The Fool, as his name suggests, does not know the concept of numbers. To communicate with others, the Fool can only count out the number he wanted to convey.
Through experience, he has developed a better way to count. To convey 15 objects, he would first count 3, followed by 5. These two numbers represent the side lengths when the objects are arranged in a rectangle. In this example, he counted a total of $3+5=8$ times.
Now, the fool would like to convey the number $N$. Can you help him to find out the minimum times of counting, using his method?

Input

The first line consists of an integer $N$.

Output

Output the answer as an integer.

Constraints

For all testcases: $1 \le N \le 10^9$
Subtask 1 (50%): $N \le 10^6$
Subtask 2 (50%): No other constraints