human
Solve in Python:
We have two integer sequences A and B of the same non-zero length.
We are allowed to swap elements A[i] and B[i].  Note that both elements are in the same index position in their respective sequences.
At the end of some number of swaps, A and B are both strictly increasing.  (A sequence is strictly increasing if and only if A[0] < A[1] < A[2] < ... < A[A.length - 1].)
Given A and B, return the minimum number of swaps to make both sequences strictly increasing.  It is guaranteed that the given input always makes it possible.
Example:
Input: A = [1,3,5,4], B = [1,2,3,7]
Output: 1
Explanation: 
Swap A[3] and B[3].  Then the sequences are:
A = [1, 3, 5, 7] and B = [1, 2, 3, 4]
which are both strictly increasing.

Note:

A, B are arrays with the same length, and that length will be in the range [1, 1000].
A[i], B[i] are integer values in the range [0, 2000].
assistant
#Here is the Python code you requested.

class Solution:
    def minSwap(self, A: List[int], B: List[int]) -> int:
        n=len(A)
        mem = {}
        def rec(index,ifSwapped):
            if index==n:
                return 0
            elif (index,ifSwapped) in mem:
                return mem[(index,ifSwapped)]
            else:
                ans=float('inf')
                #Don't swap if possible
                if A[index]>A[index-1] and B[index]>B[index-1]:
                    ans=min(ans,rec(index+1,0))
                #Swap if possible
                if A[index]>B[index-1] and B[index]>A[index-1]:
                    A[index],B[index]=B[index],A[index] #Swap
                    ans=min(ans,1+rec(index+1,1))
                    A[index],B[index]=B[index],A[index] #Swap them back
                mem[(index,ifSwapped)]=ans
                return ans
            
        ans=float('inf')
        ans=min(ans,rec(1,0))
        A[0],B[0]=B[0],A[0]
        ans=min(ans,1+rec(1,1))
        A[0],B[0]=B[0],A[0]
        
        return ans