I need mathematical express for how many combinations of input arrays create same Binary Max-Heap when we put values one by one from array using method Insert.
This heap are represent by this array [9, 7, 8, 6, 4, 2, 4, 1, 5]. If we create new heap and we start putting values using Insert, final heap will be like in picture. But also array like [4, 5, 4, 1, 9, 2, 8, 7, 6] will create same heap when we using Insert. How many arrays like this exist? We always using same numbers from origin heap but keep attention because we have 4 twice.
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