How to use parallel program to select the longest element in a list?

edit

I need to find the longest element in a list of elements of Weyl group. The way I do it is:

    winner = W.one()
    for u1 in g1:
        for u2 in g2:
            t1=u1*w*u2
            if t1.length()>winner.length():
                winner=t1
    r=winner

Here g1 and g2 are two given subsets of the Weyl group I would like to make the above faster by using parallel computations. Is there some way in Sage or Python to do this? Thank you very much!

Edit: the full codes are:

def find_permutation2(L1, L2):
    perm = Word(L1).standard_permutation() / Word(L2).standard_permutation()
    assert [L2[i-1] for i in perm] == L1
    r=perm.reduced_word()
    return r

def LongestPermWInSBWInverseSA(W,A,B): 
    t1=StablizerOfTuple(A)
    t2=StablizerOfTuple(sorted(B))
    s=W.simple_reflections()
    #print(t1,t2)
    t3=[]
    for i in t1:
        t3.append(s[i])
    t4=[]
    for i in t2:
        t4.append(s[i])
    t5=find_permutation2(B,sorted(B))
    w=W.one()
    for i in t5:
        w=w*s[i]
    #print(t4,w,t3)
    r2=LongestPermInDoubleCosetWeylGroup(W,t4,w,t3)
    r=r2

    return r


def LongestPermInDoubleCosetWeylGroup(W,S1,w,S2): 
    g1=W.subgroup(S1)
    g2=W.subgroup(S2)
    winner = W.one()
    for u1 in g1:
        for u2 in g2:
            t1=u1*w*u2
            if t1.length()>winner.length():
                winner=t1
    r=winner

    return r

def SymmetricGroupActionOnListSi(i,L): #  w=s_i,  L=[a1,a2,...,an]
    r1=[]
    for j in L:
        r1.append(j)

    t1=r1[i-1]
    r1[i-1]=r1[i]
    r1[i]=t1 

    r=r1

    return r

def StablizerOfTuple(A): # A is a list, weakly increasing
    k = len(A)
    r=[]
    for i in [1..k-1]:
        t1=SymmetricGroupActionOnListSi(i,A)
        if t1==A:
            r.append(i)
    return r

A=[1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]
B=[3, 3, 3, 5, 5, 5, 4, 4, 4, 6, 6, 6]
kk=len(A)
#print(kk)
typ='A' 
W=SymmetricGroup(kk)
w=LongestPermWInSBWInverseSA(W,A,B)
w