Equivalent Deformation

Two triangles $T_1$ and $T_2$ of the same area lie on a plane. Apply the operation below to $T_1$ several times so that $T_1$ is exactly superposed on $T_2$. A vertex of $T_1$ may land on any vertex of $T_2$. Compute the minimum number of operations needed to superpose $T_1$ on $T_2$.

Operation: choose one vertex of the triangle and move it to an arbitrary point on the line that passes through the vertex and runs parallel to the opposite side.

An operation example

The figure below shows one possible sequence of operations for the first dataset of the sample input.

The input consists of at most 2000 datasets, each in the following format.

x11 y11
x12 y12
x13 y13
x21 y21
x22 y22
x23 y23

$x_{ij}$ and $y_{ij}$ are the $x$ and $y$ coordinate of the $j$-th vertex of $T_i$.

Each dataset satisfies the following conditions.

• Every coordinate is an integer with absolute value at most 1000.
• $T_1$ and $T_2$ have the same area, and that area is positive.
• The six given vertices are all distinct points.

An empty line is placed between datasets. The input ends at end of file.

For each dataset, output the minimum number of operations in one line. If five or more operations are required, output Many instead of the count.

A vertex may have non-integral coordinates after it is moved.

For any input satisfying the conditions above, the required number of operations can be proven to be bounded by some constant.