For a positive integer (a), we define a recurrence (\{b_n\}_{n\geq 0}) as (b_n = a^{b_{n-1}}), with (b_0 = 1). We say that a positive integer (a) is (m)- tetrative if the sequence (b) stabilizes to (1) modulo (m), that is, there exists (N \ge 0) such that (b_n \equiv 1 \pmod m) for all (n \geq N). For a given (m), calculate the density of the (m)- tetrative integers. Here, the density of a set (S) is the limit ()\lim\limits_{n\rightarrow \infty}\frac{|S\cap 1,2,\ldots,n|}{n}.() Informally, it is the "proportion" of positive integers that are (m)- tetrative . It can be proven (under the constraints of this problem) that the density is well-defined and is always a rational number, whose denominator is not divisible by (998\,244\,353). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The number (m) will be given to you as a product of three integers (x), (y), and (z). The first and only line of each test case contains three integers (x), (y), (z) ((1\leq x,y,z \leq 10^6), (m = xyz \geq 2)). For each test case, print the density of (m)- tetrative integers ((a) such that its corresponding sequence (b_n) converges to (1) modulo (m)), modulo (998\,244\,353). Formally, let (M = 998\,244\,353). It can be shown that the exact answer can be expressed as an irreducible fraction (\frac{p}{q}), where (p) and (q) are integers and (q \not \equiv 0 \pmod{M}). Output the integer equal to (p \cdot q^{-1} \bmod M). In other words, output such an integer (x) that (0 \le x < M) and (x \cdot q \equiv p \pmod{M}). In the first test case, (m = 5). For example, (a=1) is (5)- tetrative since (b_n = 1) for all (n). For (a= 8), the sequence (b) is $$$[1, 8, 8^8, 8^{(8^8)}