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 $N = A \times B$.

Examples

Input

10000

Output

3

Input

1000003

Output

7

Input

9876543210

Output

6

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