24739번 - Sequinary Numerals 다국어

문제

A sequinary numeral is a sequence of digits:

d_nd_n-2...d₁d₀

where d_n is 1 or 2 and the others are 0, 1, or 2.

It represents the rational number:

d₀ + d1 * (3/2) + d₂ * (3/2)² + ... + d_n * (3/2)ⁿ

Write a program which takes a sequinary numeral as input and returns the number it represents as a proper fraction.

입력

The single line of input contains a sequinary numeral of no more than 32 digits.

출력

Output consists of a single line.

If the result is an integer, the output is the decimal integer. Otherwise, the output is N a single space and K/M where N, K and M are decimal integers where K < M and K/M is in lowest terms (GCD(K, M) = 1).

제한

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