given a DataFrame where records are stored row-wise, rearrange it
    such that records are stored column-wise.

def _preprocess(df):
    """
    given a DataFrame where records are stored row-wise, rearrange it
    such that records are stored column-wise.
    """

    df = df.stack()

    df.index.rename(["id", "time"], inplace=True)  # .reset_index()
    df.name = "value"
    df = df.reset_index()

    return df