F(4)-decomposition
The set (F(n)) consists of all infinite continued fractions ([a_0, a_1, ...]), where each partial quotient (a_i) (for (i > 0)) is less than or equal to (n). There are no restrictions on the integer part.
Your task is to express a given real number (x) as the sum of two infinite continued fractions belonging to the class (F(4)).
Input
The input consists of a single line containing the real number (x). The absolute value of (x) does not exceed (100), and it is specified with up to (11) digits after the decimal point.
Output
The output should consist of two lines. The first line should present a finite continued fraction ([a_0, a_1, ..., a_m-1]), and the second line should present another finite continued fraction ([b_0, b_1, ..., b_n-1]). These fractions are finite approximations of infinite continued fractions, whose sum exactly equals (x). The sum of the values of these finite fractions must equal (x) with a precision of at least (10^-11). If multiple valid decompositions exist, any of them can be provided. If no suitable fractions can be found, output (NO SOLUTION) on a single line.