题目描述

John likes to learn esoteric programming languages. Recently he discovered the probabilistic $\textit{programming language}$ Java2K. Built-in functions of Java2K have only a certain probability to do whatever you $\textit{intend them}$ to do.

The Java2K programming is very hard, so John designed a much simpler language for training: Java2016. $\textit{Built-in}$ operators of Java2016 are deterministic, while their operands are random. Each value in $\textit{Java2016 is}$ a positive integer in the range $0 \cdots 255$ , inclusive.

Java2016 supports six operators of three precedencies:

$$\begin{aligned}{\langle \mathrm{expression}\rangle}&\quad::=\quad{\langle \mathrm{expression}\rangle}\operatorname{`\texttt{min}\text'}{\langle \mathrm{sum}\rangle}\mid{\langle \mathrm{expression}\rangle}\operatorname{`\texttt{max}\text'}{\langle \mathrm{sum}\rangle}\mid {\langle \mathrm{sum}\rangle}\\{\langle \mathrm{sum}\rangle}&\quad::=\quad{\langle \mathrm{sum}\rangle}\operatorname{`\texttt{+}\text'}{\langle \mathrm{term}\rangle}\mid{\langle \mathrm{sum}\rangle}\operatorname{`\texttt{-}\text'}{\langle \mathrm{term}\rangle}\mid{\langle \mathrm{term}\rangle}\\{\langle \mathrm{term}\rangle}&\quad::=\quad{\langle \mathrm{term}\rangle}\operatorname{`\texttt{*}\text'}{\langle \mathrm{factor}\rangle}\mid {\langle \mathrm{term}\rangle}\operatorname{`\texttt{/}\text'}{\langle \mathrm{factor}\rangle}\mid {\langle \mathrm{factor}\rangle}\\{\langle \mathrm{factor}\rangle}&\quad::=\quad\operatorname{`\texttt{(}\text'}{\langle \mathrm{expression}\rangle}\operatorname{`\texttt{)}\text'}\mid `\texttt{?}\text'\mid {\langle \mathrm{macro}\rangle}\end{aligned} $$

Minimum $(\textit{`min'})$ and maximum $((\textit{`max'}))$ operators are defined as usual. Addition $(\text{`+'}),$ subtraction $(\text{`--'}) and$ multiplication $(\text{`}\times\text{'})$ are defined modulo $256$ . The result of the division $(\text{`}/\text{'})$ is rounded towards zero. $\textit{If}$ the divider is zero, the program crashes. The argument of the operator is a result of another $\textit{operator, evenly}$ distributed random value $(\text{`}?\text{'})$, or macro substitution.

For instance, the probability that $\text{`?/?/?'}$ is evaluated to zero is $98.2\%$, while the probability of $the crash$ is $0.8\%$.

The Java2016 program consists of zero or more macro definitions, followed by the resulting expression. $Each$ macro definition has a form of

$$\begin{aligned}{\langle \mathrm{macrodef}\rangle}&\quad::=\quad{\langle \mathrm{macro}\rangle}\operatorname{`\texttt{=}\text'}{\langle \mathrm{expression}\rangle}\\{\langle \mathrm{macro}\rangle}&\quad::=\quad\operatorname{`\texttt{a}\text'}\ldots\operatorname{`\texttt{z}\text'}\end{aligned} $$

The macro should be defined before the first use. It may not be redefined. The macro is expanded to $its definitio_n$ on each use. For instance,

a = ? max ?
(a max $a) / a

is expanded to ((? max ?) max (? max ?)) / (? max ?).

John is going to add probabilistic constants to Java2016, so for each possible constant value he needs $a progra_m$ that successfully evaluates to this value with at least one-half probability. Crashes are $\textit{counted toward}$ failures.

输入格式

The input contains a single integer $c$ -- the target constant $(0 \le c \le 255)$ .

输出格式

Output a Java2016 program that successfully evaluates to constant $c$ with probability no less than $1/2$ . $The$ total length of the program should not exceed $256$ characters (excluding spaces).

