You are given an integer $$$n$$$. You choose $$$n$$$ cells $$$(x_1,y_1), (x_2,y_2),\dots,(x_n,y_n)$$$ in the grid $$$n\times n$$$ where $$$1\le x_i\le n$$$ and $$$1\le y_i\le n$$$.

Let $$$\mathcal{H}$$$ be the set of distinct Manhattan distances between any pair of cells. Your task is to maximize the size of $$$\mathcal{H}$$$. Examples of sets and their construction are given in the notes.

If there exists more than one solution, you are allowed to output any.

Manhattan distance between cells $$$(x_1,y_1)$$$ and $$$(x_2,y_2)$$$ equals $$$|x_1-x_2|+|y_1-y_2|$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1\le t\le 50$$$) — the number of test cases.

Each of the following $$$t$$$ lines contains a single integer $$$n$$$ ($$$2\le n\le 10^3$$$).

Output

For each test case, output $$$n$$$ points which maximize the size of $$$\mathcal{H}$$$. It is not necessary to output an empty line at the end of the answer for each test case.

Note

In the first testcase we have $$$n=2$$$. One of the possible arrangements is:

$\text{[math]}$ The arrangement with cells located in $$$(1,1)$$$ and $$$(1,2)$$$. In this case $$$\mathcal{H}=\{|1-1|+|1-1|,|1-1|+|2-2|,|1-1|+|1-2|\}=\{0,0,1\}=\{0,1\}$$$. Hence, the size of $$$\mathcal{H}$$$ is $$$2$$$. It can be shown that it is the greatest possible answer.

In the second testcase we have $$$n=3$$$. The optimal arrangement is:

$\text{[math]}$ The arrangement with cells located in $$$(2,1)$$$, $$$(2,3)$$$ and $$$(3,1)$$$.

$$$\mathcal{H}$$$=$$$\{|2-2|+|1-1|,|2-2|+|3-3|,|3-3|+|1-1|,|2-2|+|1-3|,|2-3|+|1-1|,|2-3|+|3-1|\}$$$=$$$\{0,0,0,2,1,3\}$$$=$$$\{0,1,2,3\}$$$.

For $$$n=4$$$ a possible arrangement is:

$\text{[math]}$

For $$$n=5$$$ a possible arrangement is:

$\text{[math]}$

For $$$n=6$$$ a possible arrangement is:

$\text{[math]}$

Cells Arrangement

Examples