Description

Let $S_k$ be the area of the triangle enclosed by the lines $l_{k1}:y=kx+k-1$, $l_{k2}:y=(k+1)x+k$, and the $x$-axis. Find:

In this problem, there are $t$ queries in total. Each query gives $n_i$, and you need to compute the value of the expression above when $n=n_i$.

If $n<1$, the value of the sum is considered to be $0$.

Input Format

There are $t+1$ lines in total.

The first line contains an integer $t$, meaning there are $t$ sets of testdata.

The next $t$ lines each contain an integer $n_i$, with the meaning as described in the statement.

Output Format

There are $t$ lines in total.

Each line contains one number, representing the answer you computed.

The result may be a fraction. Please reduce it to the simplest fraction. Output fractions in the form xxx/xxx. For example, $\dfrac{1}{2}$ should be written as 1/2, and $\dfrac{2}{4}$ should be written as 1/2. Note that you must reduce the fraction.

Note: If the answer is $0$, output 0.

2
0
1

0
1/4

Hint

[Sample Explanation]

When $n=0$, according to the statement, output $0$.

When $n=1$, $S_1$ is the area enclosed by $y=x$, $y=2x+1$, and the $x$-axis, which is $\dfrac{1}{4}$.

[Constraints]

• For $5\%$ of the data, $t \le 100,n=0$.
• For another $20\%$ of the data, $t \le 100,n \le 2020$.
• For another $20\%$ of the data, $t \le 5 \times 10^4,n \le 5 \times 10^3$.
• For $100\%$ of the data, $1 \le t \le 2 \times 10^6,0 \le n \le 2 \times 10^6$.

[Notes / Hints]

• It is recommended to draw a diagram and think about it.
• Please remember to reduce the answer when outputting.
• Please use a fast input method.

[File Input/Output] (Simulation, not needed in submitted code)

• Filename: function.cpp.
• Input filename: function.in.
• Output filename: function.out.

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