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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

var GET=(function(){function f(s){return new g(s);}function g(s){this._s=s.trim().split("\n");this._y=0;}g.prototype.a=function(f){var s=this._s, y=this._y, r;if(typeof s[y]==="string")s[y]=s[y].split(" ").reverse();r=s[y].pop();if(!s[y].length)this._y++;return f?r:+r;};g.prototype.l=function(f){var s=this._s[this._y++].split(" ");return f?s:s.map(a=>+a);};g.prototype.m=function(n,f){var r=this._s.slice(this._y,this._y+=n).map(a=>a.split(" "));return f?r:r.map(a=>a.map(a=>+a));};g.prototype.r=function(n,f){var r=this._s.slice(this._y,this._y+=n);return f?r:r.map(a=>+a);};return f;})();
var o=GET(require("fs").readFileSync("/dev/stdin","utf8"));
function xArray(v){var a=arguments,l=a.length,r="Array(a["+--l+"]).fill(0).map(x=>{return "+v+";})";while(--l)r="Array(a["+l+"]).fill(0).map(x=>"+r+")";return eval(r);}
function unionFind(n){this.a=Array(n+1).fill(-1);}
unionFind.prototype={
  root:function(i){return this.a[i]<0?i:this.a[i]=this.root(this.a[i]);},
  same:function(x,y){return this.root(x)===this.root(y);},
  unite:function(x,y){x=this.root(x);y=this.root(y);if(x===y)return 1;if(this.a[y]<=this.a[x])this.a[y]+=this.a[x],this.a[x]=y;else this.a[x]+=this.a[y],this.a[y]=x;},
  size:function(i){return -this.a[this.root(i)];},
}

function main(){
  var n = o.a();
  var m = o.a();
  if(m&1)return -1;
  var a = o.m(m);
  var uf = new unionFind(n);
  var ans = [];
  var e = xArray("[]",n+1)
  var w = xArray(0,n+1);
  for(var i = 0; i < m; i++){
    var u = a[i][0], v = a[i][1];
    if(uf.unite(u,v)){
      ans.push(u+" "+v);
      w[u] ^= 1;
    }else{
      e[u].push(v);
      e[v].push(u);
    }
  }
  dfs(1,0);
  return ans.join("\n");

  function dfs(v,p){
    for(var V of e[v]){
      if(V === p)continue;
      dfs(V,v);
    }
    if(p === 0)return;
    if(w[v]){
      ans.push(v+" "+p);
    }else{
      ans.push(p+" "+v);
      w[p] ^= 1;
    }
  }
}

if(process.argv.length<3)require("child_process").fork("Main.js",["1"],{execArgv:["--stack-size=240000"]});
else console.log(main());