#include <bits/stdc++.h>
using namespace std;
#define prev jfwekljfwekl
typedef complex<double> P;
typedef vector<P> G;
const double EPS = 1e-9;
namespace std {
	bool operator < (const P& a, const P& b) {
		if( abs(a-b) < EPS ) return false;
		return fabs(real(a)-real(b)) < EPS ? imag(a) < imag(b) : real(a) < real(b);
	} 
}
double cross(P a,P b) { return imag(conj(a)*b); }
double dot(P a,P b) { return real(conj(a)*b);}

//??´???
struct L : public vector<P> {
	L(P a,P b) {
		push_back(a); push_back(b);
	}
	
};

int ccw(P a, P b, P c) {
	b -= a; c -= a;
	if (cross(b, c) > 0)   return +1;	// a ??? b ??§???????¨??????????????????? b ??? c(???)
	if (cross(b, c) < 0)   return -1;	// a ??? b ??§????¨??????????????????? b ??? c(???)
	if (dot(b, c) < 0) return +2;    	// a???b??§????????????a??????????¶???????b???c(c--a--b)
	if (norm(b) < norm(c)) return -2;	// a???b??§????????????b???c(a--b--c)
	return 0;							// a???b??§????????????b???c(????????? b == c)
}

bool intersectSS(const L &s, const L &t) {	// <= 0??? < ???????????¨???????????¨?????????????????????
	return	ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 && 
			ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}

P crosspoint(const L &l, const L &m) {
	double A = cross(l[1] - l[0], m[1] - m[0]);
	double B = cross(l[1] - l[0], l[1] - m[0]);
	if (abs(A) < EPS && abs(B) < EPS) return m[0];
	return m[0] + B / A * (m[1] - m[0]);
}

bool intersectSP(const L &s, const P &p) {
	return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS;
}

double area2(const G& poly) {
	double A = 0;
	for(int i = 0 ; i < poly.size() ; i++)
		A += cross(poly[i], poly[(i+1)%poly.size()]);
	return abs(A);
}

map<P,set<P>> graph;

vector<P> poly;

double myatan2(P p){
	return atan2(p.imag(),p.real());
}

double dfs(P init,P prev, P cur){
	if( abs(init-cur) < EPS ){
		return area2(poly) / 2.0;
	}
	vector< pair<double,P> > ps;
	for(auto p : graph[cur] ){
		ps.push_back({myatan2(p-cur),p});
		ps.push_back({myatan2(p-cur)+2*M_PI,p});
		ps.push_back({myatan2(p-cur)-2*M_PI,p});
	}
	
	sort(ps.begin(),ps.end());
	double target = myatan2(prev-cur);
	for(int i = 0 ; i < ps.size() ; i++){
		if( target + EPS < ps[i].first ){
			poly.push_back(cur);
			return dfs(init,cur,ps[i].second);
		}
	}
	assert(false);
	
	
}
int main(){
	int n;
	cin >> n;
	G g;
	
	set<P> ps;
	for(int i = 0 ; i < n ; i++){
		int x,y;
		cin >> x >> y;
		g.push_back(P(x,y));
		ps.insert(P(x,y));
		
	}
	
	vector<L> cand;
	auto addp = [&](P a,P b){
		if( abs(a-b) > EPS ){
			graph[a].insert(b);
			graph[b].insert(a);
		}
	};
	
	for(int i = 0 ; i+1 < n ; i++){
		cand.push_back(L(g[i],g[i+1]));
		for(int j = i+1 ; j+1 < n ; j++){	
			auto l1 = L(g[i],g[i+1]);
			auto l2 = L(g[j],g[j+1]);
			if( intersectSS(l1,l2) ){
				auto cp = crosspoint(l1,l2);
				ps.insert(cp);
			}
		}
	}
	for( auto l : cand ){
		vector< pair<double,P> > ds;
		for( auto p : ps ){
			if( intersectSP(l,p) ){
				ds.push_back({abs(l[0]-p),p});
			}
		}
		sort(ds.begin(),ds.end());
		for(int j = 0 ; j+1 < ds.size() ; j++){
			addp(ds[j].second,ds[j+1].second);
		}
	}	
	
	queue<P> Q;
	for( auto v : graph ){
		if( v.second.size() <= 1 ){
			Q.push(v.first);
		}
	}
	map<P,bool> done;
	while( Q.size() ){
		auto q = Q.front(); Q.pop();
		for(auto v : graph[q] ){
			graph[v].erase(q);
			if( graph[v].size() <= 1 ){
				Q.push(v);
			}
		}
		graph.erase(q);
	}
	if( graph.size() == 0 ){
		puts("0.0");
	}else{	
		P sp = graph.begin()->first;
		vector<P> ip(graph.begin()->second.begin(),graph.begin()->second.end());
		sort(ip.begin(),ip.end(),[&](P a,P b){
			return cross(a-sp,b-sp) >= 0;
		});
		poly.push_back(sp);
		printf("%.10lf%c",dfs(sp,sp,ip[0]),10);
	}
	
	
	
}
### Prompt

Your challenge is to write a cpp solution to the following problem:

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.

