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Farmer John has () rectangular barns on his farm, all with sides parallel to the and axes and integer corner coordinates in the range . 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.
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
Explanation of the sample:
There are barns. The first barn has its lower-left corner at and its upper-right corner at , 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.