One of the problemsetters of this contest, a KSA student, has come to like prime numbers and decided that a sequence of length $N$ that satisfies all of the following conditions is called a beautiful sequence.

• The sequence is a permutation of length $N$. In other words, each sequence element is in the range of $1,2,\cdots ,N$, and the elements are pairwise distinct.
• The difference between two distinct elements that are a prime distance apart must also be a prime number. The distance between the $i$-th element and the $j$-th element is given by $|j-i|$.

Input

Each test contains multiple test cases. The first line contains an integer $T$, the number of test cases. The description of the test cases follows.

The first and only line of each test case contains an integer $N$.

Output

For each test case, if a beautiful sequence of length $N$ exists, print YES on the first line and the space-separated elements on the second line. If a beautiful sequence of length $N$ does not exist, print NO instead.

If there are multiple solutions, print any of them.

Constraints

• $1\leq T \leq 100$
• $3\leq N \leq 300$

Scoring

Examples

Input 1

2
5
7

Output 1

YES
2 1 5 4 3
YES
6 2 3 4 5 1 7