int x) {  return neighbors[x];  } );
      }

      void bfs_init(int start) {
          visited = vector<bool>(vertices.size(), false);
          bfs_iterator = breadth_first_search_iterator<int>(start, [this](int x){ return !visited[x]; }, [this](int x) { visited[x] = true;  },
            [this](int x) {  return neighbors[x];  } );
      }

      void print_() {
          forr(i, 0, vertices.size()) {
              for (auto x : neighbors[i]) {
                  cout << i << "->" << x << endl;
              }
          }
      }

};

template<class T>
class Graph {
    // allows only single connection between two vertices
    public:
      vector<T> vertices;
      vector<set<int>> neighbors;
      depth_first_search_iterator<int> dfs_iterator;
      breadth_first_search_iterator<int> bfs_iterator;
      vector<bool> visited;

      Graph() {}

      Graph(int n) {  for (int i = 0; i < n; ++i) {  AddVertex(0);  }   }

      void AddVertex(T val) {
          vertices.push_back(val);
          neighbors.push_back(set<int>());      }

      bool EdgeExists(int i, int j) {
          return (neighbors[i].find(j) != neighbors[i].end());
     }

      void AddEdge(int i, int j) {
          if (!EdgeExists(i,j)) {
            neighbors[i].insert(j);
            if (i != j) {         neighbors[j].insert(i);         } 
          }
      }

      T& operator[](int i) {      return vertices[i];      }

      void RemoveEdge(int i, int j) {
          if (EdgeExists(i,j)) {
            neighbors[i].erase(find(neighbors[i].begin(), neighbors[i].end(), j));
            neighbors[j].erase(find(neighbors[j].begin(), neighbors[j].end(), i));
          }
      }

      void dfs_init(int start) {
          visited = vector<bool>(vertices.size(), false);
          dfs_iterator = depth_first_search_iterator<int>(start, [this](int x){ return !visited[x]; }, [this](int x) { visited[x] = true;  },
            [this](int x) {  return neighbors[x];  } );
      }

      void bfs_init(int start) {
          visited = vector<bool>(vertices.size(), false);
          bfs_iterator = breadth_first_search_iterator<int>(start, [this](int x){ return !visited[x]; }, [this](int x) { visited[x] = true;  },
            [this](int x) {  return neighbors[x];  } );
      }

      void print_() {
          forr(i, 0, vertices.size()) {
              for (auto x : neighbors[i]) {
                  if (i <= x) {  cout << i << "-" << x << endl;  }                  
              }
          }
      }
};

vector<bool> visited(200001, false);

void DoTheDeed(Graph<int>& g, vector<int>& tail, int& length, vector<int>& ans, int root) {
        visited[root] = true;
        auto b = tail.begin(), e = tail.begin() + length;
        int it = 0;
        if (length>0) {     it = lower_bound(b, e, g[root]) - tail.begin();       }
              
        // If not present change the tail element to v[i]  
        int index_before, val_before;
        bool have_increased = false;
        if (it == length)      {  
            index_before = length; val_before = tail[length];
            tail[length] = g[root];  length++; have_increased = true;   }   else    { 
                index_before = it; val_before = tail[it];
                tail[it] = g[root];   }
        ans[root] = length;
        for (auto nn : g.neighbors[root]) {
            if (!visited[nn]) {
                DoTheDeed(g, tail, length, ans, nn);
            }
        }
        tail[index_before] = val_before;
        if (have_increased) {length--;}
} 

int main()   {
    cout.precision(17);
    ll modd = 1000 * 1000 * 1000 + 7;
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    uniform_int_distribution<int> rand_gen(0, modd);   // rand_gen(rng) gets the rand no
    ll infinit = 10000000000000000;

//    auto start = chrono::steady_clock::now();

//    readint(test_cases);
    int test_cases = 1;
    forr(t, 1, test_cases) {
        readint(n);
        Graph<int> g(n);
        forr(i,0,n) {readint(kk); g[i]=kk;}
        forr(i,0,n-1) {readint(aa); readint(bb); g.AddEdge(aa-1, bb-1);}

        vector<int> tail(n, 0);
        int length = 0;

        vector<int> ans(n, 0);
        DoTheDeed(g, tail, length, ans, 0);

        for(auto x : ans) {
            cout << x << endl;
        }
        
    }

//    auto end = chrono::steady_clock::now();
//    cout << chrono::duration_cast<chrono::milliseconds>(end - start).count() << endl;

    return 0;
}

Measured memory_bytes: 50908