Kinda familiar, isn't it?

Find the minimum value of $n$ that satisfies

• $(1):$ The first digit of $n$ is $1$ .
• $(2):$ When we move the first digit of $n$ to the last digit, the number we get will be $3n$ .

Details

• Let $n = \overline{a_{k}a_{k-1}...a_{2}a_{1}}$ be the $k$ digit number. The first digit is $a_{k}$ , and the last digit is $a_{1}$ .
• This problem is from Thailand POSN, which is held today. XD