Question: List combine and multiple by a rule

Let L be a list like

L:=[[3, 2], [2, 1], [1, 2], [1, 2], [2, 3], [2, 1], [1, 2], [1, 1], [2, 1], [1, 2], [1, 1], [2, 1], [1, 1], [1, 3], [1, 2], [2, 1], [1, 3], [1, 3], [1, 3], [1, 2], [2, 2], [2, 3]]

Now we consider [3,1] and [1,3] as same 

First we form a list gives us 

Lk:=[[[1,3],4],[[1.2],11],[[2,3],3],[[2,2],1],[[1,1],3]]

That is [1,3] appears 4 times in L

[1,2] appears 11 times in L

[2,3] appears 3 times in L

[1,1] appears.3 times in L

[2,2] appears 1 times in L

now we do addtion in [1,3] which is 1+3=4 therefore [[1,3],4] become [4,4]

[2,2] becomes 2+2=4 therefore [[2,2],1] is [4,1]

[[1,2],11] become [3,11]

[[2,3],3] becomes [5,3]

[[1,1],3] becomes [2,3]

So new list is [[4,4],[3,11],[5,3],[2,3],[4,1]]

so answer is from [4,4] we get 4 *4 , from [3,11] we get 3*11 , from [5,3] we get 5*3 and from [2,3] we get 2*3 from [4,1] we get 4*1

final required answer is (4*4)*(3*11)*(5*3)*(2*3)*(4*1)  =190080

Any list L like above if given kind help with a function which can do the above operation and give the final answer that is in above case 190080