Niebieskie ksi.eczki

Palindromes

 I stage contest

A word is a palindrome if and only if it remains the same when read backwards. A palindrome is even if it has an even positive number of letters.

The word abaaba is an example of an even palindrome.

An even palindrome decomposition of a word is its division into separate parts, every one of which is an even palindrome.

### Example

For the word
`bbaabbaabbbaaaaaaaaaaaabbbaa`
the following are even palindrome decompositions:
`bbaabb aabbbaaaaaaaaaaaabbbaa`
and
`bb aa bb aa bb baaaaaaaaaaaab bb aa`

The first decomposition consists of the least possible number of even palindromes, and the second one is a decomposition having the maximal possible number of even palindromes.

Notice that a word might have many different even palindrome decompositions or might have no such a decomposition.

Write a program that:
• reads a word from the text file PAL.IN and examines whether it can be decomposed into even palindromes,
• if not, then the program writes to the file PAL.OUT only one word NIE ("no"),
• if the word can be decomposed, then the program writes the decompositions of the word into the minimal and maximal number of even palindromes.

### Input

The input file PAL.IN contains one word consisting of at least 1 and at most 200 small letters of English alphabet. The word is written in one line with no spaces between letters.

We assume that the given word is written correctly in the file PAL.IN, and your program need not verify that.

### Output

The output file PAL.OUT should contain:
• only one word NIE
or
• in the first line - a sequence of words separated by spaces, forming a decomposition of the given word into the minimal number of even palindromes
• in the second line - a decomposition of the given word into the maximal number of even palindromes

### Examples

For the file PAL.IN:
`bbaabbaabbbaaaaaaaaaaaabbbaa`
your program should create the following file PAL.OUT:
```bbaabb aabbbaaaaaaaaaaaabbbaa
bb aa bb aa bb baaaaaaaaaaaab bb aa```
For the file PAL.IN:
`abcd`
your program should create the file PAL.OUT:
`NIE`
For the file PAL.IN:
`abaaba`
your program should create the file PAL.OUT:
```abaaba
abaaba```

Your program should look for the file PAL.IN in the current directory and create the file PAL.OUT also in the current directory. The source file containing the program written by you should be named PAL.???, where ??? are substituted by at most three-letter abbreviation of the programming language used. The same program in an executable form should be written in a file PAL.EXE.