B: Hexagram

A Hexagram is a $6-$pointed star, sometimes called the Star of David. Given these

numbers:

$3,17,15,18,11,22,12,23,21,7,9,13$

There are four unique ways of assigning the numbers to vertices of the hexagram

such that all of the sets of four numbers along the lines have the same sum $(57$

in this case$).$ All other ways may be obtained from these by rotation and$/$or

reflection.

Given is aisunct numvers, in now many ways, uisregarung rotauons anu

reflections, can you assign the numbers to the vertices such that the sum of the

numbers along each of $6$ straight lines passing through $4$ vertices is the same?

The Input

There will be several test cases in the input. Each test case will consist of twelve

unique positive integers on a single line, with single spaces separating them. All

of the numbers will be less than $1,000,000.$ The input will end with a line with

twelve $0$s$.$

The Output

For each test case, output the number of ways the numbers can be assigned to

vertices such that the sum along each line of the hexagram is the same. Put

each answer on its own line. Output no extra spaces, and do not separate

answers with blank lines.

Sample Input

Sample Output

$4$

$0$

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