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;
struct point {
  int x, y;
  point() {}
  point(int a, int b) { x = a, y = b; }
};
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T power(T n, T p) {
  T res = 1;
  for (int i = 0; i < p; i++) res *= n;
  return res;
}
template <class T>
double getdist(T a, T b) {
  return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
template <class T>
T extract(string s, T ret) {
  stringstream ss(s);
  ss >> ret;
  return ret;
}
template <class T>
string tostring(T n) {
  stringstream ss;
  ss << n;
  return ss.str();
}
struct fast {
  fast() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
  }
} cincout;
map<int, int> mpp[100010];
set<pair<int, int>> ss[100010];
vector<int> adj[100010];
int color[100010], maxMap[100010], maxFreq[100010];
long long res[100010];
void dfs(int u, int prev) {
  int heavyChild = -1, mx = -1;
  for (auto v : adj[u]) {
    if (v == prev) continue;
    dfs(v, u);
    if (mx < (int)(mpp[maxMap[v]].size())) {
      heavyChild = v;
      mx = (int)(mpp[maxMap[v]].size());
    }
  }
  if (heavyChild == -1)
    maxMap[u] = u;
  else
    maxMap[u] = maxMap[heavyChild];
  mpp[maxMap[u]][color[u]]++;
  if (mpp[maxMap[u]][color[u]] > maxFreq[heavyChild])
    res[u] = color[u], maxFreq[u] = mpp[maxMap[u]][color[u]];
  else if (mpp[maxMap[u]][color[u]] == maxFreq[heavyChild])
    res[u] = color[u] + res[heavyChild], maxFreq[u] = mpp[maxMap[u]][color[u]];
  else
    res[u] = res[heavyChild], maxFreq[u] = maxFreq[heavyChild];
  for (auto v : adj[u]) {
    if (v == prev || v == heavyChild) continue;
    for (auto x : mpp[maxMap[v]]) {
      mpp[maxMap[u]][x.first] += x.second;
      if (mpp[maxMap[u]][x.first] > maxFreq[u]) {
        res[u] = x.first;
        maxFreq[u] = mpp[maxMap[u]][x.first];
      } else if (mpp[maxMap[u]][x.first] == maxFreq[u])
        res[u] += x.first;
    }
  }
}
int main() {
  int n, i, u, v;
  cin >> n;
  for (i = 1; i <= n; i++) cin >> color[i];
  for (i = 1; i < n; i++) {
    cin >> u >> v;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  dfs(1, -1);
  for (i = 1; i <= n; i++) cout << res[i] << ' ';
  return 0;
}
