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Problem 2. 6174

The number $6174$ is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule:

1. Take any four-digit number, using at least two different digits (leading zeros are allowed).
2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat.

The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding $7641 - 1467 = 6174$. For example, choose $1459$:

Write a program that simulates this process. Note that

• The input number should not contain more than 4 digits and should contain at least two different digits (i.e. not a repdigit like $1111$, $2222$, ...). These numbers are said to be invalid.

• The input number may contain less than 4 digits. For example, start with $9$:

  $$\begin{aligned} 9000&-9&=8991\\ 9981&-1899&=8082\\ 8820&-288&=8532\\ 8532&-2358&=6174 \end{aligned} $$

Hint

The functions given in [Problem 1] Basic knowledge may be helpful for this problem.

Input format

On the first line, a nonnegative integer $n$.

Then $n$ lines follow, the $i$-th of which contains a nonnegative integer $x_i$. It is guaranteed that $x_i$ is representable by int.

Output format

For each of the $n$ input integers, either report that it is invalid or simulate the Kaprekar's routine and print the steps (see below).

If for some $i$ the integer $x_i$ contains more than 4 digits, print xxx contains more than 4 digits. where xxx is replaced with $x_i$. If $x_i$ contains no more than 4 digits but is a repdigit, print xxx is a repdigit. where xxx is replaced with $x_i$.

A step in the Kaprekar's routine should be printed in the form xxx - yyy = zzz, where xxx, yyy and zzz are replaced with the corresponding numbers. Note that leading zeros are not printed (see the example below). The process stops when zzz reaches $6174$.

If the input is already $6174$, you should print nothing and start processing next input.

You don't have to start printing after all inputs are consumed! Do not waste efforts saving the things to be printed.

Example

Input

5
123456
0
22
4444
1459

Output

123456 contains more than 4 digits.
0 is a repdigit.
2200 - 22 = 2178
8721 - 1278 = 7443
7443 - 3447 = 3996
9963 - 3699 = 6264
6642 - 2466 = 4176
7641 - 1467 = 6174
4444 is a repdigit.
9541 - 1459 = 8082
8820 - 288 = 8532
8532 - 2358 = 6174

Note

Your program will not be compiled and linked against the math library, so do not use the functions in <math.h>.