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>
const long long MAXN = 1e5 + 123;
using namespace std;
long long N;
long long c[MAXN];
long long h[MAXN], now;
struct Edge {
  long long u, v, next;
} e[MAXN << 1 | 1];
void addEdge(long long u, long long v) {
  now++;
  e[now].u = u;
  e[now].v = v;
  e[now].next = h[u];
  h[u] = now;
}
long long sz[MAXN], hv[MAXN];
void cut_tree(long long x, long long fa) {
  sz[x] = 1;
  long long mx = 0;
  for (long long i = h[x]; i; i = e[i].next) {
    const long long &v = e[i].v;
    if (v == fa) continue;
    cut_tree(v, x);
    sz[x] += sz[v];
    if (sz[v] > mx) {
      mx = sz[v];
      hv[x] = v;
    }
  }
}
long long ans[MAXN];
long long cnt_col[MAXN], tot, mAx;
long long stk[MAXN], tp;
void inserts(long long x) {
  stk[++tp] = x;
  long long &m = cnt_col[c[x]];
  m++;
  if (m > mAx) {
    tot = c[x];
    mAx = m;
  } else if (m == mAx) {
    tot += c[x];
  }
}
void addfs(long long x, long long fa) {
  inserts(x);
  for (long long i = h[x]; i; i = e[i].next) {
    const long long &v = e[i].v;
    if (v == fa) continue;
    addfs(v, x);
  }
}
void brt(long long x, long long fa, long long gfa) {
  inserts(fa);
  for (long long i = h[fa]; i; i = e[i].next) {
    const long long &v = e[i].v;
    if (v == x || v == gfa) continue;
    addfs(v, fa);
  }
}
void dfs(long long x, long long fa) {
  if (!hv[x]) {
    inserts(x);
    ans[x] = c[x];
    return;
  }
  for (long long i = h[x]; i; i = e[i].next) {
    const long long &v = e[i].v;
    if (v == fa || v == hv[x]) continue;
    long long nw = tp, nmAx = mAx, ntot = tot;
    dfs(v, x);
    while (tp > nw) cnt_col[c[stk[tp--]]]--;
    mAx = nmAx;
    tot = ntot;
  }
  dfs(hv[x], x);
  brt(hv[x], x, fa);
  ans[x] = tot;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> N;
  for (long long i = 1; i <= N; i++) cin >> c[i];
  for (long long i = 1; i <= N - 1; i++) {
    long long x, y;
    cin >> x >> y;
    addEdge(x, y);
    addEdge(y, x);
  }
  cut_tree(1, 0);
  dfs(1, 0);
  for (long long i = 1; i <= N; i++) cout << ans[i] << " ";
  cout << endl;
  return 0;
}
