<p>You have <code>n</code> jobs and <code>m</code> workers. You are given three arrays: <code>difficulty</code>, <code>profit</code>, and <code>worker</code> where:</p>

<ul>
	<li><code>difficulty[i]</code> and <code>profit[i]</code> are the difficulty and the profit of the <code>i<sup>th</sup></code> job, and</li>
	<li><code>worker[j]</code> is the ability of <code>j<sup>th</sup></code> worker (i.e., the <code>j<sup>th</sup></code> worker can only complete a job with difficulty at most <code>worker[j]</code>).</li>
</ul>

<p>Every worker can be assigned <strong>at most one job</strong>, but one job can be <strong>completed multiple times</strong>.</p>

<ul>
	<li>For example, if three workers attempt the same job that pays <code>$1</code>, then the total profit will be <code>$3</code>. If a worker cannot complete any job, their profit is <code>$0</code>.</li>
</ul>

<p>Return the maximum profit we can achieve after assigning the workers to the jobs.</p>

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

<pre>
<strong>Input:</strong> difficulty = [2,4,6,8,10], profit = [10,20,30,40,50], worker = [4,5,6,7]
<strong>Output:</strong> 100
<strong>Explanation:</strong> Workers are assigned jobs of difficulty [4,4,6,6] and they get a profit of [20,20,30,30] separately.
</pre>

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

<pre>
<strong>Input:</strong> difficulty = [85,47,57], profit = [24,66,99], worker = [40,25,25]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>n == difficulty.length</code></li>
	<li><code>n == profit.length</code></li>
	<li><code>m == worker.length</code></li>
	<li><code>1 &lt;= n, m &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= difficulty[i], profit[i], worker[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    using int2 = pair<int, int>; //you lose time being greedy
    
    inline static void radix_sort(vector<int2> & pair) {
        vector<int2> bucket[64];
        
        for (auto& [x, i] : pair)
            bucket[x & 63].emplace_back(x, i);
        int index = 0;
        for (auto& B : bucket) {
            for (auto& v : B)
                pair[index++] = v;
            B.clear();
        }
        
        for (auto& [x, i] : pair)
            bucket[(x >> 6) & 63].emplace_back(x, i);
        index = 0;
        for (auto& B : bucket) {
            for (auto& v : B)
                pair[index++] = v;
            B.clear();
        }
        
        for (auto& [x, i] : pair)
            bucket[(x >> 12)].emplace_back(x, i);
        index = 0;
        for (auto& B : bucket) {
            for (auto& v : B)
                pair[index++] = v;
            B.clear();
        }
    }

    inline static void radix_sort(vector<int> & nums) {
        vector<int> bucket[64];
        for (auto x : nums)
            bucket[x & 63].emplace_back(x);
        int index = 0;
        for (auto& B : bucket) {
            for (auto v : B)
                nums[index++] = v;
            B.clear();
        }

        for (auto x : nums)
            bucket[(x >> 6) & 63].emplace_back(x);
        index = 0;
        for (auto& B : bucket) {
            for (auto v : B)
                nums[index++] = v;
            B.clear();
        }

        for (auto x : nums)
            bucket[x >> 12].emplace_back(x);
        index = 0;
        for (auto& B : bucket) {
            for (auto v : B)
                nums[index++] = v;
            B.clear();
        }
    }

    static int maxProfitAssignment(vector<int> & difficulty, vector<int> & profit, 
        vector<int> & worker) {

        const int n = profit.size(), m = worker.size();
        vector<int2> d_p(n);
        for (int i = 0; i < n; i++)
            d_p[i] = {difficulty[i], profit[i]};

        radix_sort(d_p);
        radix_sort(worker);

        int maxProfit = 0, idx = 0, bestProfit = 0;

        for (int i = 0; i < m; i++) {
            while (idx < n && worker[i] >= d_p[idx].first) {
                bestProfit = max(bestProfit, d_p[idx].second);
                idx++;
            }
            maxProfit += bestProfit;
        }
        return maxProfit;
    }
};

auto init = []() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 'c';
}();
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