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 () = Scanf.scanf "%d" @@ fun n ->
  Array.init (int_of_float (ceil @@ sqrt @@ float_of_int n)) (fun a ->
    if n mod (a + 1) = 0 then max (a + 1) (n / (a + 1))
    else max_int)
  |> Array.fold_left min max_int
  |> (fun a -> Printf.printf "%d\n" @@ succ @@ int_of_float @@ log (float_of_int a) /. log 10.)