Area Folding

Time Limit : 5 sec, Memory Limit : 65536 KB

Area Folding

You are given one polygonal line, which is a collection of line segments. Your task is to calculate the sum of areas enclosed by the polygonal line.

A point is defined to be "enclosed" if and only if the point is unreachable without crossing at least one line segment from the point at infinity.

Input

The first line contains one integers N (2 ≤ N ≤ 100). N is the number of segments.

Each of the following N lines consists of two integers Xi and Yi (-105 ≤ Xi, Yi ≤ 105, 1 ≤ i ≤ N) which represents a vertex. A polygonal line is the segments which connect (Xj, Yj) and (Xj+1, Yj+1) ((Xj, Yj) ≠ (Xj+1, Yj+1), 1 ≤ j ≤ N-1). The distance between a segment Sj and all vertices except the end points on segment Sj is guaranteed to be greater than 0.01.

Output

Output the answer in a line. The answer may be printed with an arbitrary number of decimal digits, but may not contain an absolute or relative error greater than or equal to 10-6.

Sample Input 1

5
0 0
1 1
1 0
0 1
0 0

Output for the Sample Input 1

0.5

Sample Input 2

5
0 0
1 1
1 0
0 1
1 0

Output for the Sample Input 2

0.25

Sample Input 3

21
1 1
-1 1
-1 2
-2 2
-2 1
-1 1
-1 -1
-2 -1
-2 -2
-1 -2
-1 -1
1 -1
1 -2
2 -2
2 -1
1 -1
1 1
2 1
2 2
1 2
1 1

Output for the Sample Input 3

8

Sample Input 4

16
0 0
1 0
1 1
0 1
0 2
0 3
1 3
1 2
2 2
2 3
3 3
3 2
3 1
2 1
2 0
3 0

Output for the Sample Input 4

0

Sample Input 5

7
26 52
33 12
-51 68
16 61
43 -26
87 24
12 10

Output for the Sample Input 5

2714.840579710

Source: ACM-ICPC Japan Alumni Group Summer Camp , Day 4, Tokyo, Japan, 2012-09-17
http://acm-icpc.aitea.net/