Ones

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Given any integer $0 \le n \le 100\, 000$ not divisible by $2$ or $5$, some multiple of $n$ is a number which in decimal notation is a sequence of $1$’s. How many digits are in the smallest such a multiple of $n$? There are at most $1000$ test cases.

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Sample Input 1 Sample Output 1
3
7
9901
3
6
12