<p>You are given a 2D array of axis-aligned <code>rectangles</code>. Each <code>rectangle[i] = [x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub>]</code> denotes the <code>i<sup>th</sup></code> rectangle where <code>(x<sub>i1</sub>, y<sub>i1</sub>)</code> are the coordinates of the <strong>bottom-left corner</strong>, and <code>(x<sub>i2</sub>, y<sub>i2</sub>)</code> are the coordinates of the <strong>top-right corner</strong>.</p>

<p>Calculate the <strong>total area</strong> covered by all <code>rectangles</code> in the plane. Any area covered by two or more rectangles should only be counted <strong>once</strong>.</p>

<p>Return <em>the <strong>total area</strong></em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/06/rectangle_area_ii_pic.png" style="width: 600px; height: 450px;" />
<pre>
<strong>Input:</strong> rectangles = [[0,0,2,2],[1,0,2,3],[1,0,3,1]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> A total area of 6 is covered by all three rectangles, as illustrated in the picture.
From (1,1) to (2,2), the green and red rectangles overlap.
From (1,0) to (2,3), all three rectangles overlap.
</pre>

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

<pre>
<strong>Input:</strong> rectangles = [[0,0,1000000000,1000000000]]
<strong>Output:</strong> 49
<strong>Explanation:</strong> The answer is 10<sup>18</sup> modulo (10<sup>9</sup> + 7), which is 49.
</pre>

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

<ul>
	<li><code>1 &lt;= rectangles.length &lt;= 200</code></li>
	<li><code>rectanges[i].length == 4</code></li>
	<li><code>0 &lt;= x<sub>i1</sub>, y<sub>i1</sub>, x<sub>i2</sub>, y<sub>i2</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>x<sub>i1 &lt;= </sub>x<sub>i2</sub></code></li>
	<li><code>y<sub>i1 &lt;=</sub> y<sub>i2</sub></code></li>
</ul>

class Solution {
public:
    struct Event {
        int l, r;
        bool type;
    };
    int merge_intervals(const multiset<pair<int, int>>& intervals) {
        if (intervals.empty()) return 0;
        int l = -1;
        int r = -1;
        int res = 0;
        for (const auto&[ll, rr] : intervals) {
            if (ll > r) {
                res += r - l;
                l = ll;
                r = rr;
            } else r = max(r, rr);
        }
        res += r - l;
        return res;
    }
    int rectangleArea(vector<vector<int>>& rectangles) {
        int n = rectangles.size();
        multiset<pair<int, int>> intervals;
        long long ans = 0;
        map<int, vector<Event>> events;
        for (const vector<int>& v : rectangles) {
            events[v[1]].push_back({ v[0], v[2], true });
            events[v[3]].push_back({ v[0], v[2], false });
        }
        const int MOD = 1e9+7;
        int last = events.begin()->first;
        for (const auto& [t, ev] : events) {
            long long k = merge_intervals(intervals);
            k = (k * (t - last)) % MOD;
            ans = (ans + k) % MOD;
            last = t;
            for (const Event& e : ev) {
                if (e.type) intervals.insert({ e.l, e.r });
                else intervals.erase(intervals.find({ e.l, e.r }));
            }
        }

        return ans;
    }
};
12000