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- 8

## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

In the 24 Game, a given set of four numbers must be combined using only the arithmetic operationshttps://www.codingame.com/training/medium/24-game by @Smelty

For this puzzle, your program must provide the number of possible solutions (

`ns`) and all those possible solutions, or

Solutions must be printed as expressions without spaces, for example

**EXPRESSIONS, TERMS AND SUBEXPRESSIONS**

To understand the rules for rewriting expressions, we must distinguish

**expressions, terms and subexpressions**.

**expression:**Terms separated by mathematical operators that can be evaluated from left to right. For example:

**term:**A constant or a subexpression. The expression

**subexpression:**A subexpression is an expression that must be evaluated before the parent expression can be evaluated. The expression

**REWRITING EXPRESSIONS**

**Only rewrite an expression such that it remains mathematically the same.**

Rewrite expressions according to the following three rules:

**1. Use as few parentheses as possible.**

- Remove unnecessary parentheses:

- Rewrite an expression, if necessary:

**2. Sort operators:**+ before - and * before / .

- Change the order of terms such that for their connecting operators

- Do this within a parent expression:

- Do this within a subexpression:

- This does not apply to operators in two different subexpressions: in

**3. For cases not decided by rule 2, sort terms of expressions and subexpressions**

**a)**Sort constants in ascending order:

**b)**Place constants before subexpressions:

**c)**Sort two subexpressions according to their numerical value:

In the case of equal value, sort the subexpressions as strings, based on the ASCII value of characters:

**EXAMPLE**

With values 2,2,3,5, there are 8 non-unique solutions, but after applying above described rules, only one unique solution remains.

**rule 3b**]

**rule 3a**and

**rule 3b**]

**rule 3a**]

**rule 1**and

**rule 3b**]

**rule 1**,

**rule 3a**,

**rule 3b**]

**rule 1**]

**rule 1**and

**rule 3a**]

**SORTING MULTIPLE UNIQUE SOLUTIONS**

After applying above rules, you might still end up with multiple solutions. Output them in the following order:

- Solutions without parentheses (

- Solutions with one set of parentheses (

- Solutions with two sets of parentheses (

Multiple solutions within the same category should be sorted as strings, based on the ASCII value of the characters.

**Credits to**@

**Timinator for co-authoring the goal statement and some of the test cases**

Input

**Line 1:**four space separated integers

`a`,

`b`,

`c`,

`d`

Output

**Line 1:**

`ns`)

**Next**all unique solutions as expressions without spaces

`ns`lines:Constraints

0 <=

`a`,`b`,`c`,`d`<= 100Example

Input

5 3 2 2

Output

1 3*(2*5-2)

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