Tree Height and Leaf Count

You are given a binary tree defined by a set of nodes and edges. The tree is rooted at node 1. For each edge, you are given three integers u, v and c where c indicates whether v is the left child (when c = 0) or the right child (when c = 1) of u.

Your task is to construct the binary tree from the given description, and then compute two quantities for the tree:

• The height of the tree, defined as the number of edges in the longest path from the root to a leaf. In mathematical terms, if the height of a node is \(h\) then the height of the tree is \(\max_{leaf}(h)\).
• The number of leaf nodes in the tree.
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Note: A single node is considered a leaf, and its height is defined to be 0.

inputFormat

The input starts with an integer T indicating the number of test cases. Each test case is described as follows:

1. An integer N representing the number of nodes in the tree.
2. N-1 lines each containing three integers u, v, and c separated by spaces, representing an edge from node u to node v. Here, c = 0 indicates that v is the left child and c = 1 indicates that v is the right child of u.

All input is read from standard input (stdin).

outputFormat

For each test case, output two integers on a single line: the height of the tree and the number of leaf nodes, separated by a space. The output for all test cases should be printed on standard output (stdout), each on a new line.

## sample

1
1

0 1

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