In C$++-$Since the checksum may sometimes need to be as large as $10$ to guarantee divisibility by $11,$ and the representation

of the number $10$ requires $2$ digits $(1$ to mamy$),$ a special symbol was selected by Acme Company to represent $10,$ and

that is the role played by $\text{'}$A:

The algorithm used to check a product number is relatively simple. Two sums, sum$1$ and sum$2,$ are computed over the

digits of the product number, with sum $2$ being the sum of the partial sums in sum$1$ after each digit of the product

number is added to it$.$ The checksum is the value that, when added to sum $2,$ makes the total sum evenly divisible by

An example will clarify the procedure. Consider the $($correct$)$ product number $013-162-959-$A$.$ First look at the

calculation of sum$1$:

The calculation of sum $2$ is done by computing the total of the partial sums in the calculation of sum$1.$

We now verify the correctness of the product number by noting that $165$ is$,$ indeed, evenly divisible by $11.$

Steps

To solve this problem, you can follow these steps:

Read the input using input redirection $"",$ one line at a time, and for each line, preprocess it by removing any non$-$

digit characters $($don$\text{'}$t forget $\text{'}$A$\text{'})$

Check if the preprocessed input contains exactly ten characters, and if not, print "incorrect product number".

Validate the input by checking if the first nine characters are digits and the last character is either a digit or the

letter $\text{'}$A:

Compute the sum $1$ and sum $2$ sums, as described in the problem statement.

Check if the sum$2$ sum is divisible by $11.$ If it is$,$ print the product number in the normalized form, followed by $"$is

correct." Otherwise, print "incorrect product number."

Input specification

The input data for this problem will contain one candidate product number per line of input, perhaps preceded and$/$or

followed by additional spaces. No line will contain more than $80$ characters, but the candidate product number may

contain illegal characters and more or fewer than the required ten digits. Valid product numbers may include hyphens

at arbitrary locations. The end of file marks the end of the input data.

In the context of this problem, legal characters for a product number are:

Digits $(0-9)$: The first nine characters of a product number must be digits. These digits represent the actual

product identifier.

Hyphens $(-)$: Hyphens may be included at various places in the product number to make them easier to read.

However, they have no other significance and can appear in arbitrary locations.

Capital $\text{'}$A$\text{'}$: The capital letter $\text{'}$A$\text{'}$ may appear as the tenth character in a product number, representing a checksum

value of $10.$