Implement LaTeX accent macros

Introduction

The LaTeX typesetting system uses macros for defining accents.For example, the letter ê is produced by \hat{e}.In this challenge, your task is to implement an ASCII version of this functionality.

Input

Your input is a non-empty string of printable ASCII characters.It will not contain newlines.

Output

Your output is a string consisting of two lines.The first line contains accents, and the second line the characters they belong to.It is obtained from the input as follows (A denotes an arbitrary character):

• Every \bar{A} is replaced by A with _ on top of it.
• Every \dot{A} is replaced by A with . on top of it.
• Every \hat{A} is replaced by A with ^ on top of it.
• For a -10% bonus: every \tilde{A} is replaced by A with ~ on top of it.
• All other characters have a space above them.

For example, the input

Je suis pr\hat{e}t.

results in the output

          ^Je suis pret.

Rules and scoring

You can assume that the characters \{} only occur in the macros \bar{}, \dot{} and \hat{} (and \tilde{} if you go for the bonus).All macro arguments are exact one character long, so \dot{foo} and \dot{} will not occur in the input.The output can be a newline-separated string, or a list/pair of two strings.Any amount of trailing and preceding whitespace is allowed, as long as the accents are in the correct places.In particular, if there are no accents, the output can be a single string.

You can write a full program or a function.The lowest byte count (after bonuses) wins, and standard loopholes are disallowed.

Test cases

Without bonus:

Input:No accents.Output:No accents.Input:Ch\hat{a}teauOutput:  ^ChateauInput:Som\bar{e} \dot{a}cc\hat{e}nts.Output:   _ .  ^Some accents.Input:dot hat\dot{h}a\hat{t}\hat{ }x\bar{x}dotOutput:       . ^^ _dot hathat xxdotInput:\hat{g}Hmi\hat{|}Su5Y(\dot{G}"\bar{$}id4\hat{j}gB\dot{n}#6AX'c\dot{[}\hat{)} 6\hat{[}T~_sR\hat{&}CEBOutput:^   ^     . _   ^  .      .^  ^     ^gHmi|Su5Y(G"$id4jgBn#6AX'c[) 6[T~_sR&CEB

With bonus:

Input:Ma\tilde{n}anaOutput:  ~MananaInput:\dot{L}Vz\dot{[}|M.\bar{#}0\hat{u}U^y!"\tilde{I} K.\bar{"}\hat{m}dT\tilde{$}F\bar{;}59$,/5\bar{'}K\tilde{v}R \tilde{E}X`Output:.  .   _ ^     ~   _^  ~ _      _ ~  ~LVz[|M.#0uU^y!"I K."mdT$F;59$,/5'KvR EX`