<p>You are given two integer arrays of the same length <code>nums1</code> and <code>nums2</code>. In one operation, you are allowed to swap <code>nums1[i]</code> with <code>nums2[i]</code>.</p>

<ul>
	<li>For example, if <code>nums1 = [1,2,3,<u>8</u>]</code>, and <code>nums2 = [5,6,7,<u>4</u>]</code>, you can swap the element at <code>i = 3</code> to obtain <code>nums1 = [1,2,3,4]</code> and <code>nums2 = [5,6,7,8]</code>.</li>
</ul>

<p>Return <em>the minimum number of needed operations to make </em><code>nums1</code><em> and </em><code>nums2</code><em> <strong>strictly increasing</strong></em>. The test cases are generated so that the given input always makes it possible.</p>

<p>An array <code>arr</code> is <strong>strictly increasing</strong> if and only if <code>arr[0] &lt; arr[1] &lt; arr[2] &lt; ... &lt; arr[arr.length - 1]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,3,5,4], nums2 = [1,2,3,7]
<strong>Output:</strong> 1
<strong>Explanation:</strong> 
Swap nums1[3] and nums2[3]. Then the sequences are:
nums1 = [1, 3, 5, 7] and nums2 = [1, 2, 3, 4]
which are both strictly increasing.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [0,3,5,8,9], nums2 = [2,1,4,6,9]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums1.length &lt;= 10<sup>5</sup></code></li>
	<li><code>nums2.length == nums1.length</code></li>
	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= 2 * 10<sup>5</sup></code></li>
</ul>

class Solution:
    def minSwap(self, nums1: List[int], nums2: List[int]) -> int:
        n = len(nums1)
        # swap: min swaps if we swap at current index
        # no_swap: min swaps if we do not swap at current index
        swap = 1
        no_swap = 0
        
        for i in range(1, n):
            swap_new = no_swap_new = float('inf')
            # Check if current pair is increasing without swapping
            if nums1[i] > nums1[i-1] and nums2[i] > nums2[i-1]:
                # If we do not swap at i, take the previous no_swap
                no_swap_new = min(no_swap_new, no_swap)
                # If we swap at i, take the previous swap and add 1
                swap_new = min(swap_new, swap + 1)
            # Check if current pair is increasing with swapping
            if nums1[i] > nums2[i-1] and nums2[i] > nums1[i-1]:
                # If we do not swap at i, previous state must have swapped
                no_swap_new = min(no_swap_new, swap)
                # If we swap at i, previous state must not have swapped
                swap_new = min(swap_new, no_swap + 1)
            
            swap, no_swap = swap_new, no_swap_new
        
        return min(swap, no_swap)
33805