CF1374B.Multiply by 2, divide by 6

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题目描述

You are given an integer $n$ . In one move, you can either multiply $n$ by two or divide $n$ by $6$ (if it is divisible by $6$ without the remainder).

Your task is to find the minimum number of moves needed to obtain $1$ from $n$ or determine if it's impossible to do that.

You have to answer $t$ independent test cases.

输入格式

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ( $1 \le n \le 10^9$ ).

输出格式

For each test case, print the answer — the minimum number of moves needed to obtain $1$ from $n$ if it's possible to do that or -1 if it's impossible to obtain $1$ from $n$ .

输入输出样例

输入#1

输出#1

说明/提示

Consider the sixth test case of the example. The answer can be obtained by the following sequence of moves from the given integer $15116544$ :

Divide by $6$ and get $2519424$ ;
divide by $6$ and get $419904$ ;
divide by $6$ and get $69984$ ;
divide by $6$ and get $11664$ ;
multiply by $2$ and get $23328$ ;
divide by $6$ and get $3888$ ;
divide by $6$ and get $648$ ;
divide by $6$ and get $108$ ;
multiply by $2$ and get $216$ ;
divide by $6$ and get $36$ ;
divide by $6$ and get $6$ ;
divide by $6$ and get $1$ .

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