Reconstruction
本题没有可用的提交语言。
Description
In this problem you need to reconstruct a convex polygon with $n$ vertices on the plane given a description of all triangles with vertices coinciding with the vertices of the polygon. The triangles can be given in a translated form, but not rotated.
For example, the following $4$ triangles can be reconstructed into the following rectangle:
The first line of input contains an integer $n$ ($3 \leq n \leq 50$), the number of vertices of the polygon. The next $\frac{n(n-1)(n-2)}{6}$ lines contain the description of the triangles. The $i$-th of these lines describes a single triangle with six integers $x_1$, $y_1$, $x_2$, $y_2$, $x_3$ and $y_3$ ($-10^5 \leq x_i, y_i \leq 10^5$). The points $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ are the coordinates of its vertices.
Output $n$ lines, the coordinates of the polygon; in the $i$-th line, output two integers $p_i$, $q_i$ ($-10^6 \leq p_i, q_i \leq 10^6$), with $(p_i,q_i)$ being the coordinates of the $i$-th vertex of the polygon. You can output the vertices in any order. You can output the polygon in any position on the plane, but it must be a translation of the original polygon. It is guaranteed that the solution is unique (up to translation).
Input
The first line of input contains an integer $n$ ($3 \leq n \leq 50$), the number of vertices of the polygon. The next $\frac{n(n-1)(n-2)}{6}$ lines contain the description of the triangles. The $i$-th of these lines describes a single triangle with six integers $x_1$, $y_1$, $x_2$, $y_2$, $x_3$ and $y_3$ ($-10^5 \leq x_i, y_i \leq 10^5$). The points $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ are the coordinates of its vertices.
Output
Output $n$ lines, the coordinates of the polygon; in the $i$-th line, output two integers $p_i$, $q_i$ ($-10^6 \leq p_i, q_i \leq 10^6$), with $(p_i,q_i)$ being the coordinates of the $i$-th vertex of the polygon. You can output the vertices in any order. You can output the polygon in any position on the plane, but it must be a translation of the original polygon. It is guaranteed that the solution is unique (up to translation).
4
1 1 4 5 2 5
3 1 5 2 7 2
5 6 6 3 9 7
9 1 8 4 10 5
2 1
3 5
1 4
5 5