Circles

You're given n circles. Each circle is defined by its three distinct points. Calculate the largest possible number of circles having the same radius.

Input

The first line contains one integer number n (1 ≤ n ≤ 1400). The next n lines contain six integer numbers each x_1, y_1, x_2, y_2, x_3, y_3 (0 ≤ x_i, y_i ≤ 1000) - the coordinates of three different points that do not belong to one line and define the corresponding circle.

Output

Write a single integer - the maximum number of circles having the same radius.

Examples