Lomsat gelral

难度：$\colorbox{purple}{\color{white}省选/NOI-}$

题面翻译

• 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 $c_i$。
• 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 $i\in[1,n]$，求出以 $i$ 为根的子树中，占主导地位的颜色的编号和。
• $n\le 10^5,c_i\le n$

题目描述

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 $v$ .

输入格式

The first line contains integer $n$ ( $1<=n<=10^{5}$ ) — 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.

输出格式

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

样例 #1

样例输入 #1

4
1 2 3 4
1 2
2 3
2 4

样例输出 #1

10 9 3 4

样例 #2

样例输入 #2

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

样例输出 #2

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