# UKSPC Practice Problems » Divisibility by Eleven

**Input file:** `div.in`

**Output file:** `div.out`

Write a program which accepts as input a positive integer and checks, using the algorithm described below, to see whether or not the integer is divisible by 11. This particular test for divisibility by 11 was given in 1897 by Charles L. Dodgson (a.k.a. Lewis Carroll).

## Algorithm

As long as the number being tested has more than two digits, form a new number by:

- deleting the units digit
- subtracting the deleted digit from the shortened number

The
remaining number is divisible by 11 if and only if the original number is
divisible by 11. *Note:* leading zeros are not considered part of the number and should not be
printed.

## Input Specification

The first number in the input file indicates the number of positive integers that follow. Each positive integer has a maximum of 50 digits. You may assume no leading zeros exist in the positive integers.

## Output Specification

For each positive integer in the input, the output consists of a series of numbers formed as a digit is deleted and subtracted, followed by a message indicating whether or not the original number is divisible by 11. Outputs for different positive integers are separated by blank lines.

## Sample input

1 12345678901234567900

## Sample output

*Note:* there is a typo in the 10^{th} and the following lines in
the sample output and such a message was sent to all the contestants during the competition.

12345678901234567900 1234567890123456790 123456789012345679 12345678901234558 1234567890123447 123456789012337 12345678901226 1234567890116 123456789005 12345678995 1234567884 123456784 12345674 1234563 123453 12342 1232 121 11 The number 12345678901234567900 is divisible by 11.