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## I. Jack's New Word

Time limit: 0.5 second
Memory limit: 64 MB
Jack is very laconical. He doesn't like to repeat the same thing several times. That is why the binary word which Jack has just written on a fence has no non-empty substrings of the form xyxyx, where x and y are (possibly empty) binary strings and the length of y doesn't exceed the length of x multiplied by two. For example, the Jack's word can't contain substrings `000` or `1001001` but can contain substrings `1010` and `001100110`.
Fox Trot, who was passing by, asked Jack to describe the way he obtained his new word. Jack told him that first there was an empty word on a fence and then… The following story by Jack contains only phrases of the form:
• “I prefixed the current word with `0` (or `1`)”;
• “I suffixed the current word with `0` (or `1`)”;
• “I replaced all zeroes with string `01`, and all ones with string `10`”.
Fox Trot is interested in that, but he will get bored after one hundred such phrases. Will Jack be able to finish his story?

### Input

The only input line contains a Jack's new word. This word is non-empty, consists of zeroes and ones and its length doesn't exceed 105.

### Output

If Jack has to say more than one hundred phrases to describe his word, output “−1”. In the other case output any possible description. The first line should contain a number of phrases k (1 ≤ k ≤ 100). The following k lines should describe these phrases in the order they should be pronounced. If a word should be prefixed with symbol c, output “front c”. If a word should be suffixed with symbol c, output “back c”. If all `0` should be replaced with `01` and all `1` should be replaced with `10`, output “double”.

### Sample

inputoutput
```011010011
```
```5
back 1
front 0
double
double
back 1```

### Notes

According to the story from sample output, Jack consecutively obtained: an empty string, “1”, “01”, “0110”, “01101001”, “011010011”.
Problem Author: Alex Samsonov
Problem Source: XV Open USU Championship
To submit the solution for this problem go to the Problem set: 1782. Jack's New Word