# Problem A

1's For All

The *complexity * of an integer is the minimum number
of $1$’s needed to
represent it using only addition, multiplication and
parentheses. For example, the complexity of $2$ is $2$ (writing $2$ as $1+1$) and the complexity of
$12$ is $7$ (writing $12$ as $(1+1+1)\times (1+1+1+1)$). We’ll
modify this definition slightly to allow the concatenation
operation as well. This operation (which we’ll represent using
©) takes two integers and “glues” them together, so
$12\ $©$\ 34$ becomes the four digit number
$1234$. Using this
operation, the complexity of $12$ is now $3$ (writing it either as $(1 \ $©$\ 1) + 1$ or $1\ $©$\
(1+1)$). Note that the concatenation operation ignores
any initial zeroes in the second operand: $1\ $©$\
01$ does not result in $101$ but results in $11$.

We’ll give you $1$ guess what the object of this problem is.

## Input

Each test case consists of a single line containing an integer $n$, where $0 < n \leq 100\, 000$.

## Output

Output the complexity of the number, using the revised definition above.

Sample Input 1 | Sample Output 1 |
---|---|

2 |
2 |

Sample Input 2 | Sample Output 2 |
---|---|

12 |
3 |