Collatz Sequence Analysis

This problem involves analyzing the famous Collatz sequence. Given an integer \( N \), you are required to generate the sequence based on the following rules:

• If \( N \) is even, then \( N = \frac{N}{2} \).
• If \( N \) is odd, then \( N = 3N + 1 \).

The sequence terminates when \( N = 1 \). Your task is to determine:

• The length of the sequence (i.e., the number of terms including the starting number).
• The maximum value encountered in the sequence.
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You will be given multiple test cases. For each test case, output the sequence length and the maximum value separated by a space.

inputFormat

The first line contains an integer \( T \) representing the number of test cases. Each of the following \( T \) lines contains a single integer \( N \), for which you must calculate the required Collatz sequence information.

outputFormat

For each test case, output a single line containing two space-separated integers: the length of the Collatz sequence and the maximum value encountered in the process.

## sample

3
5
3
6

6 16
8 16
9 16

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