counting inversions python

1'''for counting pairs the best algo has time complexty O(n*log(n))'''
2
3''' for collecting such pairs the best algo. has time complexity O(n*n)'''
4
5PAIRS=0
6def merge(left,right):
7    global PAIRS
8    length_1,length_2=len(left),len(right)
9    index1,index2=0,0
10    ans=[]
11    for i in range(length_1+length_2):
12        if index1==length_1:
13            ans.append(right[index2])
14            index2+=1
15        elif index2==length_2:            
16            ans.append(left[index1])
17            index1+=1
18        elif left[index1]<right[index2]:
19            ans.append(left[index1])
20            index1+=1
21        else:
22            ans.append(right[index2])
23            PAIRS+=length_1-index1
24            index2+=1
25    return ans
26def find_all_pairs(lst):
27    pairs=[]
28    for i in range(len(lst)):
29        for j in range(i,len(lst)):
30            if lst[i]>lst[j]:pairs.append((lst[j],lst[i]))
31    return pairs
32def memsort(lst):
33    global PAIRS
34    if len(lst)<3:
35        if len(lst)==2:
36            if lst[0]>lst[1]:
37                lst[1],lst[0]=lst[0],lst[1]
38                PAIRS+=1
39    else:
40        mid=len(lst)//2
41        left=lst[:mid]
42        right=lst[mid:]
43        left=memsort(left)
44        right=memsort(right)
45        lst=merge(left,right)
46    return lst
47if __name__=='__main__':
48    a=[int(i) for i in input('Enter the list of Numbers: ').split()]
49    print(find_all_pairs(a)) # for priniting all pairs
50    memsort(a)
51    print(PAIRS) # for counting such pairs