import itertools as it
import numpy as np
import numpy.linalg as la
import queue
from squares import complete_gen1

class form:
    def __init__(self):
        self.cache = dict()
        self.n = 0

    def __getitem__(self, x):
        return x*(3*x-1)//2

    def __contains__(self, x):
        while x >= self[self.n]:
            self.cache[self[self.n]] = self.n
            self.n += 1
        return x in self.cache

    def inv(self, x):
        return self.cache[x]

f = form()

def order():
    for a in it.count(2):
        for b in range(a, (f[a]-1)//3+1):
            yield a, b

def form_list():
    for a, b in order():
        n = f[a] + f[b]
        if n in f:
            c = f.inv(n)
            yield a, b, c