Boolean Expression

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.

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.

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.