21925_BarnExpansion

Farmer John has N ( 1 ≤ N ≤ 25,000 ) rectangular barns on his farm, all with sides parallel to the X and Y axes and integer corner coordinates in the range 0..1,000,000. These barns do not overlap although they may share corners and/or sides with other barns.

Since he has extra cows to milk this year, FJ would like to expand some of his barns. A barn has room to expand if it does not share a corner or a wall with any other barn. That is, FJ can expand a barn if all four of its walls can be pushed outward by at least some amount without bumping into another barn. If two barns meet at a corner, neither barn can expand.

Please determine how many barns have room to expand.

Line 1: A single integer, N

Lines 2..N+1: Four space-separated integers A, B, C, and D, describing one barn. The lower-left corner of the barn is at (A, B) and the upper right corner is at (C, D).

Line 1: A single integer that is the number of barns that can be expanded.

5
0 2 2 7
3 5 5 8
4 2 6 4
6 1 8 6
0 0 8 1

2

Explanation of the sample:

There are 5 barns. The first barn has its lower-left corner at (0, 2) and its upper-right corner at (2, 7), and so on.

Only two barns can be expanded --- the first two listed in the input. All other barns are each in contact with at least one other barn.