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 .

• 有一棵 n 个结点的以 1 号结点为根的有根树。
• 每个结点都有一个颜色，颜色是以编号表示的， i 号结点的颜色编号为 ci。
• 如果一种颜色在以 x 为根的子树内出现次数最多，称其在以 x 为根的子树中占主导地位。显然，同一子树中可能有多种颜色占主导地位。
• 你的任务是对于每一个 i∈[1,n]，求出以 i 为根的子树中，占主导地位的颜色的编号和。
• n≤10⁵,ci≤n

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.

样例二：
输入：

15
1 2 3 1 2 3 3 1 1 3 2 2 1 2 3
1 2
1 3
1 4
1 14
1 15
2 5
2 6
2 7
3 8
3 9
3 10
4 11
4 12
4 13

输出：

6 5 4 3 2 3 3 1 1 3 2 2 1 2 3

数据结构 线段树 树状数组