Lomsat gelral

Problem Source

CF 600E

Problem Description

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 Format

The first line contains integer $n\ (1 \le n \le 10^5)$ — the number of vertices in the tree.

The second line contains $n$ integers $c_i\ (1 \le c_i \le n)$, $c_i$ — the colour of the $i$-th vertex.

Each of the next $n - 1$ lines contains two integers $x_j, y_j\ (1 \le x_j, y_j \le n)$ — the edge of the tree. The first vertex is the root of the tree.

Output Format

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

Sample Input 1

4
1 2 3 4
1 2
2 3
2 4

Sample Output 1

10 9 3 4

Sample Input 2

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

Sample Output 2

6 5 4 3 2 3 3 1 1 3 2 2 1 2 3