# Problem A

Avoiding the Abyss

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You are standing on a point with integer coordinates $(x_s, y_s)$. You want to walk to the point with integer coordinates $(x_t, y_t)$. 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 $(x_l, y_l)$ and the upper right corner is on the point $(x_r, y_r)$. You cannot ever cross the swimming pool, not even on the border. However, it is dark and you do not know the coordinates $(x_l, y_l)$ and $(x_r, y_r)$. Instead, you threw a rock into the pool which revealed that the point $(x_p, y_p)$ 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.

### Input

The first line contains two integers $x_s$ and $y_s$ ($-10^4 \leq x_s, y_s \leq 10^4$).

The second line contains two integers $x_t$ and $y_t$ ($-10^4 \leq x_t, y_t \leq 10^4$).

The third line contains two integers $x_p$ and $y_p$ ($-10^4 \leq x_p, y_p \leq 10^4$).

The problem is not adaptive, i.e. for every test case there exist four integers $x_l, y_l, x_r, y_r$ ($-10^4 \leq x_l < x_r \leq 10^4$, $-10^4 \leq y_l < y_r \leq 10^4$) that constitute a swimming pool. The start and end points are always strictly outside the swimming pool, and the point $(x_p,y_p)$ is inside (or on the border). The start and end points are always distinct. Note that the problem is technically interactive, so the input will not contain an EOF character.

### Output

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

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

Sample Input 1 | Sample Output 1 |
---|---|

0 0 4 4 2 2 |
2 0 3 1 4 |