Examples

Input

5
0 0
1 1
1 0
0 1
0 0


Output

0.5


Input

5
0 0
1 1
1 0
0 1
1 0


Output

0.25


Input

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

8


Input

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

0


Input

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


Output

2714.840579710

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#define prev jfwekljfwekl
typedef complex<double> P;
typedef vector<P> G;
const double EPS = 1e-9;
namespace std {
	bool operator < (const P& a, const P& b) {
		if( abs(a-b) < EPS ) return false;
		return fabs(real(a)-real(b)) < EPS ? imag(a) < imag(b) : real(a) < real(b);
	} 
}
double cross(P a,P b) { return imag(conj(a)*b); }
double dot(P a,P b) { return real(conj(a)*b);}

//??´???
struct L : public vector<P> {
	L(P a,P b) {
		push_back(a); push_back(b);
	}
	
};

int ccw(P a, P b, P c) {
	b -= a; c -= a;
	if (cross(b, c) > 0)   return +1;	// a ??? b ??§???????¨??????????????????? b ??? c(???)
	if (cross(b, c) < 0)   return -1;	// a ??? b ??§????¨??????????????????? b ??? c(???)
	if (dot(b, c) < 0) return +2;    	// a???b??§????????????a??????????¶???????b???c(c--a--b)
	if (norm(b) < norm(c)) return -2;	// a???b??§????????????b???c(a--b--c)
	return 0;							// a???b??§????????????b???c(????????? b == c)
}

bool intersectSS(const L &s, const L &t) {	// <= 0??? < ???????????¨???????????¨?????????????????????
	return	ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 && 
			ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}

P crosspoint(const L &l, const L &m) {
	double A = cross(l[1] - l[0], m[1] - m[0]);
	double B = cross(l[1] - l[0], l[1] - m[0]);
	if (abs(A) < EPS && abs(B) < EPS) return m[0];
	return m[0] + B / A * (m[1] - m[0]);
}

bool intersectSP(const L &s, const P &p) {
	return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS;
}

double area2(const G& poly) {
	double A = 0;
	for(int i = 0 ; i < poly.size() ; i++)
		A += cross(poly[i], poly[(i+1)%poly.size()]);
	return abs(A);
}

map<P,set<P>> graph;

vector<P> poly;

double myatan2(P p){
	return atan2(p.imag(),p.real());
}

double dfs(P init,P prev, P cur){
	if( abs(init-cur) < EPS ){
		return area2(poly) / 2.0;
	}
	vector< pair<double,P> > ps;
	for(auto p : graph[cur] ){
		ps.push_back({myatan2(p-cur),p});
		ps.push_back({myatan2(p-cur)+2*M_PI,p});
		ps.push_back({myatan2(p-cur)-2*M_PI,p});
	}
	
	sort(ps.begin(),ps.end());
	double target = myatan2(prev-cur);
	for(int i = 0 ; i < ps.size() ; i++){
		if( target + EPS < ps[i].first ){
			poly.push_back(cur);
			return dfs(init,cur,ps[i].second);
		}
	}
	assert(false);
	
	
}
int main(){
	int n;
	cin >> n;
	G g;
	
	set<P> ps;
	for(int i = 0 ; i < n ; i++){
		int x,y;
		cin >> x >> y;
		g.push_back(P(x,y));
		ps.insert(P(x,y));
		
	}
	
	vector<L> cand;
	auto addp = [&](P a,P b){
		if( abs(a-b) > EPS ){
			graph[a].insert(b);
			graph[b].insert(a);
		}
	};
	
	for(int i = 0 ; i+1 < n ; i++){
		cand.push_back(L(g[i],g[i+1]));
		for(int j = i+1 ; j+1 < n ; j++){	
			auto l1 = L(g[i],g[i+1]);
			auto l2 = L(g[j],g[j+1]);
			if( intersectSS(l1,l2) ){
				auto cp = crosspoint(l1,l2);
				ps.insert(cp);
			}
		}
	}
	for( auto l : cand ){
		vector< pair<double,P> > ds;
		for( auto p : ps ){
			if( intersectSP(l,p) ){
				ds.push_back({abs(l[0]-p),p});
			}
		}
		sort(ds.begin(),ds.end());
		for(int j = 0 ; j+1 < ds.size() ; j++){
			addp(ds[j].second,ds[j+1].second);
		}
	}	
	
	queue<P> Q;
	for( auto v : graph ){
		if( v.second.size() <= 1 ){
			Q.push(v.first);
		}
	}
	map<P,bool> done;
	while( Q.size() ){
		auto q = Q.front(); Q.pop();
		for(auto v : graph[q] ){
			graph[v].erase(q);
			if( graph[v].size() <= 1 ){
				Q.push(v);
			}
		}
		graph.erase(q);
	}
	if( graph.size() == 0 ){
		puts("0.0");
	}else{	
		P sp = graph.begin()->first;
		vector<P> ip(graph.begin()->second.begin(),graph.begin()->second.end());
		sort(ip.begin(),ip.end(),[&](P a,P b){
			return cross(a-sp,b-sp) >= 0;
		});
		poly.push_back(sp);
		printf("%.10lf%c",dfs(sp,sp,ip[0]),10);
	}
	
	
	
}
```