Manager K is designing a set of 3 posters to support Japan's delegates to this year's IOI. Each poster will contain one of the three characters 'J', 'O' and 'I'. Manager K has already designed the posters containing 'J' and 'I' and is now considering the design for the 'O' poster. Currently, he is considering possible designs of the poster with Australia's starry sky as a background.
The poster is of width W and height H. We will denote the coordinates of the bottom-left corner of the poster as (0, 0) and the upper-right corner as (W, H). There are N stars already printed on the poster. The ith star Si (1 ≤ i ≤ N) is located on the poster at coordinates (Xi, Yi). There do not exist two stars with the same coordinates.
Manager K is desigining the letter 'O' in the following manner. First, he picks four distinct stars A, B, C and D out of the N stars. The circle centered at A and passing through B will be denoted as O1 and the circle centered at C and passing through D will be denoted as O2. If the two circles O1 and O2 meet the following conditions, manager K will consider the choice as a possible candidate for the poster's design:
- Circle O1 contains circle O2. In other words, all points within circle O2 and on circle O2's perimeter are contained within the interior of circle O1 (which excludes circle O1's perimeter).
- Both circles do not exceed the boundaries of the poster. In other words, all points (X, Y) within each circle and on each circle's perimeter satisfy the conditions 0 ≤ X ≤ W and 0 ≤ Y ≤ H.
Given the locations of all the stars and the dimensions of the poster, determine how many distinct choices of four points A, B, C and D define a possible candidate for manager K's poster design.
Read from standard input.
- On the first line, there are three integers, N, W and H. N represents the number of stars already printed on the poster. W and H represent the dimensions of the poster.
- On the ith line of the next N lines, there are two integers, Xi and Yi. This means that the ith star Si is located at the coordinates (Xi, Yi).
Print one integer on one line to standard output, representing the number of distinct choices of four points define a possible candidate for manager K's poster design.
All test cases satisfy the following constraints:
- 4 ≤ N ≤ 50.
- 1 ≤ W ≤ 1 000.
- 1 ≤ H ≤ 1 000.
- 0 ≤ Xi ≤ W.
- 0 ≤ Yi ≤ H.
- No two stars have the same coordinates.
Subtask 1 (80 points):
- For any choice of stars A, B, C and D that form a possible candidate, circle O1 and circle O2 do not intersect.
Subtask 2 (20 points):
No further constraints.
Sample Input 1
7 20 15
Sample Output 1
This test case corresponds to the following diagram. Star Si is represented by point i.
The following three diagrams enumerate manager K's candidates for the poster design.
Note that in the three candidates, circles O1 and O2 do not intersect.
Sample Input 2
15 20 30
Sample Output 1