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```from heapq import heappop, heapreplace, heapify

def imerge(iterables, key=None):
'''Merge multiple (potentially infinite) sorted inputs into a single sorted output.

Similar to heapq.merge and sorted(itertools.chain(*iterables)).
Like heapq.merge, returns a generator, does not pull the data into memory
all at once, and assumes that each of the input iterables is already
sorted (smallest to largest).
Unlike heapq.merge, accepts an infinite number of input iterables,
but requires all of them to come in ascending order
(that is, their starting point must be in ascending order each).

>>> list(imerge([[1,3,5,7], [2,4,8], [5,10,15,20], [], [25]]))
[1, 2, 3, 4, 5, 5, 7, 8, 10, 15, 20, 25]

'''
_heappop, _heapreplace, _heapify, _StopIteration = heappop, heapreplace, heapify, StopIteration

h = []
h_append = h.append
iterables = iter(iterables)

more_iterables = True
while len(h)<2:
try:
# raises StopIteration when no more iterables
next_item = iter(next(iterables)).next
except _StopIteration:
more_iterables = False
break
try:
v = next_item()
except _StopIteration:
# ignore empty iterables
continue
if key is not None:
highest = key(v)
else:
highest = v
h_append([highest, v, next_item])

if len(h) >= 2:
# the heap invariant should hold, if input iterables come already sorted
# XXX: make this a ValueError
assert h[1][0] >= h[0][0]

elif len(h) == 1:
# a single iterable, just send it
assert not more_iterables
_, v, next_item = h[0]
yield v
try:
while True:
yield next_item()
except _StopIteration:
return

else:
# empty
return

cur = highest
while h:
_, v, next_item = s = h[0]
yield v

try:
v = s[1] = next_item()   # raises StopIteration when no more items
except _StopIteration:
_heappop(h)              # remove empty iterator
else:
if key is not None:
cur = s[0] = key(v)
else:
cur = s[0] = v
_heapreplace(h, s)       # restore heap condition

# 'highest' is the highest known item in the heap.
# Any time we advance an iterable and get an item ('cur')
# greater than 'highest', we must bring more enough iterables
# into play to ensure no items are missed.
if more_iterables and (cur >= highest or len(h) < 2):
while cur >= highest or len(h)<2:
try:
# raises StopIteration when no more iterables
next_item = iter(next(iterables)).next
except _StopIteration:
more_iterables = False
break
try:
v = next_item()
except _StopIteration:
# ignore empty iterables
continue
if key is not None:
highest = key(v)
else:
highest = v
h_append([highest, v, next_item])
_heapify(h)
```