After thoroughly examining each iceberg, Bob the penguin has made a second revelation: some of the icebergs are in fact squares! This time, he has given you a list of ~N~ icebergs, each with coordinates ~(x_1,y_1), (x_2,y_2), (x_3,y_3), (x_4,y_4)~, in clockwise order of vertices, starting from the top left. He would like to know how many of these icebergs are in the shape of a square (~4~ sides of equal length). Keep in mind that the entire iceberg needs to be a square to count, rather than the portion above the x-axis.

Input Specification

The first line will contain the integer ~N~, representing the number of icebergs.

There will be ~N~ groups of ~4~ lines, representing the coordinates of the icebergs, where each group of ~4~ being the coordinates of a single iceberg with points ~x_i, y_i~.

Output Specification

Output one integer, representing the number of icebergs that are in the shape of square.

Constraints

For all test cases,

~1 \leq N \leq 5 \times 10^4~

~-10^3 \leq x_i,y_i \leq 10^3~

Sample Input

2
-3 2
7 2
7 -6
-3 -6
-1 1
1 1
1 -1
-1 -1

Sample Output

1

Sample Explanation

The first iceberg is in the shape of a rectangle, while the second is in the shape of a square.