Mobius brainfuck

Mobius brainfuck is like brainfuck with finite unbounded cells. After one circle every number turns into its opposite. This allows to use only increment to decrease without wrap.

Instructions

Caption text

Char	Equivalent C
+	arr[ptr]++;
>	arr[ptr++]*=-1;ptr%=N;
[	while(arr[ptr]){
]	}

IO can be added if necessary.

Turing complete

Should be TC for large enough N but I don't know how large need N be.

Interpreter

Written in JavaScript. Contains an optional output extension.

function mobius_brainfuck(program, N, useOutput=true) {
    let result = `const arr = Array(${+N}).fill(0); let ptr = 0;`;
    if(!useOutput)
        program = program.replace(/\./g, "");
    result += program.replace(/[^+>\[\].]/g, "")
                     .replace(/]/g, "}")
                     .replace(/\[/g, "while(arr[ptr]){")
                     .replace(/\+/g, "arr[ptr]++;")
                     .replace(/>/g, `arr[ptr++]*=-1;ptr%=${+N};`)
                     .replace(/\./g, "console.log(arr[ptr]);");
    eval(result);
}