tape_equilibrium() {
    local -n _a="$1"
    local _firstPart=0
    local _secondPart=0
    local _v
    for _v in "${_a[@]}"; do _secondPart=$(( _secondPart + _v )); done
    local _min=9223372036854775807
    local _i
    for ((_i = 0; _i < ${#_a[@]} - 1; _i++)); do
        _firstPart=$(( _firstPart + _i ))
        _secondPart=$(( _secondPart - _i ))
        local _diff=$(( _firstPart - _secondPart ))
        (( _diff < 0 )) && _diff=$(( -_diff ))
        (( _diff < _min )) && _min=$_diff
    done
    echo "$_min"
}