PSO

Problem Description

Particle swarm optimization ( PSO ) is a population-based stochastic optimization algorithm. In addition to the basic structure of PSO, there is also a variant called star-topology PSO, which introduces a star-shaped communication structure among particles. In this structure, there is a central particle called the leader, which is responsible for gathering and disseminating information to the rest of the particles in the swarm. Now there are $n$ particles on the star-topology. Among the $n$ particles, there is one particle as the leader, and there is an edge between the other particles and the leader. For a piece of information, it can be propagated along an edge on the topology. To examine the benefits of this topology, we need to calculate the following data: We define that $X$ is number of edges required for them to exchange information for two different particles. Please calculate the expected value and maximum value of $X$.

Input

The first line of input is a positive integer $T(T\leq 10^5)$ representing the number of test cases. For each line,input a number $n(2\leq n\leq10^9)$.

Output

For each case, output two floating-point numbers representing the he expected value rounde off and maximum value of $X$. (keep $9$ decimal places)

Sample Input

2
4
7

Sample Output

1.500000000 2.000000000
1.714285714 2.000000000

Source

2023“钉耙编程”中国大学生算法设计超级联赛（4）