#101730. [BZOJ 1730] [Usaco2005 dec]Barn Expansion 牛棚扩张

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.

约翰有 个矩形牛棚，它们的墙均与坐标轴平行，而且其坐标在 范围内。任意两个牛棚不重叠，但可能会有公共的墙。由于约翰的奶牛持续增加，他不得不考虑扩张牛棚。一个牛棚可以扩张，当且仅当它的四边均不与其它牛棚接触。如果两个牛棚有一个公共角，那它们均是不可扩张的。统计有多少牛棚可以扩张。

• Line ：A single integer,.
• Lines ：Four space-separated integers , and , describing one barn. The lower-left corner of the barn is at and the upper right corner is at .

第一行输入 ，之后 行每行输入一个牛棚的左下角和右上角坐标。

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

输出可扩张的牛棚数。

样例输入 #1

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

样例输出 #1

2

样例说明

INPUT DETAILS：
There are 5 barns. The first barn has its lower-left corner at and its upper-right corner at , and so on.

仅有前两个牛棚可以扩张。

对于 的数据，。 Gold