# Length of Longest Balanced Subsequence

Given a string `s`

containing brackets `"("`

and `")"`

, return the length of the longest subsequence of balanced brackets.

**Constraints**

`n ≤ 100,000`

where`n`

is length of`s`

.

https://binarysearch.com/problems/Length-of-Longest-Balanced-Subsequence

## Examples

### Example 1

**Input**

- s =
`())(()`

**Output**

- answer =
`4`

**Explanation**

We can take the subsequence `"()()"`

### Example 2

**Input**

- s =
`))()))()`

**Output**

- answer =
`4`

**Explanation**

We can take the subsequence “()()”. Note that characters in the subsequence do not have to be contiguous.

### Example 3

**Input**

- s =
`))((`

**Output**

- answer =
`0`

**Explanation**

We can’t take any letters from `s`

that’s balanced, so the longest balanced subsequence is “” (empty string).

### Example 4

**Input**

- s =
`((((())`

**Output**

- answer =
`4`

**Explanation**

We can make the subsequence `(())`

.

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