You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Suppose you have a special $$$x$$$-$$$y$$$-counter. This counter can store some value as a decimal number; at first, the counter has value $$$0$$$.

The counter performs the following algorithm: it prints its lowest digit and, after that, adds either $$$x$$$ or $$$y$$$ to its value. So all sequences this counter generates are starting from $$$0$$$. For example, a $$$4$$$-$$$2$$$-counter can act as follows:

1. it prints $$$0$$$, and adds $$$4$$$ to its value, so the current value is $$$4$$$, and the output is $$$0$$$;
2. it prints $$$4$$$, and adds $$$4$$$ to its value, so the current value is $$$8$$$, and the output is $$$04$$$;
3. it prints $$$8$$$, and adds $$$4$$$ to its value, so the current value is $$$12$$$, and the output is $$$048$$$;
4. it prints $$$2$$$, and adds $$$2$$$ to its value, so the current value is $$$14$$$, and the output is $$$0482$$$;
5. it prints $$$4$$$, and adds $$$4$$$ to its value, so the current value is $$$18$$$, and the output is $$$04824$$$.

This is only one of the possible outputs; for example, the same counter could generate $$$0246802468024$$$ as the output, if we chose to add $$$2$$$ during each step.

You wrote down a printed sequence from one of such $$$x$$$-$$$y$$$-counters. But the sequence was corrupted and several elements from the sequence could be erased.

Now you'd like to recover data you've lost, but you don't even know the type of the counter you used. You have a decimal string $$$s$$$ — the remaining data of the sequence.

For all $$$0 \le x, y < 10$$$, calculate the minimum number of digits you have to insert in the string $$$s$$$ to make it a possible output of the $$$x$$$-$$$y$$$-counter. Note that you can't change the order of digits in string $$$s$$$ or erase any of them; only insertions are allowed.

## Input Format
The first line contains a single string $$$s$$$ ($$$1 \le |s| \le 2 \cdot 10^6$$$, $$$s_i \in \{\text{0} - \text{9}\}$$$) — the remaining data you have. It's guaranteed that $$$s_1 = 0$$$.

## Output Format
Print a $$$10 \times 10$$$ matrix, where the $$$j$$$-th integer ($$$0$$$-indexed) on the $$$i$$$-th line ($$$0$$$-indexed too) is equal to the minimum number of digits you have to insert in the string $$$s$$$ to make it a possible output of the $$$i$$$-$$$j$$$-counter, or $$$-1$$$ if there is no way to do so.

## Examples
```input
0840
```
```output
-1 17 7 7 7 -1 2 17 2 7 
17 17 7 5 5 5 2 7 2 7 
7 7 7 4 3 7 1 7 2 5 
7 5 4 7 3 3 2 5 2 3 
7 5 3 3 7 7 1 7 2 7 
-1 5 7 3 7 -1 2 9 2 7 
2 2 1 2 1 2 2 2 0 1 
17 7 7 5 7 9 2 17 2 3 
2 2 2 2 2 2 0 2 2 2 
7 7 5 3 7 7 1 3 2 7
```

## Note
Let's take, for example, $$$4$$$-$$$3$$$-counter. One of the possible outcomes the counter could print is $$$0(4)8(1)4(7)0$$$ (lost elements are in the brackets).

One of the possible outcomes a $$$2$$$-$$$3$$$-counter could print is $$$0(35)8(1)4(7)0$$$.

The $$$6$$$-$$$8$$$-counter could print exactly the string $$$0840$$$.

Now solve the problem and return the code.