K. Do you believe that this is a real story?
time limit per test
1.5 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

On a boring Friday night, $$$\textit{Ramez}$$$ and his son $$$\textit{Molham}$$$ were sitting together. As usual every Friday, each Dad in the world should ask his son to do something. So, $$$\textit{Ramez}$$$ asked his son to solve the following problem:

He gave $$$\textit{Molham}$$$ $$$n$$$ cards, numbered from 1 to $$$n$$$ and arranged in a clockwise circle shape.

Initially, all the cards are black. And $$$\textit{Ramez}$$$ asked $$$\textit{Molham}$$$ to paint $$$n-1$$$ cards with red (if it is possible).

$$$\textit{Molham}$$$ can make the painting operation as follows:

He can paint a black card ($$$i$$$) with red if and only if there is another black card ($$$j$$$) and there is a way to get from $$$i$$$ to $$$j$$$ passing through exactly two cards differ than $$$i$$$ and $$$j$$$ .

$$$\textit{Molham}$$$ thought the problem is so easy, but $$$\textit{Ramez}$$$ did not stop here; if there are many possible orders to paint the $$$n-1$$$ cards red, he asked for the minimum lexicographically order of painting.

The coloring order is defined as follows:

If at the $$$k$$$-th operation $$$\textit{Molham}$$$ colored the card with number $$$i$$$ with red (if it is possible), then the $$$k$$$-th number of the coloring order should be $$$i$$$.

After this extra condition, $$$\textit{Molham}$$$ found the problem so hard so he asked for your help.

Input

The first line of the input will contain a single integer ($$$1 \le t \le 10^5$$$) the number of test cases.

Each of the following $$$t$$$ lines will contain a single integer ($$$4 \le n \le 10^5$$$) the number of cards .

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5\times10^5$$$.

Output

For each test case, if it is possible to paint $$$n-1$$$ cards red print "YES" (without quotes) and if not print "NO" (without quotes).

If the first line was "YES" print another line containing $$$n-1$$$ numbers, the minimum lexicographically order of coloring.

Please Note that the answer is CaSe SeNsiTiVe so print the answer (YES/NO) with capital letters.

Example
Input
2
6
7
Output
NO
YES
1 4 5 2 6 3
Note

when $$$n=6$$$ there is no way to color $$$5$$$ cards red

when $$$n=7$$$ here is the explanation of the test

first Molham will color the card with number $$$1$$$ (it is possible because we can get from the black card with number $$$5$$$ to card with number $$$1$$$ passing through cards with numbers $$$6$$$ and $$$7$$$).

then he will color card with number $$$4$$$ (using card with number $$$7$$$).

then he will color card with number $$$5$$$ (using card with number $$$2$$$).

then he will color card with number $$$2$$$ (using card with number $$$6$$$).

then he will color card with number $$$6$$$ (using card with number $$$3$$$).

finally he will color card with number $$$3$$$ (using card with number $$$7$$$).

So, the coloring order will be $$$1,4,5,2,6,3$$$.

And the previous order of coloring is the minimum lexicographically between all the possible orders of coloring.