In the Qingshui Village, there's a clever thief and a cleverer police.
There are N houses in Qingshui Village which are located in a straight line. And the N houses are numbered from 1 to N according to the direction of the line. Two houses are consided to be neighbor of each other if and only if there is no other house between them.
The thief hides in one of N houses now, and the police tries to find him out. Every day the police will choose a house to check and he will catch the thief if he hides in that house. If the thief survive the arrest of the police, in the night he will move to a neighboring house to pass through the next day.
What is the number of days the police needs to catch the thief in the worst case?
Remember that the police is a clever man.