The Earth is Flat!

Consider the following language:

\( expression = \begin{cases} c & \text {where c is a single, lower-case letter} \\ (e_1 e_2 \cdots e_t n) & \text{zero or more expressions followed by a natural number} \end{cases} \)

The left column of the table below includes sample expressions of this language. Now the flattening of an expression is defined as follows: A single letter is flattened to itself. An expression of the form ( e1 e2 ··· et n ) is flattened by concatenating n copies of the concatenation of the flattening of ei. In other words, if f(e) is the flattening of e, and + symbolizes concatenation, then f( (e1 e2 ··· et n) ) is:

\( \underbrace {f(e_1)+f(e_2) +\cdots+f(e_t)}_{once}+\overbrace {f(e_1)+f(e_2)+\cdots+f(e_t)}^{twice}+\cdots+\underbrace {f(e_1)+f(e_2)+\cdots+f(e_t)}_{n^{th} time} \)

The following tables show some sample expressions and the result of flattening each.

Write a program to flatten a given expression.

Your program will be tested on one or more test cases. Each test case is made of one correctly formed expression written on a separate line. A ’\$’ character identifies the end of line. The last line of the input, which is not part of the test cases, contains a ’\\$’ by itself (possibly with leading and/or trailing white spaces). Every expression in the input is grammatically correct according to the grammar specified above. Note that an expression may contain leading, trailing, and/or embedded spaces. Such spaces should be ignored. Letters and numbers are separated from each other by at least one space character.

For each test case expression, write its flattening on a separate line. There should be no spaces (other than newlines) in the output.