I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

## Ungolfed

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


## Explanation

First store the stack height for future purposes

([]<...>


Then while the stack is not empty (assumes that none of the characters is zero)

{...}


Subtract ninety seven (and store 3 for later optimizations)

({}[((((((()()())){}){}){}){}){}()])


If it is not zero (i.e. not a)

{...}


Subtract 4 (and store 4 for later optimizations)

({}[({}())])


If it is not zero (i.e. not e)

{...}


Subtract 4 (and store 4 for later optimizations)

({}[({})])


If it is not zero (i.e. not i)

{...}


Subtract 6 (and store 6 for later optimizations)

({}[({}()())])


If it is not zero (i.e. not o)

{...}


Subtract 6 (store 6 because the program expects one later)

({}[({})])


If it is not zero (i.e. not u)

{...}


Move the remainder to the other stack and put a zero on the active stack to escape all of the ifs

({}<>)(<>)


Once all of the ifs have been escaped remove the zero and the six

{}{}


Once all the characters have been processed subtract the height of the offset from the originally stored height.

...<>[[]]<>)


Mod by two

{(({}[<>(())<>()()])){{}({}())((<>)<>)}{}}{}<>({}<>)


I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


## Ungolfed

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


## Explanation

First store the stack height for future purposes

([]<...>


Then while the stack is not empty (assumes that none of the characters is zero)

{...}


Subtract ninety seven (and store 3 for later optimizations)

({}[((((((()()())){}){}){}){}){}()])


If it is not zero (i.e. not a)

{...}


Subtract 4 (and store 4 for later optimizations)

({}[({}())])


If it is not zero (i.e. not e)

{...}


Subtract 4 (and store 4 for later optimizations)

({}[({})])


If it is not zero (i.e. not i)

{...}


Subtract 6 (and store 6 for later optimizations)

({}[({}()())])


If it is not zero (i.e. not o)

{...}


Subtract 6 (store 6 because the program expects one later)

({}[({})])


If it is not zero (i.e. not u)

{...}


Move the remainder to the other stack and put a zero on the active stack to escape all of the ifs

({}<>)(<>)


Once all of the ifs have been escaped remove the zero and the six

{}{}


Once all the characters have been processed subtract the height of the offset from the originally stored height.

...<>[[]]<>)


Mod by two

{(({}[<>(())<>()()])){{}({}())((<>)<>)}{}}{}<>({}<>)

3 change arbitrary mod to custom mod 2

# Brain-Flak206196192192 178 + 3 = 195181 bytes

([]<{({}[((((((()()())){}){}){}){}){}()]){({}[({}())]){({}[({})]){({}[({}()())]){({}[({})]){({}<>)(<>)}}}}}{}{}}><>[[]]<>)(<(()()<>)>)<>{(({}[[<>(()])<>(({}()[({})])){{}(<({}({}))>((<>)<>)}{}<>}{}<>({}<>)


This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


# Brain-Flak206196192 + 3 = 195 bytes

Try it Online!

([]<{({}[((((((()()())){}){}){}){}){}()]){({}[({}())]){({}[({})]){({}[({}()())]){({}[({})]){({}<>)(<>)}}}}}{}{}}><>[[]]<>)(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>)


This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


# Brain-Flak206196192 178 + 3 = 181 bytes

Try it Online!

([]<{({}[((((((()()())){}){}){}){}){}()]){({}[({}())]){({}[({})]){({}[({}()())]){({}[({})]){({}<>)(<>)}}}}}{}{}}><>[[]]<>()()){(({}[<>(())<>()()])){{}({}())((<>)<>)}{}}{}<>({}<>)


This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)

2 golfed

# Brain-Flak206206196 192 + 3 = 209195 bytes

([]<{({}[((((((()()())){}){}){}){}){}()]){({}[(){}()()()]){({}[()()()({})]){({}[((){}()()){}]){({}[(()()()){})]){({}<>)(<>)}}}}}{}{}}><>[[]]<>)(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><><>)


This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


# Brain-Flak206 + 3 = 209 bytes

Try it Online!

([]<{({}[(((((()()()){}){}){}){}){}()]){({}[()()()()]){({}[()()()()]){({}[(()()()){}]){({}[(()()()){}]){({}<>)(<>)}}}}}{}}><>[[]]<>)(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)


# Brain-Flak206196 192 + 3 = 195 bytes

Try it Online!

([]<{({}[((((((()()())){}){}){}){}){}()]){({}[({}())]){({}[({})]){({}[({}()())]){({}[({})]){({}<>)(<>)}}}}}{}{}}><>[[]]<>)(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>)


This requires the -c flag to run in ASCII mode adding an extra 3 bytes to the length of the program.

I will post an explanation when I am sure I am done golfing but for now, here it is ungolfed:

([]<
{({}[(((((()()()){}){}){}){}){}()])
{
({}[()()()()])
{
({}[()()()()])
{
({}[(()()()){}])
{
({}[(()()()){}])
{
({}<>)
(<>)
}
}
}
}
}
{}
}
><>[[]]<>)
(<(()()<>)>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>)

1