# 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 `X`_{i} and `Y`_{i} `(-10`^{5} ≤ X_{i}, Y_{i} ≤ 10^{5}, 1 ≤ i ≤ N) which represents a vertex.
A polygonal line is the segments which connect `(X`_{j}, Y_{j}) and `(X`_{j+1}, Y_{j+1}) `((X`_{j}, Y_{j}) ≠ (X_{j+1}, Y_{j+1}), 1 ≤ j ≤ N-1).
The distance between a segment `S`_{j} and all vertices except the end points on segment `S`_{j} 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