Quadratic Irrationality Representation

Input

The input consists of a single line containing the continued fraction. If the fraction is finite, it is given in the format [ $a_{0}, a_{1}, \dots, a_{n - 1}$ a_0, a_1, \ldots, a_{n-1}], where $1 \leq n \leq 13$ 1 \le n \le 13. If the fraction is periodic, it is given in the format [ $a_{0}, \dots, a_{p - 1}, (a_{p}, \dots, a_{p + l - 1})$ a_0, \ldots, a_{p-1}, (a_p, \ldots, a_{p+l-1})], where $p \geq 0$ p \ge 0, $l > 0$ l > 0, and $p + l \leq 13$ p + l \le 13. The constraints for the coefficients are $- 5 \leq a_{0} \leq 5$ -5 \le a_0 \le 5 when $p > 0$ p > 0, and $1 \leq a_{i} \leq 5$ 1 \le a_i \le 5 for $i > 0$ i > 0.

Output

Output a single line representing the continued fraction as either a rational $a / c$ , where $a$ and $c$ are integers, $c > 0$ c > 0, or as a quadratic irrationality $(a + b N) / c$ (a + b\sqrt{N})/c (or $(a - b N) / c$ (a - b\sqrt{N})/c), where $a$ , $b$ , $c$ , $N$ are integers, $a, b > 0$ a, b > 0, $c > 0$ c > 0, $N > 0$ N > 0. If both representations are possible, output the rational one. If there are several possible representations, choose the one with the minimal $N$ , and among those, the one with the minimal $c$ .

Examples

Example 1

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