My Number

Taaaamara is a big fan of the Serbian quiz Slagalica. Her favorite game in the quiz is My Number. In this game you get a set of integers $S$ and one target number $T$. You can use each element of $S$ at most once and some mathematical operations to build a valid expression equal to $T$. For example, if $S = \{2, 5, 2, 15, 10\}$ and $T = 38$, one valid expression is $2 \times (15 + 5) - 2$.

Today, Taaaamara is playing a modification of this game:

• She has an array $A$ with $n$ integers, all of them target numbers.
• She needs to find an array $B$ with $k$ elements (elements of $B$ do not have to be different). All elements of $B$ must be integers in the range $[1, 10^8]$.
• She wants to build one valid expression for each target number $A_i$ using only elements from $B$. If some element appears $x$ times in $B$, each expression can use that element at most $x$ times.
• She can use the binary operators + (addition), - (subtraction), and * (multiplication). Division is not allowed. She can also use brackets.
• The length $k$ of array $B$ is not fixed, but it must not be bigger than $12$ ($k \leq 12$).

Can you help her?

The first line contains an integer $n$ ($1 \leq n \leq 124$). The second line contains $n$ integers, the array $A$ ($1 \leq A_i \leq 10^8$).

In the first line, print the integer $k \leq 12$, the length of array $B$. In the second line, print the $k$ integers of $B$. Each of the next $n$ lines contains one valid expression, where the $i$-th line has a value equal to $A_i$. Expressions must follow these rules:

• Each expression has at most 1000 characters.
• Addition uses + (ASCII 43).
• Subtraction uses - (ASCII 45).
• Multiplication uses * (ASCII 42).
• Brackets use ( (ASCII 40) and ) (ASCII 41).
• + and - cannot be used as unary operators. For example, -5 + 3 and 5 - -3 are not valid.
• Besides these characters, you can only use numbers from $B$ and spaces (ASCII 32).

Special formatting of the output is not needed.