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 .

输入描述:

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.

输出描述:

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