You're given \textbf{n} circles. Each circle is defined by its three distinct points. Calculate the largest possible number of circles having the same radius. \InputFile The first line contains one integer number \textbf{n }(\textbf{1 }≤ \textbf{n }≤ \textbf{1400}). The next \textbf{n }lines contain six integer numbers each \textbf{x_1}, \textbf{y_1}, \textbf{x_2}, \textbf{y_2}, \textbf{x_3}, \textbf{y_3} (\textbf{0 }≤ \textbf{x_i}, \textbf{y_i} ≤ \textbf{1000}) - the coordinates of three different points that do not belong to one line and define the corresponding circle. \OutputFile Write a single integer - the maximum number of circles having the same radius.