ns = set()
for c in range(1, (int(2025**(1/3)))+1):
    for b in range(c+1, (int((2025/2)**(1/3)))+1):
        for a in range(b+1, (int(2025**(1/3)))+1):
            N = a**3+2*b**3+c**3
            if N < 2025:
                ns.add((N,(a,b,c)))
# for x in sorted(ns,key=lambda x:x[1]):
#     print(x)
sq = set()
from itertools import permutations
from math import isqrt

    
for x in range(1, int(6666**0.5)+1):
    y = x**2
    if all('1'<=e<='6' for e in str(y)):
        sq.add(y)
def has_sq(s):
    n = len(s)
    for k in range(1, n + 1):
        for p in permutations(s, r=k):
            m = int(''.join(map(str, p)))
            if m in sq:
                return True
    return False

ds = []
other = []
for i in range(1, 7):
    r = [i]
    if has_sq(r):
        ds.append(r[:])
    else:
        for j in range(1, 7):
            s = r[:] + [j]
            if has_sq(s):
                ds.append(s)
            else:
                for k in range(1, 7):
                    t = s[:] + [k]
                    if has_sq(t):
                        ds.append(t)
                    else:
                        for l in range(1, 7):
                            u = t[:] + [l]
                            if has_sq(u):
                                ds.append(u)
                            else:
                                other.append(u)
print(ds)
print(other)
print(len(other))
from fractions import Fraction
a, b = Fraction(0), Fraction(0)
for d in ds:
    q = Fraction(1, 6**len(d))
    if len(d) in (1, 3):
        a += q
    else:
        b += q
print(a, b)