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Here is how Mod 10 (Luhn algorithm) checksum validation works:

Remove the checksum digit, which is the last digit of the number.
Reverse positions of all remaining digits.
For every digit in an odd position, double its value and subtract 9 if result is over 9.
Sum up values from all digits.
Add the checksum digit to the sum.
If the sum is divisible by 10 (mod 10), then the checksum is valid.
For example, given credit card number "4417123456789113":

Remove the checksum digit "3": "441712345678911".
Reverse positions: "1198 7654 3217 144".
Double values on odd positions and subtract 9 if needed: "219856146227248".
Sum up all digits: 77.
Add the checksum digit: 80.
Mod 10: 0. So the checksum is valid.

def calculate_luhn_checksum(account_number):
    """Calculate the Luhn checksum digit for an account number."""
    # Convert to list of digits
    digits = [int(d) for d in str(account_number)]
    
    # Remove last digit (checksum placeholder)
    digits_without_checksum = digits[:-1]
    
    # Reverse the digits
    digits_without_checksum.reverse()
    
    # Apply Luhn transformation
    for i in range(len(digits_without_checksum)):
        if i % 2 == 0:  # Odd positions (0-based index)
            digits_without_checksum[i] *= 2
            if digits_without_checksum[i] > 9:
                digits_without_checksum[i] -= 9
    
    # Compute sum
    total_sum = sum(digits_without_checksum)
    
    # Compute checksum digit
    checksum_digit = (10 - (total_sum % 10)) % 10
    
    return checksum_digit