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# Untitled

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1. **********************************************************************
2.
3. Problem 2: Cows on Ice [Jelle van den Hooff, 2010]
4.
5. Bessie is ice skating on a large frozen lake modelled as a 2-dimensional
6. grid with coordinates in the range -1,000,000,000..1,000,000,000.
7. N (1 <= N <= 20,000) of the lake's grid cells contain rocks
8. (conveniently numbered 1..N). The other cells contain slippery ice.
9.
10. Since Bessie is not a very good skater, she traverses the lake's
11. cells by pushing herself away from her current position near a rock
12. and sliding continuously in the same direction until she hits another
13. rock (stopping in the square before she hits the rock, of course).
14. Never good with complicated angles, Bessie can push herself only
15. straight north, east, south, or west. She can't push herself through
16. the rock, of course, and thus generally has only three possible
17. directions to move.
18.
19. Sliding is not without risks. Bessie must hit a rock or might end
20. up sliding for a very long time. She must aim her pushes carefully.
21.
22. Consider the situation depicted below; Bessie wants to get to
23. location (x=5,y=1), which is east of her current location (. = ice,
24. * = rock, B = Bessie, G = goal). If she slides directly to the east,
25. she will slide past the location since she can stop only by
26. encountering a rock head on. One way to get to (5,1) is the following:
27.
28.    (a)              (b)             (c)              (d)
29. 4 .....*.         .....*.         .....*.          .....*.
30. 3 ..*....  slide  ..*....  slide  ..*....   slide  ..*....
31. 2 ......*  north  ..B...*  east   .....B*   south  ......*
32. 1 .*B..G. ------> .*...G. ------> .*...G.  ------> .*...B.
33. 0 *....*.         *....*.         *....*.          *....*.
34.   0123456
35.
36. Bessie could slide north, east, or south in situation (a), but only
37. north has a rock for stopping. For situation (b), she can slide
38. only east for the same reason.
39.
40. For the input, rock i is located at cell X_i,Y_i (-1,000,000,000
41. <= X_i <= 1,000,000,000; -1,000,000,000 <= Y_i <= 1,000,000,000),
42. and no two rocks occupy the same position. Bessie starts at Bx,By
43. (which is next to a rock) (-1,000,000,000 <= Bx <= 1,000,000,000;
44. -1,000,000,000 <= By <= 1,000,000,000). Bessie's goal is Gx,Gy
45. (-1,000,000,000 <= Gx <= 1,000,000,000; -1,000,000,000 <= Gy <=
46. 1,000,000,000). Bessie can always reach the goal one way or another.
47.
48. Bessie doesn't mind sliding. However, pushing herself away from a
49. rock is very tiring. To prepare her, FJ would like to know the
50. minimum number of pushes Bessie needs to do.
51.
52. PROBLEM NAME: ice
53.
54. INPUT FORMAT:
55.
56. * Line 1: Five space separated integers: N, Bx, By, Gx, and Gy
57.
58. * Lines 2..N+1: Line i+1 describes a rock location with space
59.         separated integers: X_i and Y_i
60.
61. SAMPLE INPUT (file ice.in):
62.
63. 6 2 1 5 1
64. 5 4
65. 2 3
66. 1 1
67. 6 2
68. 5 0
69. 0 0
70.
71. OUTPUT FORMAT:
72.
73. * Line 1: A single integer that is the minimum number of pushes for
74.         Bessie to get to her goal
75.
76. SAMPLE OUTPUT (file ice.out):
77.
78. 3
79.
80. **********************************************************************
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