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def mapping(pi):
l = [(0,0)]
for i, e in enumerate(pi):
if e > l[-1][1]:
l.append((i,e))
l.append((len(pi), len(pi)))
D = []
for i in range(len(l)-2):
D.extend([1]*(l[i+1][1]-l[i][1])+[0]*(l[i+2][0]-l[i+1][0]))
return DyckWord(D)
parent_initializer = Permutations
element_repr = repr
levels = [2, 3, 4, 5]
for level in levels:
for elt in parent_initializer(level):
print('%s => %s' % (element_repr(elt), element_repr(mapping(elt))))
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