# Luhn

Given a number determine whether or not it is valid per the Luhn formula.

The Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers.

The task is to check if a given string is valid.

## Validating a Number

Strings of length 1 or less are not valid.

Spaces are allowed in the input, but they should be stripped before checking.

All other non-digit characters are disallowed.

### Example 1: valid credit card number

`4539 3195 0343 6467`

The first step of the Luhn algorithm is to double every second digit, starting from the right.

We will be doubling

`4_3_ 3_9_ 0_4_ 6_6_`

If doubling the number results in a number greater than 9 then subtract 9 from the product.

The results of our doubling:

`8569 6195 0383 3437`

Then sum all of the digits:

`8+5+6+9+6+1+9+5+0+3+8+3+3+4+3+7 = 80`

If the sum is evenly divisible by 10, then the number is valid.

This number is valid!

### Example 2: invalid credit card number

`8273 1232 7352 0569`

Double the second digits, starting from the right

`7253 2262 5312 0539`

Sum the digits

`7+2+5+3+2+2+6+2+5+3+1+2+0+5+3+9 = 57`

57 is not evenly divisible by 10, so this number is not valid.