You are given $2$ integers $A, B$.

Find how many digits the sum of $A$ and $B$ has when written in base ten.

Input

The input is given in the following format:

$$ \begin{aligned} &A \\ &B \end{aligned} $$

Output

Output how many digits the sum of $A$ and $B$ has when written in base ten, omitting the unit (digits).

Do not output anything other than the answer. (Do not output sentences prompting for input, etc.)

For the answer format, you may refer to the practice problems and their sample solutions.

Constraints

• $1 \le A \le 499$.
• $1 \le B \le 499$.
• All input values are integers.

Examples

Input 1

3
9

Output 1

2

Note 1

• The sum of $3$ and $9$ is $12$. Since $12$ has $2$ digits, output $2$.

Input 2

499
499

Output 2

3

Note 2

• The sum of $499$ and $499$ is $998$. Since $998$ has $3$ digits, output $3$.

Input 3

3
2

Output 3

1

Input 4

1
99

Output 4

3