$$$n$$$ points $$$a_1, a_2, ..., a_n$$$ are randomly generated inside a cube of size 1.
You are given a matrix $$$d$$$ with $$$d_{i,j}=d_{j,i}=dist(a_i, a_j)+rand(-0.1..0.1)$$$ and $$$d_{i,i}=0$$$. Here $$$dist(p, q)$$$ is the distance between points $$$\sqrt{(p_x-q_x)^2+(p_y-q_y)^2+(p_z-q_z)^2}$$$ and $$$rand(-0.1..0.1)$$$ is a random shift chosen uniformly from interval $$$[-0.1..0.1]$$$. Shifts for different pairs of points are chosen independently.
You need to construct a list of points $$$b_1, b_2, ..., b_n$$$ such that $$$\forall_{i, j} |dist(b_i, b_j)-d_{i,j}| \le 0.1$$$.
The first line contains one integer $$$n$$$ ($$$1 \le n \le 10$$$) — the number of points.
The next $$$n$$$ lines contain the description of matrix $$$d$$$. The $$$i$$$-th line contains $$$n$$$ real values $$$d_{i,j}$$$ ($$$-0.1 \le d_{i,j} \le \sqrt{3}+0.1$$$). Each value is given with 6 digits after the decimal point.
It is guaranteed that $$$d_{i,i}=0$$$ and $$$d_{i,j}=d_{j,i}$$$.
Print $$$n$$$ lines describing the points. $$$i$$$-th line should contain three real numbers $$$x_i$$$ $$$y_i$$$ $$$z_i$$$ ($$$-10.0 \le x_i, y_i, z_i \le 10.0$$$).
4 0.000000 0.758400 0.557479 0.379026 0.758400 0.000000 0.516608 0.446312 0.557479 0.516608 0.000000 0.554364 0.379026 0.446312 0.554364 0.000000
0.210269 0.581333 0.000000 0.090086 0.000000 0.458722 0.000000 0.498388 0.501723 0.204618 0.204262 0.075724
This problem has $$$30$$$ test cases.
