Guess Game

Bob plays the "guess the number right" with Alice recently,the game's rule is that Alice give Bob a upper limit number N ,then he write any of a number on paper which Bob can't know what it is and the number must be between 1 and N.Bob has many chances to guess the number and every time when Bob guesses Alice will tell him if his is bigger than the correct number or small than the correct number until he is right.
Now the Bob wanted to use binary search method to guess the right number, because he knows this method is quite fast to find the right number.

We test the problem in many cases.Each case begin with one integers N( 1<= N <= 100000 ).

Output the expected number of chances required to guess the number right, which accurate to 2 fractional digits.

2
3

1.50
1.67

erriyue

HDU 3rd “Vegetable-Birds Cup” Programming Open Contest