There are 13 caves arranged in a circle. There is a thief in one of the caves. Each day the thief can move to any one of the adjacent cave or can stay in the same cave in which he was staying the previous day. And each day, cops are allowed to enter any two caves of their choice.

What is the minimum number of days to guarantee in which cops can catch the thief?

Note:

  • Thief may or may not move to adjacent cave.
  • Cops can check any two caves, not necessarily be adjacent.
The Answer is an integer. Just put the number without any decimal places.