# Characters in Each Bracket Depth

You are a given a string `s`

containing `"X"`

, `"("`

, and `")"`

. The string has balanced brackets and in between there are some `"X"`

s along with possibly nested brackets recursively.

Return the number of `"X"`

s at each depth of brackets in `s`

, from the shallowest depth to the deepest depth.

**Constraints**

`2 ≤ n ≤ 100,000`

where`n`

is the length of`s`

https://binarysearch.com/problems/Characters-in-Each-Bracket-Depth

## Examples

### Example 1

**Input**

- s =
`(XX(XX(X))X)`

**Output**

- answer =
`[3, 2, 1]`

**Explanation**

There’s three `"X"`

s at depth `0`

. Two `"X"`

s at depth `1`

. And one `"X"`

at depth `2`

.

### Example 2

**Input**

- s =
`(())`

**Output**

- answer =
`[0, 0]`

**Explanation**

There’s no `"X"`

s but depth goes to `1`

.

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