Our everyday number system in the UK and many other parts of the world is a base$-10$ system using Arabic numerals, namely the digits $0,1,$dots,$9.$ Integers larger than $9$ are

represented by sequences of these elementary numerals. The numerical value encoded by such a sequence is determined by multiplying each numeral by ${10}^k,$ where $k$ is the

position of the numeral counted from the back and starting at zero, and then summing together the contributions from all numerals. For example,

$5207=5{10}^3+2{10}^2+0{10}^1+7{10}^3$

The built$-$in int function in Python can take a string $($type str$)$ representing such a number and convert it to a Python integer $($type int$).$ Write a similar function convert$\_$base$9\_$int

that takes a string and converts it to a Python integer according to the following number system:

the base is $9,$ i$.$e$,$ the individual digits have to be multiplied by powers of $9$ to obtain the numerical value;

digits are represented by lower$-$case letters $\text{'}a\text{'},\text{'}$b$\text{'},\text{'}$c$\text{'},\text{'}$d$\text{'},...,$ i$.$e$.,\text{'}$a$\text{'}$ is equivalent to the digit $0,\text{'}b\text{'}$ is equivalent to the digit $1,$ and so on$.$

For example,

defe $=39^3+29^2+59^1+29^9=2396$

Answer: $($penalty regime: $0,0,0,0,50,50\%)$