Removing Parentheses

The two expressions (((x)+(y))(t)) and (x+y)t are equal. Given an expression, write a program that removes as many parentheses as possible without changing its value and prints the result.

An expression consists only of additions and multiplications, and every variable is a single lowercase letter. An expression is defined by the following grammar.

E : P | P '+' E
P : F | F P
F : V | '(' E ')'
V : 'a' | 'b' | ... | 'z'

Associativity may be used for both addition and multiplication: x+(y+z) = (x+y)+z = x+y+z and x(yz) = (xy)z = xyz. However, commutativity and distributivity may NOT be used. Parentheses have the highest precedence, followed by multiplication, and then addition.

The input consists of several test cases. Each test case is one expression that satisfies the grammar above, given on its own line. Each expression has length at most 1000. The input continues until end of file (EOF).

For each test case, print the expression obtained by removing as many parentheses as possible while preserving its value, one per line.