<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 {
public:
    int solve(vector<int>& nums1, vector<int>& nums2, int idx, int flag, vector<vector<int>> &dp){
        if(idx == nums1.size())
            return 0;
        
        if(dp[idx][flag] != -1) return dp[idx][flag];        
        int a=0, b=0;         
        if(flag){
            b = nums1[idx-1];
            a = nums2[idx-1];
        }
        else{
            a = nums1[idx-1];
            b = nums2[idx-1];
        }
        int num=1e6;
        if(a < nums1[idx] && b < nums2[idx])
            num = solve(nums1, nums2, idx+1, 0, dp);
        if(a < nums2[idx] && b < nums1[idx])
            num = min(num, 1 + solve(nums1, nums2, idx+1, 1, dp));
              
        return dp[idx][flag] = num;
    }
    int minSwap(vector<int>& nums1, vector<int>& nums2) {
        vector<vector<int>> dp(nums1.size()+1, vector<int> (2, 0));  
        for(int i=nums1.size()-1;i>=1;i--){
            for(int flag=1;flag>=0;flag--){
                int a=0, b=0;
                if(flag){
                    a = nums2[i-1];
                    b = nums1[i-1];
                }
                else{
                    a = nums1[i-1];
                    b = nums2[i-1];
                }
                int num=1e6;
                if(a < nums1[i] && b < nums2[i])
                    num = dp[i+1][0];
                if(a < nums2[i] && b < nums1[i])
                    num = min(num, 1 + dp[i+1][1]);
                dp[i][flag] = num;
            }
        }
        return min(1 + dp[1][1], dp[1][0]);
    }
};
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