Axis of symmetry of the quadrilateral

Given the coordinates of the successive vertices of a convex quadrilateral. How many axes of symmetry does this figure?

Input

In one line contains 8 digits x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 – coordinates of the vertices of a quadrilateral.

-50 ≤ x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_{4 }≤ 50

Output

One number - the number of axes of symmetry.

Examples