Interview Questions/Coding/Reactor Compression Steps

Reactor Compression Steps

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Medium

Reactor Compression Steps

A reactor value can be changed with two operations: divide it by 6 if it is currently divisible by 6, or multiply it by 2. For each starting value n, find the minimum number of operations needed to make the value exactly 1. If no sequence of allowed operations can reach 1, print -1. Input Format: The first line contains t, the number of test cases. Each test case contains n. Output Format: For each test case, print the minimum operation count, or -1 if the target cannot be reached.

Examples

Example 1

Input:

1
12

Output:

-1

Explanation: Dividing 12 by 6 gives 2, and from 2 the allowed operations cannot reach 1. Other allowed sequences also fail to reach exactly 1.

Approach hint

Start with the simplest clear approach, explain the trade-off, then move toward the cleaner answer.

Common mistake

Skipping assumptions, edge cases, or trade-offs can make an otherwise good answer feel incomplete.

solution.cpp