#include <iostream>
#include <vector>

using namespace std;

#define rep(i,n) for(int i=0; i<(int)(n); i++)

const int N = 2e5;
int a[N], r[N], b[N+1];
vector<int> e[N];

int find(int v) {
  int l = 0, r = N;
  while(l + 1 < r) {
    int m = (r + l) / 2;
    if(b[m] < v) l = m;
    else r = m;
  }
  if(v <= b[l]) return l;
  else return r;
}

int dfs(int c, int p) {
  int x = find(a[c]), y = b[x];
  b[x] = a[c];
  r[c] = find(1e9+1);
  for(auto i : e[c]) {
    if(i != p) dfs(i, c);
  }
  b[x] = y;
  return 0;
}

int main() {
  int n;
  cin >> n;
  rep(i,n) cin >> a[i];
  rep(i,n-1) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    e[u].push_back(v);
    e[v].push_back(u);
  }

  rep(i,N+1) b[i] = 1e9+1;
  dfs(0, -1);

  rep(i,n) cout << r[i] << endl;
  return 0;
}