Problem:
Score : 200 points

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?

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}.

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.

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

Solution in Ruby (2.3.3) (judge verdict: Accepted)

def min2(a,b)
    return a>b ? b : a
end
def max2(a,b)
    return a<b ? b : a
end

def get_dist(xx,yy)
    score = 0
    for x,y in xx.zip(yy)
        score += (y-x)**2
    end
    return score
end

def is_nomal(v)
    l = 0
    r = v

    if  v ==1 
         return true
    end

    while r - l > 1
        center = (r+l)/2
        center2 = center**2

        if center2 == v
            return true
        elsif center2 > v
            r = center
        else
            l = center
        end
    

    end

    return false

end

N = gets.to_i

Xlist = (1..N).map{|i| gets.split.map{|j| j.to_i}}
count =0
for i in 0...N-1
    for j in i+1...N

        if is_nomal(get_dist(Xlist[i],Xlist[j]))
            count +=1
        end

    end
end
puts count