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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def interfaces(root):
    '''
    Generate a dictionary with all available interfaces relative to root.
    Symlinks are not followed.

    CLI example:
     .. code-block:: bash

        salt '*' sysfs.interfaces block/bcache0/bcache

    Output example:
     .. code-block:: json

       {
          "r": [
            "state",
            "partial_stripes_expensive",
            "writeback_rate_debug",
            "stripe_size",
            "dirty_data",
            "stats_total/cache_hits",
            "stats_total/cache_bypass_misses",
            "stats_total/bypassed",
            "stats_total/cache_readaheads",
            "stats_total/cache_hit_ratio",
            "stats_total/cache_miss_collisions",
            "stats_total/cache_misses",
            "stats_total/cache_bypass_hits",
          ],
          "rw": [
            "writeback_rate",
            "writeback_rate_update_seconds",
            "cache_mode",
            "writeback_delay",
            "label",
            "writeback_running",
            "writeback_metadata",
            "running",
            "writeback_rate_p_term_inverse",
            "sequential_cutoff",
            "writeback_percent",
            "writeback_rate_d_term",
            "readahead"
          ],
          "w": [
            "stop",
            "clear_stats",
            "attach",
            "detach"
          ]
       }

    .. note::
      * 'r' interfaces are read-only
      * 'w' interfaces are write-only (e.g. actions)
      * 'rw' are interfaces that can both be read or written
    '''

    root = target(root)
    if root is False or not os.path.isdir(root):
        log.error('SysFS %s not a dir', root)
        return False

    readwrites = []
    reads = []
    writes = []

    for path, _, files in salt.utils.path.os_walk(root, followlinks=False):
        for afile in files:
            canpath = os.path.join(path, afile)

            if not os.path.isfile(canpath):
                continue

            stat_mode = os.stat(canpath).st_mode
            is_r = bool(stat.S_IRUSR & stat_mode)
            is_w = bool(stat.S_IWUSR & stat_mode)

            relpath = os.path.relpath(canpath, root)
            if is_w:
                if is_r:
                    readwrites.append(relpath)
                else:
                    writes.append(relpath)
            elif is_r:
                reads.append(relpath)
            else:
                log.warning('Unable to find any interfaces in %s', canpath)

    return {
        'r': reads,
        'w': writes,
        'rw': readwrites
    }