Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

Do not get perplexed with the name of problem, it has nothing to do with integral calculus. We will concentrate on integration of simple algebraic expressions.

Complex algebraic expressions consisting of integers, addition and multiplication operators and parentheses can be represented by the following BNF notations –

According to the above grammar, both operators are left associative and multiplication is given higher precedence. So, 2 + 3*4 is same as 2 + (3*4). Similarly, 2 + 3 + 4 is same as (2+3) + 4. On the other hand, (2 + 3) * 4 is different to 2 + 3 * 4. It may be surprising but 2 + 3 + 4 is different to 2 + (3 + 4) as in this case, the order of evaluation is different.-

Consider the expression (2+3)*4 + (2 +3)*5 + 6

The above picture depicts two different ways of representing the expression in hand if we follow the given grammar. The left one is known as the AST (Abstract Syntax Tree) and the other one is DAG (common sub-expression is handled once). Such a representation clearly shows the way of evaluating an algebraic expression. Here, each non-leaf node is assigned a unique variable name. As a result, we can have a sequence of simple expressions to evaluate the expression –

In both cases, f denotes the original expression (2+3)*4 + (2+3)*5 + 6. Here, you have to integrate a sequence of simple expressions into the original one. A simple expression will always be of the form –

variable = (variable | integer)  (+ | *)  (variable | integer)

For a given sequence of simple expressions, there can be several original expressions. Consider the following cases –

We need the first one, i.e. expression having minimum number of literals.

Input

The input file will start with an integer, T (1≤T≤100) denoting the number of tests. Each input will start with a positive integer, N (1≤N≤50) which is the number of simple expressions. Subsequent lines will contain the simple expressions defined above. The input will be valid, i.e. it will be always possible to construct a correct expression. Also, variable names will be referenced once they have been assigned. Either variable name or integers can have at most 10 characters. The integers will be always positive here (no unary minus) and variable names will contain letters only. Spaces will be used to separate numbers, variables and operators.

Output

For each input, print “Expression #D: “ followed by the expression denoted by the last variable in the list of simple expressions. Here D is the test number, starting from 1. The length of any expression will not be greater than 5000.