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EXAMPLE
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The third and fourth elements of S are (2,2) and (3,1), and their product is (6,2), which is the 17th element.
The first few rows of the multiplication table A are:
0, [0, 0, 0, 0, 0, 0, 0, 0, 0, ...]
1, [0, 1, 2, 3, 4, 5, 6, 7, 8, ...]
2, [0, 2, 7, 8, 16, 17, 18, 29, 30, ...]
3, [0, 3, 8, 10, 17, 19, 21, 30, 32, ...]
4, [0, 4, 16, 17, 37, 38, 39, 67, 68, ...]
5, [0, 5, 17, 19, 38, 40, 42, 68, 70, ...]
6, [0, 6, 18, 21, 39, 42, 45, 69, 72, ...]
7, [0, 7, 29, 30, 67, 68, 69, 121, 122, ...]
8, [0, 8, 30, 32, 68, 70, 72, 122, 124, ...]
...
The first few antidiagonals are:
0, [0]
1, [0, 0]
2, [0, 1, 0]
3, [0, 2, 2, 0]
4, [0, 3, 7, 3, 0]
5, [0, 4, 8, 8, 4, 0]
6, [0, 5, 16, 10, 16, 5, 0]
7, [0, 6, 17, 17, 17, 17, 6, 0]
8, [0, 7, 18, 19, 37, 19, 18, 7, 0]
9, [0, 8, 29, 21, 38, 38, 21, 29, 8, 0]
10, [0, 9, 30, 30, 39, 40, 39, 30, 30, 9, 0]
...
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