You are given a rooted tree with root in vertex 1. Each vertex is coloured in some colour.

Let's call colour c dominating in the subtree of vertex v if there are no other colours that appear in the subtree of vertex v more times than colour c. So it's possible that two or more colours will be dominating in the subtree of some vertex.

The subtree of vertex v is the vertex v and all other vertices that contains vertex v in each path to the root.

For each vertex v find the sum of all dominating colours in the subtree of vertex v.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of vertices in the tree.

The second line contains n integers ci (1 ≤ ci ≤ n), ci — the colour of the i-th vertex.

Each of the next n - 1 lines contains two integers xj, yj (1 ≤ xj, yj ≤ n) — the edge of the tree. The first vertex is the root of the tree.

Output

Print n integers — the sums of dominating colours for each vertex.

Examples

Input

4
1 2 3 4
1 2
2 3
2 4


Output

10 9 3 4


Input

15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13


Output

6 5 4 3 2 3 3 1 1 3 2 2 1 2 3
#include <bits/stdc++.h>
using namespace std;
const int DIM = 1e5 + 5;
int Cnt_Color[DIM], Color[DIM], N, Sz[DIM], Apmax[DIM];
long long Spcd[DIM];
bool Heavy[DIM];
vector<int> edge[DIM];
void get_sz(int nod, int father) {
  Sz[nod] = 1;
  for (auto son : edge[nod]) {
    if (son != father) {
      get_sz(son, nod);
      Sz[nod] += Sz[son];
    }
  }
}
void add(int nod, int father, int x, int &Ans, long long &S) {
  Cnt_Color[Color[nod]] += x;
  if (Ans < Cnt_Color[Color[nod]])
    Ans = Cnt_Color[Color[nod]], S = Color[nod];
  else if (Ans == Cnt_Color[Color[nod]])
    S += Color[nod];
  for (auto son : edge[nod]) {
    if (son != father && Heavy[son] == false) add(son, nod, x, Ans, S);
  }
}
void dfs(int nod, int father, bool keep) {
  int Max_Sz = -1, HeavyChild = -1;
  for (auto son : edge[nod]) {
    if (son != father && Sz[son] > Max_Sz) Max_Sz = Sz[son], HeavyChild = son;
  }
  for (auto son : edge[nod]) {
    if (son != father && son != HeavyChild) dfs(son, nod, false);
  }
  if (HeavyChild != -1) {
    dfs(HeavyChild, nod, true);
    Heavy[HeavyChild] = true;
    Apmax[nod] = Apmax[HeavyChild];
    Spcd[nod] = Spcd[HeavyChild];
  }
  add(nod, father, 1, Apmax[nod], Spcd[nod]);
  if (HeavyChild != -1) Heavy[HeavyChild] = false;
  if (keep == false) {
    int Aux = 0;
    long long Aux1 = 0;
    add(nod, father, -1, Aux, Aux1);
  }
}
int main() {
  cin >> N;
  for (int i = 1; i <= N; i++) cin >> Color[i];
  for (int i = 1; i < N; i++) {
    int x, y;
    cin >> x >> y;
    edge[x].push_back(y);
    edge[y].push_back(x);
  }
  get_sz(1, 0);
  dfs(1, 0, true);
  for (int i = 1; i <= N; i++) cout << Spcd[i] << " ";
  return 0;
}
