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 TAM = 100000 + 15;
const long long MOD = 1000000007LL;
const double PI = 3.14159265359;
long long add(long long x, long long y) { return (x + y + 2 * MOD) % MOD; }
long long mult(long long x, long long y) {
  return (add(x, 0) * add(y, 0)) % MOD;
}
long long fast_expo(long long x, long long y) {
  if (x == 0) return 0;
  if (y == 0) return 1;
  long long res = 1;
  long long mid = fast_expo(x, y / 2);
  if (y % 2 != 0) res = x;
  return mult(mult(mid, mid), res);
}
long long inver(long long x) { return fast_expo(x, MOD - 2); }
long long gcd(long long e1, long long e2) {
  if (e2 == 0) return e1;
  return gcd(e2, e1 % e2);
}
int n;
map<int, int> mapa[TAM];
int color[TAM];
vector<int> G[TAM];
long long dom[TAM];
int tam[TAM];
int cant[TAM];
void dfs_tam(int u, int pd = -1) {
  tam[u] = 1;
  for (int v : G[u]) {
    if (v != pd) {
      dfs_tam(v, u);
      tam[u] += tam[v];
    }
  }
}
void dfs(int u, int pd = -1) {
  int m = -1, val = -1;
  for (int v : G[u]) {
    if (v != pd) {
      if (tam[v] > val) {
        m = v;
        val = tam[v];
      }
    }
  }
  if (m == -1) {
    mapa[u][color[u]]++;
    dom[u] = color[u];
    cant[u] = 1;
    return;
  }
  for (int v : G[u]) {
    if (v != pd) {
      dfs(v, u);
    }
  }
  swap(mapa[u], mapa[m]);
  dom[u] = dom[m];
  cant[u] = cant[m];
  mapa[u][color[u]]++;
  if (mapa[u][color[u]] > cant[u]) {
    cant[u] = mapa[u][color[u]];
    dom[u] = 1LL * color[u];
  } else if (mapa[u][color[u]] == cant[u]) {
    dom[u] += 1LL * color[u];
  }
  for (int v : G[u]) {
    if (v != pd && v != m) {
      int k, t;
      for (map<int, int>::iterator it = mapa[v].begin(); it != mapa[v].end();
           it++) {
        k = it->first;
        t = it->second;
        mapa[u][k] += t;
        if (mapa[u][k] > cant[u]) {
          cant[u] = mapa[u][k];
          dom[u] = 1LL * k;
        } else if (mapa[u][k] == cant[u]) {
          dom[u] += 1LL * k;
        }
      }
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%d", &color[i]);
  int u, v;
  for (int i = 0; i < n - 1; i++) {
    scanf("%d%d", &u, &v);
    G[u - 1].push_back(v - 1);
    G[v - 1].push_back(u - 1);
  }
  dfs_tam(0);
  dfs(0);
  for (int i = 0; i < n; i++) cout << 1LL * dom[i] << " ";
  cout << endl;
  return 0;
}
