You are given an integer . You want to break it down into three non-negative integers , , and such that and maximizes:
Print out the maximum such value of given .
Input Specification
The first line will contain the integer .
Output Specification
Output the maximum such value of .
Subtasks
Subtask 1 [20%]
Subtask 2 [80%]
No further constraints.
Sample Input
4
Sample Output
7
Explanation for Sample
One possible solution would be .
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