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Задачі

Mesmerization of The Count

Mesmerization of The Count

Ліміт часу 1 секунда
Ліміт використання пам'яті 64 MiB

"Sesame Street’s" The Count has gone bad. He has escaped the hard-scrabble New York streets where he gained his fame and now haunts Oregon, surprising and killing unwary programmers throughout the state. Only one defense has been found: he is mesmerized by equations of the form

(a/b)^3 + (c/b)^3 = n

for natural numbers a, b, c, and n. For instance,

(415280564497/348671682660)^3 + (676702467503/348671682660)^3 = 9

stopped him in his tracks for a good 20 minutes, giving mathematician Henry Dudeney enough time to escape a certain death. Unfortunately, large numbers like this are too hard to memorize, so shorter ones such as

(2/1)^3 + (1/1)^3 = 9

are better. Each such equation is only good for one mesmerization, so your job is to write a program that will generate new such equations. In particular, you will be given n, and your job is to generate values for the natural numbers a, b, cthat satisfy the first equation. When multiple solutions exist, you should report the one with the minimum possible suma + b + c + b, such that the value of a/b is greater than or equal to the value of c/b. You may assume such a solution is unique. If you cannot find three natural numbers a, b, c such that a + b + c + b is less than 4000, you should print "No value.".

Вхідні дані

The input will be a sequence of lines; each line will contain a single natural number less than 10000. Input is terminated with a 0, which should not be processed.

Вихідні дані

For any valid equation you find, print the equation with the appropriate values for a, b, and c. A single space should precede and follow the + and the = in the equation. When no valid equation exists, print "No value.".

Приклад

Вхідні дані #1
1
9
7
6000
0
Вихідні дані #1
No value.
(2/1)^3 + (1/1)^3 = 9
(5/3)^3 + (4/3)^3 = 7
(370/21)^3 + (170/21)^3 = 6000
Джерело ACM ICPC North America - Pacific Northwest 2010