Arkady and Rectangles

题意：按顺序在坐标轴上画n个颜色为1⋯n的矩形（数字大的颜色覆盖数字小的颜色），问最后能看到多少种颜色。 翻译者：louhao088

Arkady has got an infinite plane painted in color $ 0 $ . Then he draws $ n $ rectangles filled with paint with sides parallel to the Cartesian coordinate axes, one after another. The color of the $ i $ -th rectangle is $ i $ (rectangles are enumerated from $ 1 $ to $ n $ in the order he draws them). It is possible that new rectangles cover some of the previous ones completely or partially. Count the number of different colors on the plane after Arkady draws all the rectangles.

The first line contains a single integer $ n $ ( $ 1 \le n \le 100\,000 $ ) — the number of rectangles. The $ i $ -th of the next $ n $ lines contains $ 4 $ integers $ x_1 $ , $ y_1 $ , $ x_2 $ and $ y_2 $ ( $ -10^9 \le x_1 < x_2 \le 10^9 $ , $ -10^9 \le y_1 < y_2 \le 10^9 $ ) — the coordinates of corners of the $ i $ -th rectangle.

In the single line print the number of different colors in the plane, including color $ 0 $ .

5
-1 -1 1 1
-4 0 0 4
0 0 4 4
-4 -4 0 0
0 -4 4 0

5

4
0 0 4 4
-4 -4 0 0
0 -4 4 0
-2 -4 2 4

5

 That's how the plane looks in the first sample That's how the plane looks in the second sample $ 0 $ = white, $ 1 $ = cyan, $ 2 $ = blue, $ 3 $ = purple, $ 4 $ = yellow, $ 5 $ = red.