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Farey sequences are named after the British geologist John Farey. The Farey sequence of order $N$ consists all the fractions $a/b$ that satisfy the following conditions:
$0 \leq a \leq b$
$1 \leq b \leq N$
The greatest common divisor of $a$ and $b$ equals $1$.
The sequence is monotonically increasing.
For example, the Farey sequence of order 5 is: $0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1.$
By letting the denominators of the Farey sequence of order $N$ be $d[1]$, $d[2]$, $\cdots$, $d[k]$, the Farey sum of order $N$ is the sum of $d[i]/d[i+1]$ for all $1 \leq i \leq k-1$.
For example, the Farey sum of order 5 is $1/5+5/4+4/3+3/5+5/2+2/5+5/3+3/4+4/5+5/1=29/2$.
Now given integer $N$, it is your task to compute the Farey sum of order $N$.
The first line of the input contains an integer $T$ ($1 \leq T \leq 10000$), the number of test cases. There is only one line of input per test case containing a single integer $N$ ($1 \leq N \leq 10^{6}$), of which the Farey sum of the order $N$ is to be computed.
For each test case, there is a single line of output consisting the Farey sum as a decimal fraction in lowest terms. If the denominator is 1, only the numerator should be printed.
2
2
5
5/2
29/2
no