## implementation

fun sievePrimes(n) =
let
val isPrime = Array.array(n, true)
fun fill(i, j) =
if j < n
then ( Array.update(isPrime, j, false) ; fill(i, j+i) )
else ()
fun go(i) =
if i = Array.length isPrime
then ()
else if not(Array.sub(isPrime, i))
then go(i+1)
else ( fill(i, 2*i) ; go(i+1) )
in
Array.update(isPrime, 0, false) ;
Array.update(isPrime, 1, false) ;
go(2) ;
isPrime
end

fun listPrimes(n) =
let
val primes = sievePrimes(n)
val primes = Array.foldli (fn (i, isPrime, acc) => if isPrime then i :: acc else acc) [] primes
val primes = Vector.fromList(List.rev(primes))
in
primes
end

fun factorize(n) =
let
val primes = listPrimes( ceil(Math.sqrt(Real.fromLargeInt(n))) + 3 )
val factors = ref []
val n = ref n
in
Vector.app (fn (p) =>
let
val p = Int.toLarge(p)
in
while !n mod p = 0 do (
factors := p :: !factors ;
n := !n div p
)
end
) primes ;
if !n <> 1 then factors := !n :: !factors else () ;
List.rev(!factors)
end

fun digitLength(n) =
let
fun go(0, acc) = acc
| go(n, acc) = go(n div 10, acc + 1)
in
go(n : LargeInt.int, 0)
end

fun solve(n) =
let
fun go([], a, b) = Int.max(digitLength(a), digitLength(b))
| go(p :: qs, a, b) = Int.min(go(qs, p * a, b), go(qs, a, p * b))
val factors = factorize(n)
in
go(factors, 1, 1)
end

fun readInt() = TextIO.scanStream (LargeInt.scan StringCvt.DEC) TextIO.stdIn