Beautiful Sequence

You are given an integer N representing the length of a sequence. Your task is to determine whether a Beautiful Sequence exists for the given N and, if it does, output the sequence. A sequence is considered Beautiful if it meets the following criteria:

• If \(N = 1\), the sequence is \([1]\).
• If \(N = 2\), the sequence is \([1, 2]\).
• If \(N = 3\), a Beautiful Sequence does not exist.
• If \(N \ge 4\), a Beautiful Sequence is constructed by alternating 1 and 2, i.e. for \(i = 1,2,\ldots,N\), the \(i^{th}\) element is given by:</p>

\(a_i = \begin{cases} 1 & \text{if } i \text{ is odd}\\ 2 & \text{if } i \text{ is even} \end{cases}\)

For each test case, if a Beautiful Sequence exists, output YES followed by the sequence elements separated by spaces; otherwise, output NO.

inputFormat

The first line of input contains an integer T representing the number of test cases. Each of the following T lines contains a single integer N, the length of the sequence.

Input is read from stdin.

outputFormat

For each test case, output one line. If a Beautiful Sequence exists for the given N, output YES followed by the sequence elements (separated by a single space). If not, output NO.

Output is written to stdout.

## sample

3
1
2
3

YES 1
YES 1 2
NO

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