import numpy as np

def longest_common_prefix(xs, ys):
    min_len = min(len(xs), len(ys))
    idxs = (xs[:min_len] != ys[:min_len]).nonzero()[0]
    if len(idxs) > 0:
        return idxs[0]
    else:
        return min_len
    
# Like np.cumsum, but with a leading zero.
def cumsum0(x, axis):
    pad_width = len(x.shape) * [(0,0)]
    pad_width[axis] = (1,0)
    return np.cumsum(np.pad(x, pad_width), axis=axis)