<p>Given two integer arrays&nbsp;<code>arr1</code> and <code>arr2</code>, return the minimum number of operations (possibly zero) needed&nbsp;to make <code>arr1</code> strictly increasing.</p>

<p>In one operation, you can choose two indices&nbsp;<code>0 &lt;=&nbsp;i &lt; arr1.length</code>&nbsp;and&nbsp;<code>0 &lt;= j &lt; arr2.length</code>&nbsp;and do the assignment&nbsp;<code>arr1[i] = arr2[j]</code>.</p>

<p>If there is no way to make&nbsp;<code>arr1</code>&nbsp;strictly increasing,&nbsp;return&nbsp;<code>-1</code>.</p>

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

<pre>
<strong>Input:</strong> arr1 = [1,5,3,6,7], arr2 = [1,3,2,4]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Replace <code>5</code> with <code>2</code>, then <code>arr1 = [1, 2, 3, 6, 7]</code>.
</pre>

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

<pre>
<strong>Input:</strong> arr1 = [1,5,3,6,7], arr2 = [4,3,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Replace <code>5</code> with <code>3</code> and then replace <code>3</code> with <code>4</code>. <code>arr1 = [1, 3, 4, 6, 7]</code>.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,5,3,6,7], arr2 = [1,6,3,3]
<strong>Output:</strong> -1
<strong>Explanation:</strong> You can&#39;t make <code>arr1</code> strictly increasing.</pre>

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

<ul>
	<li><code>1 &lt;= arr1.length, arr2.length &lt;= 2000</code></li>
	<li><code>0 &lt;= arr1[i], arr2[i] &lt;= 10^9</code></li>
</ul>

<p>&nbsp;</p>

class Solution {

private:

    int helper(int idx, int prev, vector<int> &arr1, vector<int> &arr2, map<pair<int, int>, int> &dp) {

        //Base case

        if(idx == arr1.size()) {

            return 0;

        }

        //Explore all paths;

        if(dp.find({idx, prev}) != dp.end()) {

            return dp[{idx, prev}];

        }

        int replace = 1e9, not_replace = 1e9;

        //Replace

        int i = upper_bound(arr2.begin(), arr2.end(), prev) - arr2.begin();

        if(i < arr2.size()) {

            replace = 1 + helper(idx + 1, arr2[i], arr1, arr2, dp);            

        }

        //Not replace

        if(arr1[idx] > prev) {

            not_replace = helper(idx + 1, arr1[idx], arr1, arr2, dp);

        }

        return dp[{idx, prev}] = min(replace, not_replace);

    }

public:

    int makeArrayIncreasing(vector<int>& arr1, vector<int>& arr2) {

        map<pair<int, int>, int> dp;

        sort(arr2.begin(), arr2.end());

        int res = helper(0, -1, arr1, arr2, dp);

        return res >= 1e9 ? -1 : res;

    }

};
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