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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#define debug_interval ','
#define dump_interval ' '
#define debug_toggle 1
//{
#include<bits/stdc++.h>
using namespace std;
#define hi cerr<<"hi"<<endl;
#define int long long
#define INT_MAX LLONG_MAX
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define fi first
#define se second
#define mp make_pair
#define rev reverse
#define dans dump(ans)
#define MOD 1000000007
#define amp(v,n) (v).count(n)?v[n]++:v[n]=1
#define sysp system("pause")
#define PI acos(-1)
#define pf push_front
#define ins insert
#define fh(x,v) for(auto x:v)

//{
inline int toInt(string s){int v;istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x){ostringstream sout;sout<<x;return sout.str();}
template<class...A> inline void dump(){cout<<endl;}
template<class...A> inline void dump_rest() {cout<<endl;}
template<class T, class...A> inline void dump_rest(const T& first, const A&... rest){cout<<dump_interval<<first;dump_rest(rest...);}
template<class T,class...A> inline void dump(const T&first,const A&...rest){cout<<first;dump_rest(rest...);}
template<class...A> inline void debug(){cerr<<endl;}
template<class...A> inline void debug_rest() {cerr<<endl;}
template<class T, class...A> inline void debug_rest(const T& first, const A&... rest){cerr<<debug_interval<<first;debug_rest(rest...);}
template<class T,class...A> inline void debug(const T&first,const A&...rest){if(debug_toggle)cerr<<first,debug_rest(rest...);}
unsigned XorShift(void){static unsigned x = 123456789;static unsigned y = 362436069;static unsigned z = 521288629;static unsigned w = 88675123;unsigned t;t = x ^ (x << 11);x = y; y = z; z = w;return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));}
//}

typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}
template<int m>class mint{private:int i;public:mint() : i(0){}mint(int i): i((i%m+m)%m){}mint operator+(const mint& o){return o.i+i;}mint operator*(const mint& o){return o.i*i;}mint operator-(){return -i;}operator int() {return i;}};
//template<class T>vector<T> var_vec(size_t a){return vector<T>(a);}
//template<class T, class... Ts>auto var_vec(size_t a, Ts... ts){return vector<decltype(var_vec<T>(ts...))>(a, var_vec<T>(ts...));}

//}

int mem[1000];

main(){
	int n,d;
	cin>>n>>d;
	int p[n][d];rep(i,n)rep(j,d)cin>>p[i][j];
	vint v;
	rep(i,1000)mem[i]=i*i;
	int ans=0;
	for(int i=0;i<n-1;i++){
		for(int j=i+1;j<n;j++){
			int t=0;
			for(int k=0;k<d;k++){
				t+=(p[i][k]-p[j][k])*(p[i][k]-p[j][k]);
			}
			rep(k,1000){
				ans+=(mem[k]==t);
			}
		}
	}
	dans;
}