#Lagrange.py
# every natural number is the sum of four squares (can incl. 0)
#e.g. 45 = 0^2+2^2+4^2+5^2  also 0^2+0^2+3^2+6^2
#This program finds all the Lagrange sums for one integer

import math

n = int(input("Enter N: "))
lagrange_sums = set()   #set of tuples of 4 sorted numbers
#test:
#lagrange_sums.add([1,2,3])   #can't have set of lists
#lagrange_sums.add((1,2,3))   #can have set of tuples
#    tuple(list)   #construct a tuple from a list OK

for a in range(0,int(math.sqrt(n))+1):
    for b in range(0,int(math.sqrt(n))+1):
        for c in range(0,int(math.sqrt(n))+1):
             for d in range(0,int(math.sqrt(n))+1):
                 if a*a+b*b+c*c+d*d == n:   #sort the a,b,c,d so no dups
                     if tuple(sorted([a,b,c,d])) not in lagrange_sums:
                         print(n,"   ",a," ",b," ",c," ",d,"   ",(a*a+b*b+c*c+d*d))
                         lagrange_sums.add(tuple(sorted([a,b,c,d])))

print("#Lagrange sums for",n," is",len(lagrange_sums))