13482번 - Java2016 스페셜 저지다국어

문제

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

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

Java2016 supports six operators of three precedencies:

⟨expression⟩ ::= ⟨expression⟩‘min’⟨sum⟩ | ⟨expression⟩‘max’⟨sum⟩ | ⟨sum⟩
⟨sum⟩ ::= ⟨sum⟩‘+’⟨term⟩ | ⟨sum⟩‘-’⟨term⟩ | ⟨term⟩
⟨term⟩ ::= ⟨term⟩‘*’⟨factor⟩ | ⟨term⟩‘/’⟨factor⟩ | ⟨factor⟩
⟨factor⟩ ::= ‘(’⟨expression⟩‘)’ | ‘?’ | ⟨macro⟩

Minimum (‘min’) and maximum (‘max’) operators are defined as usual. Addition (‘+’), subtraction (‘-’) and multiplication (‘*’) are defined modulo 256. The result of the division (‘/’) is rounded towards zero. If the divider is zero, the program crashes. The argument of the operator is a result of another operator, evenly distributed random value (‘?’), or macro substitution.

For instance, the probability that “?/?/?” 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

⟨macrodef⟩ ::= ⟨macro⟩‘=’⟨expression⟩
⟨macro⟩ ::= ‘a’ . . . ‘z’

The macro should be defined before the first use. It may not be redefined. The macro is expanded to its definition 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 program that successfully evaluates to this value with at least one-half probability. Crashes are counted toward failures.

입력

The input contains a single integer c — the target constant (0 ≤ c ≤ 255).

출력

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).

제한

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