# 2
def heapify(value, heap1, heap2):
    try:
        value1, size1, depth1 = next(heap1)
    except StopIteration:
        value1, size1, depth1 = 999999999, 0, 0

    try:
        value2, size2, depth2 = next(heap2)
    except StopIteration:
        value2, size2, depth2 = 999999999, 0, 0

    size = size1 + size2 + 1
    depth = max(depth1, depth2) + 1

    if size > 0:
        if value < value1 and value < value2:
            print(f'case 1: ({value}, {size}, {depth})')

            yield (value, size, depth)
            yield heapify(value1, safely_next(heap1), safely_next(heap1))
            yield heapify(value2, safely_next(heap2), safely_next(heap2))
            return

        if value1 < value and value1 < value2 and size1 > 0:
            print(f'case 2: ({value1}, {size}, {depth})')

            yield (value1, size, depth)
            yield heapify(value, safely_next(heap1), safely_next(heap1))
            yield heapify(value2, safely_next(heap2), safely_next(heap2))
            return

        if value2 <= value and value2 <= value1 and size2 > 0:
            print(f'case 3: ({value2}, {size}, {depth})')

            yield (value2, size, depth)
            yield heapify(value1, safely_next(heap1), safely_next(heap1))
            yield heapify(value, safely_next(heap2), safely_next(heap2))
            return