Digital Time

+1 vote
asked Jul 26, 2018 by ravindra reddy (340 points)

Digital Time

Problem Description

The objective is to form the maximum possible time in the HH:MM:SS format using any six of nine given single digits (not necessarily distinct)

Given a set of nine single (not necessarily distinct) digits, say 0, 0, 1, 3, 4, 6, 7, 8, 9, it is possible to form many distinct times in a 24 hour time format HH:MM:SS, such as 17:36:40 or 10:30:41 by using each of the digits only once. The objective is to find the maximum possible valid time (00:00:01 to 24:00:00) that can be formed using some six of the nine digits exactly once. In this case, it is 19:48:37.

Input Format

A line consisting of a sequence of 9 (not necessarily distinct) single digits (any of 0-9) separated by commas. The sequence will be non-decreasing

Output

The maximum possible time in a 24 hour clock (00:00:01 to 24:00:00) in a HH:MM:SS form that can be formed by using some six of the nine given digits (in any order) precisely once each. If no combination of any six digits will form a valid time, the output should be the word Impossible

Explanation

Example 1

Input

0,0,1,1,3,5,6,7,7

Output

17:57:36

The maximum valid time in a 24 hour clock that can be formed using some six of the 9 digits precisely once is 17:57:36

Example 2

Input

3,3,3,3,3,3,3,3,3

Output

Impossible

No set of six digits from the input may be used to form a valid time.

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