<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 {
public:
    unordered_map<string, int> dp; 
    bool check(int i, vector<int>& arr1) {
        return i + 1 < arr1.size() && arr1[i] >= arr1[i + 1];
    }
    int solve(int i, int prev, vector<int>& arr1, vector<int>& arr2) {
        if(i == arr1.size()) return 0;

        string key = to_string(i) + '#' + to_string(prev);

        if(dp.find(key) != dp.end())
            return dp[key];

        int res = 1e9;

        if(check(i, arr1)) {
            int next = arr1[i + 1];
            auto it = lower_bound(arr2.begin(), arr2.end(), next);

            bool found = false;
            if(it != arr2.begin()) {
                it--;
                if(prev < *it) {
                    found = true;
                    res = min(res, 1 + solve(i + 1, *it, arr1, arr2));
                }
            }

            it = upper_bound(arr2.begin(), arr2.end(), prev);

            if(it != arr2.end()) {
                res = min(res, 1 + solve(i + 1, *it, arr1, arr2));
            }
        }

        if(arr1[i] > prev) {
            res = min(res, solve(i + 1, arr1[i], arr1, arr2));
        } 

        auto it = upper_bound(arr2.begin(), arr2.end(), prev);

        if(it != arr2.end()) {
            res = min(res, 1 + solve(i + 1, *it, arr1, arr2));
        }

        return dp[key] = res;
    }
    int makeArrayIncreasing(vector<int>& arr1, vector<int>& arr2) {
        sort(arr2.begin(), arr2.end());

        int ans = solve(0, -1, arr1, arr2);

        return ans >= 1e9 ? -1 : ans;
    }
};
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