<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 __init__(self):
        self.dp=[]
    def minSwap(self, nums1: List[int], nums2: List[int]) -> int:
        n=len(nums1)
        print(n)
        self.dp=[[[-1 for i in range(n)]for j in range(2)]for k in range(2)]
        ans=self.solve(0,nums1,nums2,n,0)
        # print(self.dp[0])
        # print(self.dp[1])
        return ans
    
    def solve(self,i,nums1,nums2,n,prev):
        if i>=n:
            return 0
        if self.dp[prev][0][i]!=-1 and self.dp[prev][1][i]!=-1:
            return min(self.dp[prev][0][i],self.dp[prev][1][i])
        # flg0=False
        # flg1=False
        if i-1>=0:
            if prev==1:
                prevnum1=nums2[i-1]
                prevnum2=nums1[i-1]
            else:
                prevnum1=nums1[i-1]
                prevnum2=nums2[i-1]
        if self.dp[prev][0][i]==-1:
            if i-1>=0:
                if nums1[i]>prevnum1 and nums2[i]>prevnum2:
                    self.dp[prev][0][i]=self.solve(i+1,nums1,nums2,n,0)
                else:
                    self.dp[prev][0][i]=float('inf')
            else:
                self.dp[prev][0][i]=self.solve(i+1,nums1,nums2,n,0)
        if self.dp[prev][1][i]==-1:
            if i-1>=0:
                if nums1[i]>prevnum2 and nums2[i]>prevnum1:
                    # temp=nums1[i]
                    # nums1[i]=nums2[i]
                    # nums2[i]=temp
                    self.dp[prev][1][i]=1+self.solve(i+1,nums1,nums2,n,1)
                else:
                    self.dp[prev][1][i]=float('inf')
            else:
                # temp=nums1[i]
                # nums1[i]=nums2[i]
                # nums2[i]=temp
                self.dp[prev][1][i]=1+self.solve(i+1,nums1,nums2,n,1)
        
        
        return min(self.dp[prev][0][i],self.dp[prev][1][i])




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