# J :: Unlucky 89

Time Limit: 3 Seconds Memory Limit: 32768 KB

Amir 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, Amir starts to study some problems about right triangles. He call a right triangle 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. Amir 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? Amir is expecting a precise answer.

## Input

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})

## Output

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

`Numerator2` is 0 and `Integer2` is 1, then "1 x " part should be omitted too. The numerator and the denominator need to be right-aligned. The "---" part should be as same long as the corresponding denominator.

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.

Hint:

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.

## Sample Input

1 8 9 89 99999999

## 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 * **********************************************Submit

Source: 14th Iran Nationwide Internet Contest