Exact Arithmetic

Let $X$ be the set of all rational numbers and all numbers of the form $q \sqrt{r}$, where $q$ is a non-zero rational number and $r$ is an integer greater than $1$. Here, $r$ must not have a square number other than $1$ as a divisor. Also, let $X^{*}$ be the set of all numbers that can be expressed as a sum of one or more elements of $X$.

Consider the machine $Y$, a stack-based calculator that operates on values in $X^{*}$ and has the instructions shown below.

• push $n$: pushes the integer specified in the operand onto the stack.
• add: pops two values $x_1$ and $x_2$ from the top of the stack in this order, then pushes $(x_2 + x_1)$.
• sub: pops two values $x_1$ and $x_2$ from the top of the stack in this order, then pushes $(x_2 - x_1)$.
• mul: pops two values $x_1$ and $x_2$ from the top of the stack in this order, then pushes $(x_2 \cdot x_1)$.
• div: pops two values $x_1$ and $x_2$ from the top of the stack in this order, then pushes $(x_2 / x_1)$. Here, $x_1$ must be a non-zero value in $X$ (not in $X^{*}$).
• sqrt: pops one value $x$ from the stack and pushes the square root of $x$. Here, $x$ must be a non-negative rational number.
• disp: pops one value $x$ from the stack and outputs the string representation of $x$ to the display. The representation rules are stated below.
• stop: terminates the calculation. The stack must be empty when this instruction is called.

Initially, the stack is empty. A sufficient number of values must be present on the stack when every instruction is executed. In addition, because of the limits of machine $Y$, no more values can be pushed when the stack already holds $256$ values. There are also several restrictions on the values pushed onto the stack:

• For rational numbers, neither the numerator nor the denominator in lowest terms may exceed $32\,768$ in absolute value.
• For any element of $X$ of the form $q \sqrt{r} = (a / b) \sqrt{r}$, both $|a \sqrt{r}| \le 32\,768$ and $|b| \le 32\,768$ must hold.

For any element of $X^{*}$, each term in the sum must satisfy the conditions above.

The rules for the string representations of values on machine $Y$ are as follows:

• A rational number is represented either as an integer or as an irreducible fraction whose denominator is greater than $1$.
• A fraction is represented as $\mathit{num}$/$\mathit{den}$, where $\mathit{num}$ is the numerator and $\mathit{den}$ is the denominator. The sign character - precedes negative numbers.
• A number of the form $q \sqrt{r}$ is represented as $\mathit{rep}$*sqrt($r$), except when $|q| = 1$; in that case it is represented as sqrt($r$) for $q = 1$ or -sqrt($r$) for $q = -1$. Here, $\mathit{rep}$ is the string representation of $q$.
• A sum of two or more elements of $X$ is represented by joining the string representations of all its non-zero elements with the binary operator +. All terms with the same rooted number are merged into a single term, and the terms must appear in ascending order of their root component. For this rule, every rational number is regarded as carrying $\sqrt{1}$. There is exactly one space character before and after each binary operator +. No space characters appear anywhere else.

The following are a few examples of valid string representations:

0
1
-1/10
2*sqrt(2) + 1/2*sqrt(3) + -1/2*sqrt(5)
1/2 + sqrt(10) + -sqrt(30)

Your task is to write a program that simulates machine $Y$.

The input is a sequence of no more than $3000$ instructions. Each line contains a single instruction. You may assume that every instruction is called in a legal way. The instruction "stop" appears only once, at the end of the entire input.

Output the strings that machine $Y$ displays. Write each string on a separate line.