Tsinghua Academy Lighthouse

Lighthouse (Lighthouse) Description

As shown in the following figure, If another lighthouse are in gray area, they can beacons each other.

For example, in following figure, (b, R) is a pair of lighthouse which can beacons each other, while (b, G), (R, g) Yes not .

Input

1st Line:n

2nd ~ (N + 1) th Line:each line is X Y, means a lighthouse are on the point (X, Y).

Output

How many pairs of lighthourses can beacons each other

(For every lighthouses, X coordinates won ' t is the same, Y coordinates won ' t be the same)

Example

Input

32 24 35 1

Output

1

Restrictions

For 90% test cases:1 <= N <= 3 * 105

For 95% test cases:1 <= N <= 106

For all test cases:1 <= n <= 4 * 106

For every lighthouses, X coordinates won ' t is the same, Y coordinates won ' t be the same.

1 <= x, y <= 10^8

Time:2 sec

memory:256 MB

Hints

The range of int is usually [ -231, 231-1], and it may be too small.

In the video there are explanations I altogether didn't see, drunk.

is to ask for the reverse order on the line.

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View Code

Then optimize the code, and my paragraph will not be the last point. It is not necessary to do more sorting operations.

Tsinghua Academy Lighthouse