<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:
    int rectangleArea(vector<vector<int>>& rectangles) {
        const int modulo = 1e9 + 7;
        set <int> xset,yset;
        for (auto rect : rectangles)
        {
            xset.insert(rect[0]);
            xset.insert(rect[2]);
            yset.insert(rect[1]);
            yset.insert(rect[3]);
        }
        map<int,set<int>> grid;
        long long ans = 0;
        for (auto rect : rectangles)
        {
            auto xit = xset.find(rect[0]);
            auto xitafter = ++xit;
            xit --;
            auto ytemp = yset.find(rect[1]);
            auto yitaftertemp = ++ytemp;
            ytemp --;
            while (*(xit) != rect[2])
            {
                auto yit = ytemp;
                auto yitafter = yitaftertemp;
                while (*(yit) != rect[3]){
                    if (grid.find(*xit) == grid.end())
                    {
                        grid[*xit].insert(*(yit));
                        ans += ((long long)(*xitafter-*xit) *(long long)(*yitafter-*yit)%modulo);
                        ans %= modulo;
                    }
                    else
                    {
                        if (grid[*xit].find(*yit) == grid[*xit].end())
                        {
                            grid[*xit].insert(*(yit));
                            ans += ((long long)(*xitafter-*xit) *(long long)(*yitafter-*yit)%modulo);
                            ans %= modulo;                         
                        }
                    }
                    yit = yitafter;
                    yitafter ++;
                }
                xit = xitafter;
                xitafter++;
            }
        }
        return ans;
    }
};
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