题目大意

John 喜欢学习深奥的编程语言。最近，他发现了概率编程语言 Java2K。Java2K 的内置函数只有一定的概率去执行你想让它们做的事情。

Java2K 编程非常困难，因此 John 设计了一种简单得多的语言用于训练：Java2016。Java2016 的内置运算符是确定性的，而它们的操作数是随机的。Java2016 中的每个值都是 $0$ 到 $255$ (包含 $0$ 和 $255$) 中的整数。

Java2016 支持分为三个优先级的六种运算符：

$$\begin{aligned}{\langle \mathrm{expression}\rangle}&\quad::=\quad{\langle \mathrm{expression}\rangle}\operatorname{`\texttt{min}\text'}{\langle \mathrm{sum}\rangle}\mid{\langle \mathrm{expression}\rangle}\operatorname{`\texttt{max}\text'}{\langle \mathrm{sum}\rangle}\mid {\langle \mathrm{sum}\rangle}\\{\langle \mathrm{sum}\rangle}&\quad::=\quad{\langle \mathrm{sum}\rangle}\operatorname{`\texttt{+}\text'}{\langle \mathrm{term}\rangle}\mid{\langle \mathrm{sum}\rangle}\operatorname{`\texttt{-}\text'}{\langle \mathrm{term}\rangle}\mid{\langle \mathrm{term}\rangle}\\{\langle \mathrm{term}\rangle}&\quad::=\quad{\langle \mathrm{term}\rangle}\operatorname{`\texttt{*}\text'}{\langle \mathrm{factor}\rangle}\mid {\langle \mathrm{term}\rangle}\operatorname{`\texttt{/}\text'}{\langle \mathrm{factor}\rangle}\mid {\langle \mathrm{factor}\rangle}\\{\langle \mathrm{factor}\rangle}&\quad::=\quad\operatorname{`\texttt{(}\text'}{\langle \mathrm{expression}\rangle}\operatorname{`\texttt{)}\text'}\mid `\texttt{?}\text'\mid {\langle \mathrm{macro}\rangle}\end{aligned} $$

最小 ($\operatorname{`\texttt{min}\text'}$) 和最大 ($\operatorname{`\texttt{max}\text'}$) 运算符的定义和通常一样。加法 ($\operatorname{`\texttt{+}\text'}$)、减法 ($\operatorname{`\texttt{-}\text'}$) 和乘法 ($\operatorname{`\texttt{*}\text'}$) 是在模 $256$ 的意义下定义的。除法 ($`\operatorname{\texttt{/}\text'}$) 的结果向 $0$ 取整。如果除数是 $0$，程序就会崩溃。运算符的参数是另一个运算符的结果、均匀分布的随机数 ($\operatorname{`\texttt{?}\text'}$) 或宏代换的结果。

例如，$``\texttt{?/?/?}\text{''}$ 有 $98.2\%$ 的概率计算得到 $0$，而崩溃的概率为 $0.8\%$。

Java2016 程序由零个或多个宏定义以及随后的结果表达式组成。每条宏定义都形如

$$\begin{aligned}{\langle \mathrm{macrodef}\rangle}&\quad::=\quad{\langle \mathrm{macro}\rangle}\operatorname{`\texttt{=}\text'}{\langle \mathrm{expression}\rangle}\\{\langle \mathrm{macro}\rangle}&\quad::=\quad\operatorname{`\texttt{a}\text'}\ldots\operatorname{`\texttt{z}\text'}\end{aligned} $$

宏必须在第一次使用前被定义。宏不能被重复定义。宏在每次使用时都会被展开成它的定义。例如，

$$\texttt{a = ? max ?}\\\texttt{(a max a) / a}$$

会被展开成 $``\texttt{((? max ?) max (? max ?)) / (? max ?)}\text{''}$。

John 将要把概率常量加入 Java2016，因此对每个可能的常量，他需要一个程序能以至少一半的概率成功计算出这个值。崩溃被算作失败。

输入

输入包含一个整数 $c$ ($0\le c\le 255$)，表示目标常量。

输出

输出一个 Java2016 程序，它需要能够以至少 $1/2$ 的概率成功计算出常量 $c$。程序的总长度不应超过 $256$ 个字符 (空格不计算在内)。

0

? /?/ ?

1

a = ? max ?
(a max a) / a

提示

Time limit: 2 s, Memory limit: 512 MB.