<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:
    struct pair_hash {
        template <class T1, class T2>
        size_t operator () (const pair<T1, T2>& p) const {
            auto h1 = hash<T1>{}(p.first);
            auto h2 = hash<T2>{}(p.second);
            return h1 ^ h2;
        }
    };

    unordered_map<pair<long long, long long>, long long, pair_hash> map;

    int func(vector<int>& a1, vector<int>& a2, int i, long long pre) {
        if (i >= a1.size()) {
            return 0;
        }
        if (map.find({i, pre}) != map.end()) return map[{i, pre}];

        int opt1 = 1e9;
        int opt2 = 1e9;

        // Option 1: Keep the current element if it is greater than 'pre'
        if (pre < a1[i]) {
            opt1 = func(a1, a2, i + 1, a1[i]);
        }

        // Option 2: Replace the current element with a valid element from 'a2'
        auto it = upper_bound(a2.begin(), a2.end(), pre);
        if (it != a2.end()) {
            int j = it - a2.begin();
            opt2 = 1 + func(a1, a2, i + 1, a2[j]);
        }

        int result = min(opt1, opt2);
        map[{i, pre}] = result;
        return result;
    }

    int makeArrayIncreasing(vector<int>& arr1, vector<int>& arr2) {
        sort(arr2.begin(), arr2.end());
        int a = func(arr1, arr2, 0, INT_MIN);
        return a == 1e9 ? -1 : a;
    }
};

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