Problem J. Javanese Cryptoanalysis

Author:ACM ICPC NEERC 2008 Jury | Mikhail Dvorkin   Time limit:2 sec
Input file:javanese.in   Memory limit:256 Mb
Output file:javanese.out  

Statement

Javanese is the language of the people in the Central and Eastern parts of the island of Java, Indonesia.

In 1926, a standard orthography using the English Alphabet was created for the Javanese language. This writing system uses all letters from A to Z. The five letters A, E, I, O, and U are vowels, while all other letters are consonants. In Javanese words vowels and consonants always alternate. This property is quite useful when deciphering encrypted Javanese texts.

A text s consists of words, each word contains only capital letters. Let's call text s legitimate if in each word of s vowels and consonants alternate (no two vowels and no two consonants are located next to each other).

A simple substitution cipher is applied to a text s. That is, a bijection f: A ↦ A is chosen, where A is the set of capital letters. The encoded text t is obtained from s by substituting each letter c with f(c).

You're given the encoded text t. Find any legitimate text s that can be encoded as t, or detect that there is no such legitimate s.

Input file format

The input file contains the encoded text t, a list of words separated by spaces and/or line breaks. Each word consists only of capital letters (A to Z).

The input file contains no more than 105 characters.

Output file format

If the text t cannot be an encoded legitimate text, output only one word "impossible".

Otherwise, output any legitimate text s that can be encoded into t. Separate words of s with spaces and/or line breaks. All letters in s should be capital.

Sample tests

No. Input file (javanese.in) Output file (javanese.out)
1
O RISK LIP FOCUS LUCKY
A CODE FOR VALID FILES
2
NEERC
impossible

0.080s 0.011s 13