시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 512 MB 4 2 2 50.000%

## 문제

You are given a boolean expression, consisting of <<0>>, <<1>>, operations <<&>> (boolean "AND"), <<|>> (boolean "OR"), <<^>> (<<XOR>>, boolean  "exclusive OR"), and parentheses. A correct boolean expression can be defined recursively: an expression is correct, if it is either equal to one character  <<0>> or <<1>>, or it is an application of some boolean operation to two correct boolean expressions. For simplicity, every application of a boolean operation is put into parentheses. The given expression does not contain spaces or any other characters except the ones described above. For instance, <<((0|1)|0)>>, <<(0&1)>> and <<0>> are correct expressions, and <<0|1>>, <<0|1&1>> and <<(0)>> are not.

Calculate the result of this expression. By the way, the expression is changing! You are also given $m$ queries to change a character at some position. Calculate the value of the given expression after each query.

## 입력

First line contains string $S$, a correct boolean expression with at most $800\,000$ characters.

Next line contains a single integer $m$ ($1 \le m \le 400\,000$) --- number of queries. Then, $m$ lines follow. Each line contains an integer and a character $p_i$ $c_i$, meaning that you should change a character at position $p_i$ to $c_i$. It's guaranteed that the expression remains correct after every query.

## 출력

Output $m+1$ characters <<0>> or <<1>> on a single line. First character should be equal to the value of the original expression. Next $m$ characters should be equal to the value of the expression after each query.

## 서브태스크

번호 배점 제한
1 10

$|S| \le 5$, $m \le 10$

2 10

$|S| \le 200$, $m \le 200$

3 20

$|S| \le 2\,000$, $m \le 2\,000$

4 25

$|S| \le 200\,000$, $m \le 100\,000$

5 35

$|S| \le 800\,000$, $m \le 400\,000$

## 예제 입력 1

((1&1)^(0|1))
3
11 0
7 |
5 0


## 예제 출력 1

0110


## 채점 및 기타 정보

• 예제는 채점하지 않는다.