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.