Let S be a set of all six-digit integers.

Let S1 be a subset of S, including all members of S such that each consists

of distinct digits.

Let S2 be a subset of S1, including all members of S1 each with 5 being the difference between its largest digit and its lowest one.

Let S3 be a subset of S2, comprising all elements of S2 divisible by 143.

What is the cardinality of S3 ?

Explain your way of reasoning.