1’s For All

문제

The complexity of an integer is the minimum number of $11$'s needed to represent it using only addition, multiplication and parentheses. For example, the complexity of $22$ is $22$ (writing $22$ as $1+11+1$) and the complexity of $1212$ is $77$ (writing $1212$ as $(1+1+1)\times (1+1+1+1)(1+1+1)\backslash times\; (1+1+1+1)$). 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 $1212\backslash$©$34\backslash \; 34$ becomes the four digit number $12341234$. Using this operation, the complexity of $1212$ is now $33$ (writing it either as $(1(1\; \backslash$©$1)+1\backslash \; 1)\; +\; 1$ or $11\backslash$©$(1+1)\backslash \; (1+1)$).  Note that the concatenation operation ignores any initial zeroes in the second operand: $11\backslash$©$01\backslash \; 01$ does not result in $101101$ but results in $1111$.

We'll give you $11$ guess what the object of this problem is.

입력

Each test case consists of a single line containing an integer $nn$, where .

출력

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