Digits in Multiplication

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

inputFormat

Input

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

N

outputFormat

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

样例

1000003

7