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Doraemon's Number Game III

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Doraemon likes to play number game with Nobita.

One day, Doraemon came up with an idea, he gave a number a in base 10 and a number x (x < 10), and then he let Nobita multiplies the first digit of a with x and add the second digit of a, then multiplies x again and add the third digit of a. Do the above rules until there is only one digit (the leftmost digit of a is called the first digit).

For example, let a = 123, x = 2. Then, 123 → (1*2+2)*2+3=11 → 1*2+1=3. That is to say, Nobita should give the answer 3.

Sometimes a is too large, Nobita cannot work it out, can you help him?

#### Input

Input contains multiple cases, process to the end of file. Each case contains one line which contains only one number a (the length of a would not exceed 100000) as described above.

#### Output

For each case, you need to output the number when x = 1, 2 ... 9. You should output the nine numbers in one line separated by a single space.

```123
```

#### Sample Output

```6 3 4 9 8 7 9 9 9
```

Author: QU, Zhe
Contest: ZOJ Monthly, December 2010
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