
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
