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Decrypt the Dragon Scroll
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 484Accepted: 142

Description

Those who have see the film of "Kong Fu Panda" must be impressive when Po opens the dragon scroll, because nothing was recorded on it! Po was surprising at the situation; Tai Lung and Master Shifu were also surprising since no body believes that the mystic dragon scroll is just a blank paper. After Tai Lung was defeated, Po found Master Wugui’s Diary and know that the dragon scroll recorded some messages long long years ago, but these messages were blurred due to abrasions. Master Wugui has copied these blurred messages and he wants someone to recover these messages. The messages has a specific length, and each position could be digit, '?' or ','. It is known that each message recorded some strictly increasing positive integers (without leading zeroes) separated by commas and Po is asked to recover these numbers.

Input

There are multiple test cases. Each test case contains string in a line represented. The length of the string will not exceed 500. The format is shown in the sample input.

Output

If the message has no appropriate solution, print "impossible", else print the decrypted message. If there exists multiple solutions, output the one whose first number is the smallest; if there is a tie, output the one whose second number is the smallest; and so on.

Sample Input

?,10,?????????????????,16,??
?2?5??7?,??
???????????????????????????????,???

Sample Output

impossible
12,50,70,71
1,2,3,4,5,6,7,8,9,10,11,100,101,102

Source

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