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A string is a *valid parentheses string* (denoted VPS) if and only if it consists of `"("`

and `")"`

characters only, and:

- It is the empty string, or
- It can be written as
`AB`

(`A`

concatenated with`B`

), where`A`

and`B`

are VPS's, or - It can be written as
`(A)`

, where`A`

is a VPS.

We can similarly define the *nesting depth* `depth(S)`

of any VPS `S`

as follows:

`depth("") = 0`

`depth(A + B) = max(depth(A), depth(B))`

, where`A`

and`B`

are VPS's`depth("(" + A + ")") = 1 + depth(A)`

, where`A`

is a VPS.

For example, `""`

, `"()()"`

, and `"()(()())"`

are VPS's (with nesting depths 0, 1, and 2), and `")("`

and `"(()"`

are not VPS's.

Given a VPS seq, split it into two disjoint subsequences `A`

and `B`

, such that `A`

and `B`

are VPS's (and `A.length + B.length = seq.length`

).

Now choose **any** such `A`

and `B`

such that `max(depth(A), depth(B))`

is the minimum possible value.

Return an `answer`

array (of length `seq.length`

) that encodes such a choice of `A`

and `B`

: `answer[i] = 0`

if `seq[i]`

is part of `A`

, else `answer[i] = 1`

. Note that even though multiple answers may exist, you may return any of them.

**Example 1:**

Input:seq = "(()())"Output:[0,1,1,1,1,0]

**Example 2:**

Input:seq = "()(())()"Output:[0,0,0,1,1,0,1,1]

**Constraints:**

`1 <= seq.size <= 10000`