CF600E.Lomsat gelral

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 $v$ .

The first line contains integer $n$ ( $1<=n<=10^{5}$ ) — the number of vertices in the tree.

The second line contains $n$ integers $c_{i}$ ( $1<=c_{i}<=n$ ), $c_{i}$ — the colour of the $i$ -th vertex.

Each of the next $n-1$ lines contains two integers $x_{j},y_{j}$ ( $1<=x_{j},y_{j}<=n$ ) — the edge of the tree. The first vertex is the root of the tree.

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