Algorithm title: UVA 10169

Problem B

Urn-ball probabilities!

Input:standard input

Output:standard output

Time Limit:3 seconds

Assume that you have two urns before. Initially, one urn has one ball and the other urn has two balls and exactly one ball into each urn is red. At this initial stage your are asked to pick up two balls, one from each urn. Then one white ball are added in each urn and your are again asked to pick up one ball from each urn Then again one white BA ll is added in each urn. This process continues to a certain time. Remember that's the picked ball the urn after each pick up. You'll have to determine the probability of your pickups both of the picked balls were red and also the prob Ability that all of the your picked balls were certain red after steps.

Input

The input file contains several lines of inputs. Each line of the input file contains a unsigned integer N (n<1000000) indicating how many times you'll pick up. Course after each pick up a increment in balls occurs as described previously.

Output

For each line of input print a single line of output containing a floating point number and integer. The floating-point number indicates the probability that your have picked up two red balls to at least one of your pick-ups and the second integer denotes how many consecutive zeros are after decimal point in the There value Of your pick ups has both balls as red.

Sample Input:

1

2

20

Sample Output:

0.500000 0

0.583333 1

0.688850 38