Enjoying a casual afternoon walk in the coordinate system, little Luka has encountered
A region is a set of points such that every two points can be connected with a continuous curve, without cutting through any of the circles.
One of the possible layouts of circles
Input Specification
The first line of input contains the integer
Each of the following
All the circles in the input will be unique.
Output Specification
The first and only line of output must contain the required number from the task.
Scoring
In test cases worth
Sample Input 1
2
1 3
5 1
Sample Output 1
3
Sample Input 2
3
2 2
1 1
3 1
Sample Output 2
5
Sample Input 3
4
7 5
-9 11
11 9
0 20
Sample Output 3
6
Explanation for Sample Output 3
The example corresponds to the image in the task statement.
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