def branching_symmetric_group(la, p):
    """
    Return a dictionary from partitions to multiplicities.
    """
    la = Partition(la)
    l = {la: 1}
    for i in range(la.size()-p):
        l_new = dict()
        for mu in l:
            for r, _ in mu.removable_cells():
                nu = mu.remove_cell(r)
                l_new[nu] = l_new.get(nu, 0) + l[mu]
        l = l_new
    return l

def statistic(la):
    """Return the largest number such that the restriction of the
    irreducible representation corresponding to la has a component
    relative prime to 2.
    """
    la = Partition(la)    
    for m in range(la.size(), 0, -1):
        if any(gcd(StandardTableaux(mu).cardinality(), 2) == 1
               for mu in branching_symmetric_group(la, m)):
            return la.size()-m