Time Limit: 2 sec / Memory Limit: 1024 MB

Score : `100` points

### Problem Statement

You have `Q` triangles, numbered `1` through `Q`.

The coordinates of the vertices of the `i`-th triangle are `(x_{i1}, y_{i1})`, `(x_{i2}, y_{i2})` and `(x_{i3}, y_{i3})` in counterclockwise order.
Here, `x_{i1}`, `x_{i2}`, `x_{i3}`, `y_{i1}`, `y_{i2}` and `y_{i3}` are all integers.

For each triangle, determine if there exists a grid point contained in its interior (excluding the boundary). If it exists, construct one such point.

### Constraints

- All input values are integers.
`1 \leq Q \leq 10``000``0 \leq x_{i1}, x_{i2}, x_{i3}, y_{i1}, y_{i2}, y_{i3} \leq 10^9``(x_{i1}, y_{i1})`,`(x_{i2}, y_{i2})`and`(x_{i3}, y_{i3})`are in counterclockwise order.- The areas of the triangles are not
`0`.

### Input

Input is given from Standard Input in the following format:

Qx_{11}y_{11}x_{12}y_{12}x_{13}y_{13}x_{21}y_{21}x_{22}y_{22}x_{23}y_{23}:x_{Q1}y_{Q1}x_{Q2}y_{Q2}x_{Q3}y_{Q3}

### Output

Output should contain `Q` lines.

In the `i`-th line, if there is no grid point contained in the interior (excluding the boundary) of the `i`-th triangle, print `-1 -1`

.
If it exists, choose one such grid point, then print its `x`-coordinate and `y`-coordinate with a space in between.

### Sample Input 1

4 1 7 3 5 5 7 1 4 1 2 5 4 6 1 7 1 7 6 11 3 11 4 8 5

### Sample Output 1

3 6 2 3 -1 -1 10 4