def statistic(pi):
    return max(len(p) for p in to_vacillating(pi))

def to_vacillating(pi):
    """Return the vacillating tableau associated to the set partition pi.

    INPUT:

    - pi, a set partition

    OUTPUT:

    - a vacillating tableau.

    EXAMPLES:

    sage: pi = SetPartition([[1,4,5,7], [2,6],[3]])
    sage: to_vacillating(pi)
    [[], [], [1], [1], [1, 1], [1, 1], [1, 1], [1], [2], [1], [1, 1], [1], [1], [], []]
    """
    T = [StandardTableau([])]
    perm = pi.to_permutation()
    mrep = perm.inverse()
    for j in range(pi.size(), 0, -1):
        prev = mrep(j)
        next = perm(j)
        if j == next: # singleton block
            T += [T[-1], T[-1]]
        elif next < j: # maximal element of a non-singleton block
# do nothing, then insert prev
            T += [T[-1], T[-1].schensted_insert(prev)]
        elif prev > j: # minimal element of a non-singleton block
# delete j then do nothing
            if max(T[-1].entries()) == j:
                new = T[-1].restrict(j-1)
                T += [new, new]
            else:
                print("ERROR")
        else: # transient
# delete j then insert prev
            new = T[-1].restrict(j-1)
            T += [new, new.schensted_insert(prev)]

    return [t.shape() for t in T[::-1]]