You are given a rooted tree consisting of $n$ nodes. The nodes are numbered $1,2,\ldots,n$ , and node $1$ is the root. Each node has a color.
Your task is to determine for each node the number of distinct colors in the subtree of the node.
The first input line contains an integer $n$ : the number of nodes. The nodes are numbered $1,2,\ldots,n$ .
The next line consists of $n$ integers $c_1,c_2,\ldots,c_n$ : the color of each node.
Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$ : there is an edge between nodes $a$ and $b$ .
Print $n$ integers: for each node $1,2,\ldots,n$ , the number of distinct colors.
5 2 3 2 2 1 1 2 1 3 3 4 3 5\n · · · · \n · \n · \n · \n · \n
3 1 2 1 1· · · · \n