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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

This puzzle builds on the concepts explored in the puzzle 24: The Long Game by @jddingemanse. Significant insight can be gained by solving that puzzle before working through this one:https://www.codingame.com/training/hard/24-the-long-game

In this puzzle, you are given an

`equation`with a variable

**x**somewhere in that equation. Your task is to

**REARRANGE**the terms of the expressions on either side of the equal sign to produce an equation in the following form:

`expression`

The

`expression`on the right side of the equal sign must be in "standard form" per the rules identified in 24: The Long Game. For your convenience, those rules are copied below.

**To see these rules applied to a sample expression, please refer back to 24: The Long Game.**

**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:

Input

**Line 1:**An integer

`numEquations`indicating the number of equations to be solved (rearranged).

**Next**A string

`numEquations`lines:`equation`.

Output

**Line 1:**A string '

`expression`' with the expression rewritten in standard form.

Constraints

`numEquations`<= 40

length(

`equation`) < 100

`equation`is always a valid equation and contains only one

The following two constraints ensure each

`equation`is in the set of equations fully covered by the rules of 24: The Long Game.

There is no explicit zero term anywhere in any

`equation`.

No expression or subexpression in the

`equation`will ever begin with a negative sign (

Example

Input

6 3+x=7 x+44=6 18=29+x 310=x+429 x+4+9+2+23+18=13+26+3+1 8+4+10+67+234=x+87+98+12+65

Output

x=7-3 x=6-44 x=18-29 x=310-429 x=1+3+13+26-2-4-9-18-23 x=4+8+10+67+234-12-65-87-98

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