# 3408. Barn Expansion

Farmer John has $N$ ($1 \le N \le 25\,000$) rectangular barns on his farm, all with sides parallel to the $X$ and $Y$ axes and integer corner coordinates in the range $[0,10^6]$. 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.

### 输入格式

• 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 $(C,D)$.

### 输出格式

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

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

### 提示

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.

2 人解决，2 人已尝试。

2 份提交通过，共有 13 份提交。

8.5 EMB 奖励。