Contest Duration: ~ (local time)
F - 早解き / Speed Solving

Time Limit: 1 sec / Memory Limit: 256 MB

### 問題文

^(41,3)?

という式を左から順に読んでいくと、 6 文字目まで読んだ時点、 つまり

^(41,3

まで読んだ時点で、関数の2番目の入力が3 もしくは 30 以上 39 以下であることがわかるため、式の値は 41 であることが確定する。

アイちゃんは他のゴリラより早く問題を解きたいので、先頭から１文字ずつ読んでいき、式の値が分かった時点でその問題を読むのをやめることにした。 それぞれの式について、式の値とアイちゃんが読む必要のある文字数の最小値を求めよ。

### 制約

• 1 \leq Q \leq 200
• それぞれの式に含まれる文字数は 1000 以下である。

### 入力

Q
statement_1
...
statement_Q


statement_i (1 \leq i \leq Q) は、以下の BNF の形式で与えられる。

<statement> ::= <expression> ?
<expression> ::= (^ | _)  ( <expression> , <expression> ) | <number>
<number> :: = 0 | 1 | 2 | ... | 98 | 99


### 入力例1

4
_(4,51)?
^(99,_(3,67))?
_(0,87)?
3?


### 出力例1

4 5
99 4
0 3
3 2

• 1 番目の例では、 5 文字目を読んだ時点、つまり _(4,5 の時点で式の値が 4 であるとわかる。
• 2 番目の例では、 4 文字目を読んだ時点、つまり ^(99 の時点で式の値が 99 であるとわかる。
• 3 番目の例では、 3 文字目を読んだ時点、つまり _(0 の時点で式の値が 0 であるとわかる。
• 4 番目の例では、 終端記号を読み込むまで式の値が 3 であるとわからない。

### 入力例2

7
_(23,^(_(22,40),4))?
_(0,99)?
^(99,_(^(19,2),5))?
_(^(43,20),^(30,29))?
^(_(20,3),_(50,41))?
^(_(20,3),_(3,41))?
^(_(20,3),_(4,41))?


### 出力例2

22 18
0 3
99 4
30 17
41 17
3 14
4 15


Score : 150 points

### Problem Statement

Gorillas in Kyoto University are good at math. They are currently trying to solve problems to find the value of an expression that contains two functions, _ , ^. Each of these functions takes two input values. _ function returns the smaller of the two input values and ^ function returns the larger. Gorillas know that integers in the expression are non-negative and less than or equal to 99, but can not find out the length of the expression until they read a terminal symbol ? that represents the end of the expression. The number of characters included in each expression is less than or equal to 1000, but they do not even know this fact. Ai, a smart gorilla, noticed that she may be able to know the value of the expression even if they don't read the whole expression.

For example,

Assume you read the following sentence from the left.

^(41,3)?

When you read the sixth character, that is, when you read the following expression,

^(41,3

you can tell the second input value of the funcion is whether 3 or an integer between 30 and 39, and the value turns out 41.

Since Ai wants to solve problems earlier than other gorillas, she decided to solve the problems such that she reads as fewer characters as possible from the left. For each expression, Find the value of the expression and the minimum number of characters Ai needs to read to know the value.

### Constraints

• 1 \leq Q \leq 200
• The number of characters each expression contains is less than or equal to 1000.

### Input

The input consists of multiple test cases and is given from Standard Input in the following format:

Q
statement_1
...
statement_Q


Each statement_i (1 \leq i \leq Q) is given in the following BNF format.

<statement> ::= <expression> ?
<expression> ::= (^ | _)  ( <expression> , <expression> ) | <number>
<number> :: = 0 | 1 | 2 | ... | 98 | 99


### Output

Output consists of Q lines. On line i (1 \leq i \leq Q), print the value of the expression and the number of character Ai needs to read for the test case i separated by space.

### Sample Input 1

4
_(4,51)?
^(99,_(3,67))?
_(0,87)?
3?


### Sample Output 1

4 5
99 4
0 3
3 2

• For the first test case, when you read the fifth character, that is, when you read _(4,5, you will know the value is 4.
• For the second test case, when you read the fourth character, that is, when you read ^(99, you will know the value is 99.
• For the third test case, when you read the third character, that is, when you read _(0, you will know the value is 0.
• For the fourth test case, you will not know the value is 3 untill you read the terminal symbol.

### Sample Input 2

7
_(23,^(_(22,40),4))?
_(0,99)?
^(99,_(^(19,2),5))?
_(^(43,20),^(30,29))?
^(_(20,3),_(50,41))?
^(_(20,3),_(3,41))?
^(_(20,3),_(4,41))?


### Sample Output 2

22 18
0 3
99 4
30 17
41 17
3 14
4 15


KUPC2016