ass="time-limit">

time limit per test

3 seconds

memory limit per test

256 megabytes

Akito decided to study a new powerful spell. Since it possesses immeasurable strength, it certainly requires a lot of space and careful preparation. For this, Akito went out into the field. Let's represent the field as a Cartesian coordinate system.

For the spell, Akito needs to place $$$0 \le n \le 500$$$ staffs at distinct integer coordinates in the field such that there will be exactly $$$k$$$ pairs $$$(i, j)$$$ such that $$$1 \le i \lt j \le n$$$ and $$$\rho(i, j) = d(i, j)$$$.

Here, for two points with integer coordinates $$$a = (x_a, y_a)$$$ and $$$b = (x_b, y_b)$$$, $$$\rho(a, b) = \sqrt{(x_a - x_b)^2 + (y_a - y_b)^2}$$$ and $$$d(a, b) = |x_a - x_b| + |y_a - y_b|$$$.

Input

The first line of input contains a single number $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

In the only line of each test case, there is a single number $$$k$$$ ($$$0 \le k \le 10^5$$$) — the number of pairs of staffs for which the equality $$$\rho(i, j) = d(i, j)$$$ must hold.

Output

For each test case, the first line of output should print the number $$$n$$$ ($$$0 \le n \le 500$$$) — the number of placed staffs.

In the following $$$n$$$ lines, pairs of integers $$$x_i, y_i$$$ $$$(-10^9 \le x_i, y_i \le 10^9)$$$ should be printed — the coordinates of the $$$i$$$-th staff. The points in which staffs stand must be distinct.

18:["geometry","binary search","constructive algorithms","brute force"] 17:{"tags":"$18","ratingMin":null,"ratingMax":null,"q":"","order":"BY_ID_DESC","page":1,"showTags":true,"hideSolved":f

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