E. Lomsat gelral
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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
41 2 3 41 22 32 4
Output
10 9 3 4
Input
151 2 3 1 2 3 3 1 1 3 2 2 1 2 31 21 31 41 141 152 52 62 73 83 93 104 114 124 13
Output
6 5 4 3 2 3 3 1 1 3 2 2 1 2 3