A. GCD MEX
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a positive integer $$$n$$$. Your task is to construct an array $$$a$$$ of size $$$|a|$$$ such that $$$|a| \le n$$$.

Let $$$b$$$ be an empty array. For every pair of indices $$$i$$$ and $$$j$$$ such that $$$1 \le i \lt j \le |a|$$$, we add the greatest common divisor (GCD) of $$$a_i$$$ and $$$a_j$$$ to array $$$b$$$.

Your constructed array $$$a$$$ must satisfy the condition that the MEX of the array $$$b$$$ (containing all pairwise GCDs $$$gcd(a_i, a_j)$$$ for $$$i \neq j$$$) is at least $$$n$$$.

The MEX (Minimum Excluded value) of a set of positive integers is the smallest positive integer that is not present in the set. The MEX of an empty set of positive integers is $$$1$$$.

Input

The input consists of $$$t$$$ test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 30$$$) – the number of test cases. Each of the following $$$t$$$ lines contains a single integer $$$n$$$ ($$$1 \le n \le 30$$$).

Output

For each test case, output two lines. The first line should contain a single integer, the size of the constructed array $$$a$$$. The second line should contain $$$|a|$$$ space-separated integers, the elements of the array $$$a$$$. The elements $$$a_i$$$ must satisfy $$$1 \le a_i \le 10^{18}$$$.

Example
Input
2
2
3
Output
2
1 2
3
1 2 4