Periodic decimal fraction is usually written as: [entire_part.non-periodic_part (period)]. Any simple fraction can be represented as a periodic decimal fraction and vice versa. For example, the decimal fraction 0.2(45) corresponds to a fraction 27 / 110. Your task is to convert the periodic fraction to a simple periodic fraction.

Input

The first line contains the periodic decimal fraction x (0 < x < 1) in the format described in the statement. The total number of digits in the period and non-periodic part of the fraction does not exceed 8. Non-periodic part may be absent, the periodic part can't be absent (but it can be equal to any non-negative number).

Output

Print the representation of the fraction x as a simple fraction p / q, where p and q are mutually prime integers.

Examples

Input

0.2(45)


Output

27/110


Input

0.75(0)


Output

3/4

Source: codeforces | Difficulty: HARD


Solutions: