from itertools import permutations, compress
 
m = 3
n = 3
 
def prettyPrint( single_division ):
    def clean(it):
        items = ", ".join(it)
        return "{" + items + "}"
 
    def cleanIntSet(single_set):
        str_set = map(str, single_set)
        return clean( str_set ) 
 
    sets = map( cleanIntSet, single_division )
    return clean(sets)
 
def candidates(n,m):
    def makeCandidate(perm):
        solution = []
        integers = range(1,n*m+1)
 
        for setNumber in range(m):
            mask = map(lambda x: x == setNumber, perm)
            singleSet = compress(integers, mask)
            solution.append(frozenset(singleSet))
 
        return frozenset(solution)
 
    permutationBase = [i for j in range(n) for i in range(m)]
    allPermutations = set( permutations(permutationBase) )
 
    return { makeCandidate(perm) for perm in allPermutations }
 
def isCorrectDivision(division):
    sums = map(sum, division)
    return len(set(sums)) == 1
 
answers = filter(isCorrectDivision,candidates(n,m))
for answer in answers:
    print( prettyPrint(answer) )
 
 

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