Limits 1s, 512 MB

Definition:

We all know how to measure the linear distance between two points AA and BB. It is measured by the length of the straight line drawn from AA to BB. However, if we want to measure the angular distance between AA and BB, we will need a third point as reference. The angular distance from point AA to point BB with respect to point CC is defined by the angle ACB\angle ACB.

Look at the figure for clarification.

Here, rr is the linear distance between AA and BB. φφ and θθ are both angular distance between AA and BB, but with respect to point CC and DD respectively.

Problem Statement:

Meena’s school is so far far away from her home that she and her friends get super হয়রান every day from all the walking. Moreover, they get poor attendance marks (as they can’t reach school timely) and often fail to return home “সূর্য ডোবনের আগে”. So, with the term-final approaching, Meena decides to build three beautiful houses near her school so that they can attend school more easily. One house is for herself, one is for her brother Raju, and one is for her friend Rita. You can consider these houses and the school as four distinct points on a 2-Dimensional plane.

Meena also has three wishes regarding these houses:

  • Meena wants to connect the four buildings (three houses and one school) with straight lines to enclose an area XX, and she wants the value of XX to be as large as possible.

  • As they want to live near each other as well as the school, the maximum linear distance between any two buildings can be no more than mm.

  • Angular distance from the school to each house with respect to the other two houses will be equal to one another.

Being only good at দুই এর ঘরের নামতা, Meena can’t figure out what will be the maximum value of XX for a given mm. So she calls you, as you are her friend, and says,

বন্ধুরা তিনটা ইচ্ছা পূরণ করবো,

তুমিও আসো তুমিও আসো সাহায্য করতে আসো

Can you be a good friend and help Meena?

Input

First line of input contains an integer tt (t10000t \le 10000), which denotes the number of testcases. Next tt lines each represents one testcase. Each testcase has only one integer mm (1m100001 \le m \le 10000), denoting the maximum linear distance between any two buildings.

Output

For each testcase, print a double type number with exactly two digits after the decimal point, denoting the maximum possible value of XX.

Sample

InputOutput
2
4
22
8.00
242.00

Please note that the only purpose of the figures presented in the description is to help you understand the problem statement. These figures are freestyle drawings and may not satisfy the given conditions

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Statistics

92% Solution Ratio
Pheonix98Earliest, Aug '17
Marzuq01Fastest, 0.0s
Maesha_MULightest, 131 kB
bokaifShortest, 48B
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