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 $1 \le i < j \le n$ 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 $d(a, b) = |x_a - x_b| + |y_a - y_b|$.

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.

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.