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#4671. 独立矩形

統計

平面上有 $N$ 个边平行于坐标轴的矩形。请注意,这些矩形可能会相交。

请找出选择两个矩形的方法数,使得以下两个条件同时满足:

  • 这两个矩形的交集面积必须大于零。
  • 不存在其他任何矩形与这两个矩形中的任意一个有面积大于零的交集。

输入格式

第一行包含一个整数 $N$ ($2 \le N \le 10^5$),表示矩形的数量。接下来的 $N$ 行描述这些矩形,每行一个矩形。每行包含四个整数 $x_1, y_1, x_2, y_2$ ($0 \le x_1 < x_2 \le 10^6$, $0 \le y_1 < y_2 \le 10^6$),分别表示矩形左下角和右上角的坐标。

输出格式

输出一个整数,表示选择两个矩形的方法数。

样例

输入 1

3
0 0 3 3
2 2 4 4
5 8 8 12

输出 1

1

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