The Fibonacci sequence is defined by the recurrence relation:

$F_n=F_{n-1}+F_{n-2},$ where $F_1=1$ and $F_2=1.$

Hence the first $12$ terms will be:

$F_1=1$

$F_2=1$

$F_3=2$

$F_4=3$

$F_5=5$

$F_6=8$

$F_7=13$

$F_8=21$

$F_9=34$

$F_{10}=55$

$F_{11}=89$

$F_{12}=144$

The $12$ th term, $F_{12},$ is the first term to contain three digits.

Write a function in Python that takes an input $n$ and returns the index of the first term in the Fibonacci sequence to contain $n$ digits?

$($Hint: store the values of the previous two Fibonacci numbers$)$