return
        dictionary
            e in es -> f in fs

def viterbi_alignment(es, fs, t, a):
    '''
    return
        dictionary
            e in es -> f in fs
    '''
    max_a = collections.defaultdict(float)
    l_e = len(es)
    l_f = len(fs)
    for (j, e) in enumerate(es, 1):
        current_max = (0, -1)
        for (i, f) in enumerate(fs, 1):
            val = t[(e, f)] * a[(i, j, l_e, l_f)]
            # select the first one among the maximum candidates
            if current_max[1] < val:
                current_max = (i, val)
        max_a[j] = current_max[0]
    return max_a