main input = print eol (fac (parse input))
fac2 = yy (\ self n acc -> ifLtEq n n1 acc (self (pred n) (times n acc)) )
fac n = fac2 n n1

eol = cons n10 endOfOutput
chr d = plus d n48
pr2 = yy (\ self end cns n -> ifLt n n10 (cns (chr n) end) (cns (chr (mod n n10)) (self end cns (div n n10))))
print end n = append (reverse (pr2 nil cons n)) end
ord d = minus d n48
parse n = parse2 n n0
parse2 = yy (\ self input acc -> ifGtEq (car input) n57 acc (ifLt (car input) n48 acc (self (cdr input) (plus (times n10 acc) (ord (car input)))) ) )
reverse l = rev2 l nil
rev2 = yy (\ self l a -> if3 (isNull l) a (self (cdr l) (cons (car l) a)) )
append = yy (\ self a b -> if3 (isNull a) b (cons (car a) (self (cdr a) b)) )
true = \ x y -> x
false = \ x y -> y
if3 p x y = p x y
cons x y = \ f -> f x y
car lst = lst true
cdr lst = lst false
nil = \ f -> true
isNull lst = lst (\ x y -> false)
nth n lst = car ((n cdr) lst)
kk x y = x
eq a b = ( nth b ((a (cons false)) (cons true (listOf false))) )
ifEq m n x y = if3 (eq m n) x y
ifLtEq  m n x y = (m pow (kk x)) (n pow (kk y))
ifGt    m n x y = ifLtEq m n y x
ifGtEq  m n x y = ifLtEq n m x y
ifLt    m n x y = ifLtEq n m y x
endOfOutput = \f -> n256
listOf elt = yy (cons elt)
yy f = (\ x -> x x) (\ self -> f (self self) )
succ a = \ f x -> (f ((a f) x))
plus a = a succ
times a b = \ f -> a (b f)
pow a b = b a
pred n = \ f x -> n (\ g h -> h (g f)) (\ u -> x) (\ u -> u)
minus big small = (small pred) big
mod = yy (\self big small -> ifGt big small (self (minus big small) small) (ifEq big small n0 big) )
div big small = div2 big small n0
div2 = yy (\self dividend divisor acc -> ifGtEq dividend divisor (self (minus dividend divisor) divisor (succ acc)) acc)
n0 = \ f x -> x
n1 = \ f -> f
n2 = succ n1
n3 = succ n2
n4 = (\ x -> (x x)) n2
n5 = succ n4
n10 = times n2 n5
n16 = (\ x -> x x x) n2
n27 = (\x -> x x) n3
n28 = succ n27
n48 = times n3 n16
n56 = times n2 n28
n57 = succ n56
n256 = (\ x -> (x x)) n4