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 Go (1.6) (judge verdict: Wrong Answer)

package main
 
import (
	"bufio"
	"os"
	"strconv"
	"fmt"
	"math"
)
 
var sc = bufio.NewScanner(os.Stdin)
var ReadString func() string
 
func init() {
	ReadString = newReadString()
}
 
/*------ scan ------*/
 
func newReadString() func() string {
	sc.Buffer(make([]byte, 1024), 2048)
	sc.Split(bufio.ScanWords)
	return func() string {
		if !sc.Scan() {
			panic("scanできなかった")
		}
		return sc.Text()
	}
}
 
func ReadLine() string {
	if !sc.Scan() {
		panic("line をscanできなかった")
	}
	return sc.Text()
}
 
func ReadInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		fmt.Println("parseInt失敗")
		panic(err.Error())
	}
	return int64(i)
}
 
func ReadInt() int {
	i := ReadInt64()
	return int(i)
}
 
func ReadIntSlice(n int) []int {
	arr := make([]int, n)
	for i := 0; i < n; i++ {
		arr[i] = ReadInt()
	}
	return arr
}
 
func ReadInt64Slice(n int) []int64 {
	arr := make([]int64, n)
	for i := 0; i < n; i++ {
		arr[i] = ReadInt64()
	}
	return arr
}
 
/*------ number util ------*/
 
func GetIntAbs(n int) int {
	if n < 0 {
		return -n
	}
	return n
}
 
func Atoi(a string) int {
	i, err := strconv.Atoi(a)
	if err != nil {
		panic(err.Error())
	}
	return i
}
 
func FindMin(arr []int) int {
	if len(arr) == 0 {
		return 0
	}
	min := arr[0]
	for _, v := range arr {
		if v < min {
			min = v
		}
	}
	return min
}
 
func FindMax(arr []int) int {
	if len(arr) == 0 {
		return 0
	}
	max := arr[0]
	for _, v := range arr {
		if v > max {
			max = v
		}
	}
	return max
}
 
 
func main() {
	n := ReadInt()
	d := ReadInt()
	x := make([][]int, n)
	var cnt int
	for i := 0; i < n; i++ {
		xd := ReadIntSlice(d)
		x[i] = xd
	}
 
	for i := 0; i + 1 < n; i++ {
      for inner := i + 1; inner < n; inner++ {
 
		// diff求める
		curDiff := 0
		for j := 0; j < d; j++ {
          diff := GetIntAbs(x[i][j] - x[inner][j])
			curDiff += diff * diff
		}
		rs := math.Sqrt(float64(curDiff))
        intRs := int(rs)
		if float64(intRs) == math.Ceil(rs) {
			cnt += 1
		}
      }
	}
  if d == 1 {
    fmt.Println(cnt * 2)
  } else {
	fmt.Println(cnt)
  }
}