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 ≤ 10⁵) — 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.