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Marin wants you to count number of permutations that are beautiful. A beautiful permutation of length $$$n$$$ is a permutation that has the following property: $$$$$$ \gcd (1 \cdot p_1, \, 2 \cdot p_2, \, \dots, \, n \cdot p_n) > 1, $$$$$$ where $$$\gcd$$$ is the greatest common divisor.
A permutation is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3, 4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases.
Each test case consists of one line containing one integer $$$n$$$ ($$$1 \le n \le 10^3$$$).
For each test case, print one integer — number of beautiful permutations. Because the answer can be very big, please print the answer modulo $$$998\,244\,353$$$.
71234561000
0 1 0 4 0 36 665702330
In first test case, we only have one permutation which is $$$[1]$$$ but it is not beautiful because $$$\gcd(1 \cdot 1) = 1$$$.
In second test case, we only have one beautiful permutation which is $$$[2, 1]$$$ because $$$\gcd(1 \cdot 2, 2 \cdot 1) = 2$$$.
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Provedor Codeforces
Código CF1658B
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Datas 09/05/2023 10:23:27
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