WC 7.1 Expected Number of Chocolates

You have a bag with n different types of chocolates, one of each type. You pick one chocolate randomly each time from the bag, and then place it back in the bag. On an average, how many times will you need to pick chocolates from the bag to have picked one chocolate of each type at least once?

Input

n=100

Output

The expected number of chocolates that need to be picked. Round your answer to the nearest integer greater than the answer.

Examples

Sample Input
1
2
Sample Output
1.0
3.0

This challenge is worth 80 points.

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