C. Carrying Conundrum
bitmasks; combinatorics; dp; math
Alice has just learned addition. However, she hasn't learned the concept of ""carrying"" fully — instead of carrying to the next column, she carries to the column two columns to the left.For example, the regular way to evaluate the sum \(2039 + 2976\) would be as shown: However, Alice evaluates it as shown: In particular, this is what she does: add \(9\) and \(6\) to make \(15\), and carry the \(1\) to the column two columns to the left, i. e. to the column ""\(0\) \(9\)""; add \(3\) and \(7\) to make \(10\) and carry the \(1\) to the column two columns to the left, i. e. to the column ""\(2\) \(2\)""; add \(1\), \(0\), and \(9\) to make \(10\) and carry the \(1\) to the column two columns to the left, i. e. to the column above the plus sign; add \(1\), \(2\) and \(2\) to make \(5\); add \(1\) to make \(1\). Thus, she ends up with the incorrect result of \(15005\).Alice comes up to Bob and says that she has added two numbers to get a result of \(n\). However, Bob knows that Alice adds in her own way. Help Bob find the number of ordered pairs of positive integers such that when Alice adds them, she will get a result of \(n\). Note that pairs \((a, b)\) and \((b, a)\) are considered different if \(a \ne b\).
The input consists of multiple test cases. The first line contains an integer \(t\) (\(1 \leq t \leq 1000\)) — the number of test cases. The description of the test cases follows.The only line of each test case contains an integer \(n\) (\(2 \leq n \leq 10^9\)) — the number Alice shows Bob.
For each test case, output one integer — the number of ordered pairs of positive integers such that when Alice adds them, she will get a result of \(n\).
In the first test case, when Alice evaluates any of the sums \(1 + 9\), \(2 + 8\), \(3 + 7\), \(4 + 6\), \(5 + 5\), \(6 + 4\), \(7 + 3\), \(8 + 2\), or \(9 + 1\), she will get a result of \(100\). The picture below shows how Alice evaluates \(6 + 4\):