ISBN Validator

Every book published worldwide is assigned an ISBN-13 (International Standard Book Number). Bookstores, libraries, and online retailers use this 13-digit code to uniquely identify books in their inventory systems.

An ISBN-13 has the format: $d_1{d}_2{d}_3{d}_4{d}_5{d}_6{d}_7{d}_8{d}_9{d}_{10}{d}_{11}{d}_{12}{d}_{13}$

The first 12 digits identify the book. The 13th digit is a check digit, calculated as follows:

1. Multiply each of the first 12 digits by alternating weights of $1$ and $3$ (first digit times $1$, second digit times $3$, third digit times $1$, and so on).
2. Sum all 12 weighted values.
3. Compute the remainder when dividing the sum by $10$.
4. If the remainder is $0$, the check digit is $0$. Otherwise, the check digit is $10$ minus the remainder.

Given a 13-digit ISBN string, determine if it is VALID or INVALID.

Then, regardless of whether it was valid, output the CORRECT check digit (the one computed by the algorithm above).

Input: A single line containing a 13-character string of digits.

Output: Two lines. The first line is VALID or INVALID. The second line is the correct check digit (a single digit $0$-$9$).

9780306406157

VALID
7