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: $$ \gcd (1 \cdot p_1, , 2 \cdot p_2, , \dots, , n \cdot p_n) \gt 1,$$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).

Input

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 $n$ ($1 \le n \le 10^3$).

Output

For each test case, print one integer — number of beautiful permutations. Because the answer can be very big, please print the answer modulo $998\,244\,353$.

Note

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 $\gcd(1 \cdot 2, 2 \cdot 1) = 2$.

Samples

7
1
2
3
4
5
6
1000

0
1
0
4
0
36
665702330