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Contest: Task: Related: TaskF TaskH

Score : $600$ points

Problem Statement

We have a sequence $2,22,222,2222,\ldots$, where the $i$-th term is an $i$-digit integer whose digits are all $2$.

Where does a multiple of $K$ appear in this sequence for the first time? If the first multiple of $K$ is the $x$-th term of the sequence, print $x$; if there is no multiple of $K$, print -1.

Given $T$ cases, solve each of them.

Constraints

  • $1 \leq T \leq 200$
  • $1 \leq K \leq 10^8$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$T$
$\text{case}_1$
$\text{case}_2$
$\vdots$
$\text{case}_T$

Each case is in the following format:

$K$

Output

Print $T$ lines. The $i$-th line should contain the answer for $\text{case}_i$.

Sample Input 1

4
1
7
10
999983

Sample Output 1

1
6
-1
999982

We have four cases.

  • $2$ is a multiple of $1$.
  • None of $2,22,222,2222,22222$ is a multiple of $7$, but $222222$ is.
  • None of $2,22,\ldots$ is a multiple of $10$.