def histogram(values, mode=0, bin_function=None):
    """Return a list of (value, count) pairs, summarizing the input values.
    Sorted by increasing value, or if mode=1, by decreasing count.
    If bin_function is given, map it over values first."""
    if bin_function:
        values = map(bin_function, values)

    bins = {}
    for val in values:
        bins[val] = bins.get(val, 0) + 1

    if mode:
        return sorted(list(bins.items()), key=lambda x: (x[1], x[0]),
                      reverse=True)
    else:
        return sorted(bins.items())