#include <bits/stdc++.h>
using namespace std;
long double get() {
  double x;
  scanf("%lf", &x);
  return x;
}
struct P {
  long double x, y;
  P() {}
  P(long double x, long double y) : x(x), y(y) {}
  void read() { x = get(), y = get(); }
};
P operator+(const P &A, const P &B) { return P(A.x + B.x, A.y + B.y); }
P operator-(const P &A, const P &B) { return P(A.x - B.x, A.y - B.y); }
long double Cross(const P &A, const P &B) { return A.x * B.y - A.y * B.x; }
long double Dot(const P &A, const P &B) { return A.x * B.x + A.y * B.y; }
long double Length(const P &A) { return sqrt(Dot(A, A)); }
const long double eps = 1e-15;
inline int dcmp(long double x) { return (x > eps) - (x < -eps); }
const int maxn = 1001;
int n, m;
P p[maxn];
vector<pair<long double, long double> > vec;
inline void add(long double x, long double flag) {
  vec.push_back(make_pair(x, -flag));
}
long double get(const P &p, const P &v, const P &q, const P &w) {
  P u = p - q;
  return Cross(w, u) / Cross(v, w);
}
void getSegmentInter(const P &p, const P &v, const P &q, const P &w) {
  if (!dcmp(Cross(v, w))) {
    if (!dcmp(Cross(v, q - p))) {
      long double l = Dot(v, q - p) / Dot(v, v);
      long double r = Dot(v, q + w - p) / Dot(v, v);
      if (l > r) swap(l, r);
      add(l, +1);
      add(r, -1);
    }
  } else {
    static int num = 0;
    long double tmp = get(q, w, p, v);
    if (dcmp(tmp) >= 0 && dcmp(tmp - 1) <= 0) {
      long double rate = 1;
      if (dcmp(tmp) == 0 || dcmp(tmp - 1) == 0) rate = .5;
      tmp = get(p, v, q, w);
      add(tmp, dcmp(Cross(w, v)) > 0 ? +rate : -rate);
    }
  }
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; i++) p[i].read();
  p[n] = p[0];
  while (m--) {
    P a, b;
    a.read();
    b.read();
    vec.clear();
    for (int i = 0; i < n; i++)
      getSegmentInter(a, b - a, p[i], p[i + 1] - p[i]);
    sort(vec.begin(), vec.end());
    long double ans = 0, k = 0;
    for (size_t i = 0; i + 1 < vec.size(); i++) {
      k += vec[i].second;
      if (dcmp(k)) ans += vec[i + 1].first - vec[i].first;
    }
    ans *= Length(b - a);
    printf("%.20f\n", double(ans));
  }
}

### Prompt

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

Given simple (without self-intersections) n-gon. It is not necessary convex. Also you are given m lines. For each line find the length of common part of the line and the n-gon.

The boundary of n-gon belongs to polygon. It is possible that n-gon contains 180-degree angles.

Input

The first line contains integers n and m (3 ≤ n ≤ 1000;1 ≤ m ≤ 100). The following n lines contain coordinates of polygon vertices (in clockwise or counterclockwise direction). All vertices are distinct.

The following m lines contain line descriptions. Each of them contains two distict points of a line by their coordinates.

All given in the input coordinates are real numbers, given with at most two digits after decimal point. They do not exceed 105 by absolute values.

Output

Print m lines, the i-th line should contain the length of common part of the given n-gon and the i-th line. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

4 3
0 0
1 0
1 1
0 1
0 0 1 1
0 0 0 1
0 0 1 -1


Output

1.41421356237309514547
1.00000000000000000000
0.00000000000000000000

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long double get() {
  double x;
  scanf("%lf", &x);
  return x;
}
struct P {
  long double x, y;
  P() {}
  P(long double x, long double y) : x(x), y(y) {}
  void read() { x = get(), y = get(); }
};
P operator+(const P &A, const P &B) { return P(A.x + B.x, A.y + B.y); }
P operator-(const P &A, const P &B) { return P(A.x - B.x, A.y - B.y); }
long double Cross(const P &A, const P &B) { return A.x * B.y - A.y * B.x; }
long double Dot(const P &A, const P &B) { return A.x * B.x + A.y * B.y; }
long double Length(const P &A) { return sqrt(Dot(A, A)); }
const long double eps = 1e-15;
inline int dcmp(long double x) { return (x > eps) - (x < -eps); }
const int maxn = 1001;
int n, m;
P p[maxn];
vector<pair<long double, long double> > vec;
inline void add(long double x, long double flag) {
  vec.push_back(make_pair(x, -flag));
}
long double get(const P &p, const P &v, const P &q, const P &w) {
  P u = p - q;
  return Cross(w, u) / Cross(v, w);
}
void getSegmentInter(const P &p, const P &v, const P &q, const P &w) {
  if (!dcmp(Cross(v, w))) {
    if (!dcmp(Cross(v, q - p))) {
      long double l = Dot(v, q - p) / Dot(v, v);
      long double r = Dot(v, q + w - p) / Dot(v, v);
      if (l > r) swap(l, r);
      add(l, +1);
      add(r, -1);
    }
  } else {
    static int num = 0;
    long double tmp = get(q, w, p, v);
    if (dcmp(tmp) >= 0 && dcmp(tmp - 1) <= 0) {
      long double rate = 1;
      if (dcmp(tmp) == 0 || dcmp(tmp - 1) == 0) rate = .5;
      tmp = get(p, v, q, w);
      add(tmp, dcmp(Cross(w, v)) > 0 ? +rate : -rate);
    }
  }
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; i++) p[i].read();
  p[n] = p[0];
  while (m--) {
    P a, b;
    a.read();
    b.read();
    vec.clear();
    for (int i = 0; i < n; i++)
      getSegmentInter(a, b - a, p[i], p[i + 1] - p[i]);
    sort(vec.begin(), vec.end());
    long double ans = 0, k = 0;
    for (size_t i = 0; i + 1 < vec.size(); i++) {
      k += vec[i].second;
      if (dcmp(k)) ans += vec[i + 1].first - vec[i].first;
    }
    ans *= Length(b - a);
    printf("%.20f\n", double(ans));
  }
}

```