# 1896. Minimum Cost to Change the Final Value of Expression

## Description

You are given a **valid** boolean expression as a string `expression`

consisting of the characters `'1'`

,`'0'`

,`'&'`

(bitwise **AND** operator),`'|'`

(bitwise **OR** operator),`'('`

, and `')'`

.

- For example,
`"()1|1"`

and`"(1)&()"`

are**not valid**while`"1"`

,`"(((1))|(0))"`

, and`"1|(0&(1))"`

are**valid**expressions.

Return* the minimum cost to change the final value of the expression*.

- For example, if
`expression = "1|1|(0&0)&1"`

, its**value**is`1|1|(0&0)&1 = 1|1|0&1 = 1|0&1 = 1&1 = 1`

. We want to apply operations so that the**new**expression evaluates to`0`

.

The **cost** of changing the final value of an expression is the **number of operations** performed on the expression. The types of **operations** are described as follows:

- Turn a
`'1'`

into a`'0'`

. - Turn a
`'0'`

into a`'1'`

. - Turn a
`'&'`

into a`'|'`

. - Turn a
`'|'`

into a`'&'`

.

**Note:** `'&'`

does **not** take precedence over `'|'`

in the **order of calculation**. Evaluate parentheses **first**, then in **left-to-right** order.

**Example 1:**

Input:expression = "1&(0|1)"Output:1Explanation:We can turn "1&(01)" into "1&(0|1)" by changing the '|' to a '&' using 1 operation. The new expression evaluates to 0.&

**Example 2:**

Input:expression = "(0&0)&(0&0&0)"Output:3Explanation:We can turn "(0)&0(0&0&0)" into "(0&)|1(0&0&0)" using 3 operations. The new expression evaluates to 1.|

**Example 3:**

Input:expression = "(0|(1|0&1))"Output:1Explanation:We can turn "(0|(|0&1))" into "(0|(1|0&1))" using 1 operation. The new expression evaluates to 0.0

**Constraints:**

`1 <= expression.length <= 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`

).