Problem:
Score : 300 points

Problem Statement

You are given an integer N.

For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.

For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.

Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

1 \leq N \leq 10^{10}

N is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let digits n =
  let rec aux m ans =
    if m < 1 then ans else aux (m / 10) (succ ans)
  in
  aux n 0

let solve n =
  let b = sqrt n |> int_of_float in
  let intn = int_of_float n in
  let rec aux b' =
    if intn mod b' = 0 then max (digits b') (digits (intn / b'))
    else aux (pred b')
  in
  aux b

let () = Scanf.scanf "%f\n" solve |> Printf.printf "%d\n"