Problem Statement

There are N points in a D-dimensional space.
The coordinates of the i-th point are (X_{i1}, X_{i2}, ..., X_{iD}).
The distance between two points with coordinates (y_1, y_2, ..., y_D) and (z_1, z_2, ..., z_D) is $\sqrt{(y_1 - z_1)^2 + (y_2 - z_2)^2 + ... + (y_D - z_D)^2}$.
How many pairs (i, j) (i < j) are there such that the distance between the i-th point and the j-th point is an integer?

Input

Input is given from Standard Input in the following format:
N D
X_{11} X_{12} ... X_{1D}
X_{21} X_{22} ... X_{2D}
$\vdots$
X_{N1} X_{N2} ... X_{ND}

Output

Print the number of pairs (i, j) (i < j) such that the distance between the i-th point and the j-th point is an integer.

Constraints

• All values in input are integers.
• $2 \leq N \leq 10$
• $1 \leq D \leq 10$
• -$20 \leq X_{ij} \leq 20$
• No two given points have the same coordinates. That is, if $i \neq j, there exists k$ such that $X_{ik} \neq X_{jk}$.

Sample Input 1

3 2
1 2
5 5
-2 8

Sample Output 1

1

The number of pairs with an integer distance is one, as follows:

• The distance between the first point and the second point is $\sqrt{|1-5|^2 + |2-5|^2} = 5,$ which is an integer.
• The distance between the second point and the third point is $\sqrt{|5-(-2)|^2 + |5-8|^2} = \sqrt{58},$ which is not an integer.
• The distance between the third point and the first point is $\sqrt{|-2-1|^2+|8-2|^2} = 3\sqrt{5},$ which is not an integer.

Sample Input 2

3 4
-3 7 8 2
-12 1 10 2
-2 8 9 3

Sample Output 2

2

Sample Input 3

5 1
1
2
3
4
5

Sample Output 3

10

见题面 Input 部分

见题面 Output 部分