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-----
10000

-----Sample Output-----
3

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

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