You are given a valid boolean expression represented by a string expression that consists of the characters $'1'$, $'0'$, $'&'$, $'|'$, $'('$, and }$')'$.

The operators evaluate as follows:

• $'1'$ evaluates to true, and $'0'$ evaluates to false.

• $'&'$ represents the boolean AND operation, while $'|'$ represents the boolean OR operation.

• Operations are evaluated from left to right, while respecting the precedence of parentheses.

In one operation, you can flip any single character:

• Change a $'1'$ to a $'0'$ or a $'0'$ to a $'1'$.

• Change a $'&'$ to a $'|'$ or a $'|'$ to a $'&'$.

Return the minimum number of operations required to change the final evaluated boolean value of the expression.

Constraints:

• $1 \leq$ expression.length $\leq 10^5$

• expression only contains $'1'$, $'0'$, $'&'$, $'|'$, $'('$, and }$')'$.

• All parentheses are properly matched.

• There will be no empty parentheses (i.e., "()" is not a substring of expression).

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.