Problem:
Problem B: Lagrange's Four-Square Theorem

The fact that any positive integer has a representation as the sum of at most four positive
squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The
first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission
however is not to explain the original proof nor to discover a new proof but to show that the
theorem holds for some specific numbers by counting how many such possible representations
there are.

For a given positive integer n, you should report the number of all representations of n as the
sum of at most four positive squares. The order of addition does not matter, e.g. you should
consider 42 + 32 and 32 + 42 are the same representation.

For example, let’s check the case of 25. This integer has just three representations 12 +22 +22 +42 ,
32 + 42 , and 52 . Thus you should report 3 in this case. Be careful not to count 42 + 32 and
32 + 42 separately.

Input

The input is composed of at most 255 lines, each containing a single positive integer less than
215 , followed by a line containing a single zero. The last line is not a part of the input data.

Output

The output should be composed of lines, each containing a single integer. No other characters
should appear in the output.

The output integer corresponding to the input integer n is the number of all representations
of n as the sum of at most four positive squares.

Sample Input

1
25
2003
211
20007
0

Output for the Sample Input

1
3
48
7
738

Solution in JavaScript (judge verdict: Accepted)

var input = require('fs').readFileSync('/dev/stdin', 'utf8');
var arr=input.trim().split("\n").map(Number);
arr.some(function(v){
   if(v==0)return true;
   var cnt=0;
   for(var a=1;a<=181;a++){
      var A=a*a;
      if(v<A)break;
      if(A==v)cnt++;
      for(var b=a;b<=181;b++){
         var B=A+b*b;
         if(v<B)break;
         if(B==v)cnt++;
         for(var c=b;c<=181;c++){
            var C=B+c*c;
            if(v<C)break;
            if(C==v)cnt++;
            for(var d=c;d<=181;d++){
               var D=C+d*d;
               if(v<D)break;
               if(D==v)cnt++;
   }}}}
   console.log(cnt);
});