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#2933. 三进制数字

統計

“Sequinary” 数(sequinary numeral)是一个数字序列:

$$d_n d_{n-1} \dots d_1 d_0$$

其中 $d_n$ 为 $1$ 或 $2$,其余数字为 $0$、$1$ 或 $2$。

它表示的有理数为:

$$d_0 + d_1 \cdot (3/2) + d_2 \cdot (3/2)^2 + \dots + d_n \cdot (3/2)^n$$

编写一个程序,输入一个 sequinary 数,并以真分数的形式输出它所表示的数值。

输入格式

输入包含一行,为一个不超过 $32$ 位的 sequinary 数。

输出格式

输出包含一行。

如果结果是一个整数,则输出该整数。否则,输出 $N$、一个空格以及 $K/M$,其中 $N$、$K$ 和 $M$ 为十进制整数,$K < M$ 且 $K/M$ 为最简分数(即 $\gcd(K, M) = 1$)。

样例

样例输入 1

2101

样例输出 1

10

样例输入 2

201

样例输出 2

5 1/2

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