William thinks 89 is an unlucky number for him. But he still wants to know more about 89. He knows 89 is the 24th prime number, and also a Fibonacci number after searching on the internet.

Recently, William starts to study some problems about right triangles.
He call a right triangle is unlucky if lengths of its both legs are integers
and the length of the hypotenuse is a multiple of
√89.
For example, a right triangle with three edges (5,8,√89) is unlucky,
(4,47,5√89),
(17,44,5√89),
and (10,16,2√89) are also unlucky.
He thinks each unlucky triangle has an energy which is defined by its hypotenuse.
The energy of an unlucky triangle is its hypotenuse divided by √89.
For example, the energy of (5,8,√89) is 1, and the energy of (71,100,13√89) is 13.
William is very curious about the average circumference of all the unlucky triangles whose energy is less than or equal to `n`.
The circumference of a triangle is the sum of its three sides.
Can you help him? William is expecting a precise answer.

There are multiple cases. Each case is an integer number `n` in a line.
(1≤ `n`≤ 10^{8}, the sum of `n` in the whole input is less than 2*10^{8})

Each output for one case has 5 lines. Each output should be in the following format:

*************************************************** * Numerator1 Numerator2 __* *Integer1------------ + Integer2------------ x V89* * Denominator1 Denominator2 * ***************************************************Each mixed fraction should be irreducible. When numerator is 0, the proper fraction part should be omitted. If

Note the characters other than digits used in the output: '*'(Asterisk, ascii code 42), ' '(Space, ascii code 32), '_'(Underscore, ascii code 95), '-'(Hyphen or minus sign, ascii code 45), 'x'(letter x, ascii code 120), and 'V'(letter V, ascii code 86).

Print a blank line after each case. Please refer to the sample output.

********** * __* *13 + V89* * * ********** *************** * 3 __* *58 + 4- x V89* * 5 * *************** **************** * 4 __* *63-- + 5 x V89* * 11 * **************** ******************** * 37 13 __* *598-- + 48-- x V89* * 90 18 * ******************** ********************************************** * 93224754 97600661 __* *620114538--------- + 51235071--------- x V89* * 106191655 318574965 * **********************************************

If `n` is 10^{8}, there are 637149947 kinds of right triangles in different shapes and sizes.

Explanation for `n`=8, we can find 10 unlucky right triangles whose energy is no more than 8. They are
(5,8,√89),
(10,16,2√89),
(15,24,3√89),
(20,32,4√89),
(4,47,5√89),
(17,44,5√89),
(25,40,5√89),
(30,48,6√89),
(35,56,7√89),
and (40,64,8√89).
The sum of circumferences is 580+46√89,
so the average circumference is (580+46√89)/10.

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