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from sys import stdout
from primefac import primefac
from math import sqrt
# -- "any sufficiently well-commented lisp program contains an ML program in its comments"
# def solution (p a b : N) := a^2 + b^2 = (ab + 1) p^2
# def sym (p a b : N) : solution p a b -> solution p b a
# def sol0 (p : N) : solution p 0 p
# def generator (p a b : N) (p > 0) (a <= b) : solution p a b -> solution p b (b * p^2 - a)