Lomsat gelral
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.
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.
Print n integers — the sums of dominating colours for each vertex.
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.
4<br>1 2 3 4<br>1 2<br>2 3<br>2 4<br>
15<br>1 2 3 1 2 3 3 1 1 3 2 2 1 2 3<br>1 2<br>1 3<br>1 4<br>1 14<br>1 15<br>2 5<br>2 6<br>2 7<br>3 8<br>3 9<br>3 10<br>4 11<br>4 12<br>4 13<br>
10 9 3 4<br>
6 5 4 3 2 3 3 1 1 3 2 2 1 2 3<br>