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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(let ((n (read))
    (ans 0)
    (a 0)
    (b 0))
    (loop for i from 1 while (<= (* i i) n) do
        (if (zerop (rem n i))
        (progn
            (setq a i)
            (setq b (/ n i))
            (if (= ans 0)
                (setq ans (max (length (princ-to-string a)) (length (princ-to-string b))))
                (if (> ans (max (length (princ-to-string a)) (length (princ-to-string b))))
                    (setq ans (max (length (princ-to-string a)) (length (princ-to-string b))))
                )
            )
            (if (not (= (* i i) n))
                (progn
                    (setq a i)
                    (setq b (/ n i))
                    (if (> ans (max (length (princ-to-string a)) (length (princ-to-string b))))
                    (setq ans (max (length (princ-to-string a)) (length (princ-to-string b))))
                )
                )
            )
        )
        )
    )
    (princ ans)
)