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

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <map>
#include <queue>
#include <set>
#include <functional>
#include <ctime>
#include <numeric>
#include <unordered_set>
#include <unordered_map>

using namespace std;

#define fst first
#define snd second
#define all(c) ((c).begin()), ((c).end())

const double EPS = 1e-8;
int sign(double x) {
  if (x < -EPS) return -1;
  if (x > +EPS) return +1;
  return 0;
}
struct point {
  typedef double T;
  T x, y; 
  point &operator+=(point p) { x += p.x; y += p.y; return *this; }
  point &operator-=(point p) { x -= p.x; y -= p.y; return *this; }
  point &operator*=(T a)     { x *= a;   y *= a;   return *this; }
  point &operator/=(T a)     { return *this *= (1.0/a); }
  point operator-() const    { return {-x, -y}; }
  bool operator<(point p) const { 
    int s = sign(x - p.x);
    return s ? s < 0 : sign(y - p.y) < 0;
  }
};
bool operator==(point p, point q) { return !(p < q) && !(q < p); }
point operator+(point p, point q) { return p += q; }
point operator-(point p, point q) { return p -= q; }
point operator*(point::T a, point p) { return p *= a; }
point operator*(point p, point::T a) { return p *= a; }
point operator/(point p, point::T a) { return p /= a; }
point::T dot(point p, point q) { return p.x*q.x+p.y*q.y; }
point::T cross(point p, point q) { return p.x*q.y-p.y*q.x; } // left turn > 0
point::T norm2(point p) { return dot(p,p); }
point orth(point p) { return {-p.y, p.x}; }
point::T norm(point p) { return sqrt(dot(p,p)); }
point::T arg(point p) { return atan2(p.y, p.x); }

struct segment { point p, q; };
vector<point> intersect(segment s, segment t) {
  auto a = cross(s.q - s.p, t.q - t.p);
  auto b = cross(t.p - s.p, t.q - t.p); 
  auto c = cross(s.q - s.p, s.p - t.p);
  if (a < 0) { a = -a; b = -b; c = -c; }
  if (sign(b) < 0 || sign(a-b) < 0 ||
      sign(c) < 0 || sign(a-c) < 0) return {};      // disjoint
  if (sign(a) != 0) return {s.p + b/a*(s.q - s.p)}; // properly crossing
  vector<point> ps;                                 // same line
  auto insert_if_possible = [&](point p) {
    for (auto q: ps) if (sign(dot(p-q, p-q)) == 0) return;
    ps.push_back(p);
  };
  if (sign(dot(s.p-t.p, s.q-t.p)) <= 0) insert_if_possible(t.p);
  if (sign(dot(s.p-t.q, s.q-t.q)) <= 0) insert_if_possible(t.q);
  if (sign(dot(t.p-s.p, t.q-s.p)) <= 0) insert_if_possible(s.p);
  if (sign(dot(t.p-s.q, t.q-s.q)) <= 0) insert_if_possible(s.q);
  return ps;
}
struct arrangement {
  struct edge {
    int src, dst;
    point::T weight;
    size_t id, rev;
  };
  int n;
  vector<point> ps; // ps[id[p]] = p, id[ps[k]] = k
  map<point,int> id; 
  vector<vector<edge>> adj;
  arrangement(vector<segment> ss) : n(0) {
    vector<vector<pair<point::T, int>>> group(ss.size());
    auto append = [&](int i, point p) {
      if (!id.count(p)) { id[p] = n++; ps.push_back(p); }
      group[i].push_back({norm(ss[i].p - p), id[p]});
    };
    for (int i = 0; i < ss.size(); ++i) {
      append(i, ss[i].p);
      append(i, ss[i].q);
      for (int j = 0; j < i; ++j) {
        auto qs = intersect(ss[i], ss[j]);
        if (qs.size() == 1) {
          append(i, qs[0]);
          append(j, qs[0]);
        }
      }
    }
    adj.resize(n);
    for (auto &vs: group) {
      sort(all(vs));
      for (int i = 0; i+1 < vs.size(); ++i) {
        auto u = vs[i].snd, v = vs[i+1].snd;
        if (u == v) continue;
        auto len = vs[i+1].fst - vs[i].fst;
        adj[u].push_back({u, v, len});
        adj[v].push_back({v, u, len});
      }
    }
    // remove duplicates and orient edges
    vector<unordered_map<int, int>> idx(n);
    for (int u = 0; u < n; ++u) {
      auto eq = [&](edge e, edge f) { return e.dst == f.dst; };
      auto lt = [&](edge e, edge f) { return e.dst <  f.dst; };
      sort(all(adj[u]), lt);
      adj[u].erase(unique(all(adj[u]), eq), adj[u].end());
      sort(all(adj[u]), [&](edge e, edge f) {
        return arg(ps[e.dst] - ps[e.src]) > arg(ps[f.dst] - ps[f.src]);
      });
      for (int i = 0; i < adj[u].size(); ++i) {
        adj[u][i].id = i;
        int v = adj[u][i].dst;
        idx[u][v] = i;
        if (idx[v].count(u)) {
          int j = idx[v][u];
          adj[u][i].rev = j;
          adj[v][j].rev = i;
        }
      }
    }
  }
  template <class F>
  void traverse(edge e, F func) {
    edge s = e;
    do {
      func(e);
      int j = adj[e.dst][e.rev].id + 1;
      if (j >= adj[e.dst].size()) j = 0;
      e = adj[e.dst][j];
    } while (e.src != s.src || e.dst != s.dst);
  }
  void traverse_all_faces() {
    vector<unordered_set<int>> visited(n);
    point::T ans = 0;
    for (int u = 0; u < n; ++u) {
      for (edge e: adj[u]) {
        if (!visited[e.src].count(e.dst)) {
          point::T area = 0;
          traverse(e, [&](edge e) { 
            visited[e.src].insert(e.dst);
            area += cross(ps[e.src], ps[e.dst]); 
          });
          if (area > 0) ans += area;
        }
      }
    }
    printf("%.12f\n", ans/2);
  }
};
int main() {
  int n; scanf("%d", &n);
  vector<point> ps(n);
  for (int i = 0; i < n; ++i) 
    scanf("%lf %lf", &ps[i].x, &ps[i].y);
  vector<segment> ss;
  for (int i = 0; i+1 < n; ++i) 
    ss.push_back({ps[i], ps[i+1]});
  arrangement arr(ss);
  arr.traverse_all_faces();
}