Avoiding the Abyss

문제

You are standing on a point with integer coordinates $(x_s,y_s)(x\_s,\; y\_s)$. You want to walk to the point with integer coordinates $(x_t,y_t)(x\_t,\; y\_t)$. To do this, you can walk along a sequence of line segments. But there is a swimming pool in your way. The swimming pool is an axis aligned rectangle whose lower left corner is on the point $(x_l,y_l)(x\_l,\; y\_l)$ and the upper right corner is on the point $(x_r,y_r)(x\_r,\; y\_r)$. You cannot ever cross the swimming pool, not even on the border. However, it is dark and you do not know the coordinates $(x_l,y_l)(x\_l,\; y\_l)$ and $(x_r,y_r)(x\_r,\; y\_r)$. Instead, you threw a rock into the pool which revealed that the point $(x_p,y_p)(x\_p,\; y\_p)$ is in the pool (or on the boundary).

Find a way to walk from the start to the end point along a sequence of line segments, so that you never cross the swimming pool.

입력

The first line contains two integers $x_{s}x\_s$ and $y_{s}y\_s$ ($-{10}^4\le x_s,y_s\le {10}^4-10^4\; \backslash leq\; x\_s,\; y\_s\; \backslash leq\; 10^4$).

The second line contains two integers $x_{t}x\_t$ and $y_{t}y\_t$ ($-{10}^4\le x_t,y_t\le {10}^4-10^4\; \backslash leq\; x\_t,\; y\_t\; \backslash leq\; 10^4$).

The third line contains two integers $x_{p}x\_p$ and $y_{p}y\_p$ ($-{10}^4\le x_p,y_p\le {10}^4-10^4\; \backslash leq\; x\_p,\; y\_p\; \backslash leq\; 10^4$).

The problem is not adaptive, i.e. for every test case there exist four integers $x_l,y_l,x_r,y_{r}x\_l,\; y\_l,\; x\_r,\; y\_r$ (, ) that constitute a swimming pool. The start and end points are always strictly outside the swimming pool, and the point $(x_p,y_p)(x\_p,y\_p)$ is inside (or on the border). The start and end points are always distinct.

출력

First, print one integer $NN$ ($0\le N\le 100\; \backslash leq\; N\; \backslash leq\; 10$), the number of points in between the start and end point that you want to visit. Then, print $NN$ lines, the $ii$th containing two integers $x_i,y_{i}x\_i,\; y\_i$. These coordinates must satisfy $-{10}^9\le x_i,y_i\le {10}^9-10^9\; \backslash leq\; x\_i,\; y\_i\; \backslash leq\; 10^9$. Note that these are not the same bounds than on the other coordinates.

This means that you will walk along straight line segments between $(x_s,y_s),(x_1,y_1),\dots ,(x_N,y_N),(x_t,y_t)(x\_s,\; y\_s),\; (x\_1,\; y\_1),\; \backslash dots,\; (x\_N,\; y\_N),\; (x\_t,\; y\_t)$ such that none of the line segments touch the swimming pool. It can be proven that a solution always exists.