#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
const int MOD = 1e9 + 7;
const int MX = 2e5 + 5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1, 0, -1, 0}, yd[4] = {0, 1, 0, -1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
template <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class U>
T fstTrue(T lo, T hi, U first) {
  hi++;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo) / 2;
    first(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U first) {
  lo--;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo + 1) / 2;
    first(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <class T>
void remDup(vector<T>& v) {
  sort(begin(v), end(v));
  v.erase(unique(begin(v), end(v)), end(v));
}
template <class T, class U>
void erase(T& t, const U& u) {
  auto it = t.find(u);
  assert(it != end(t));
  t.erase(u);
}
template <class T>
void re(complex<T>& c);
template <class T, class U>
void re(pair<T, U>& p);
template <class T>
void re(vector<T>& v);
template <class T, size_t SZ>
void re(AR<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(db& d) {
  str t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  str t;
  re(t);
  d = stold(t);
}
template <class T, class... U>
void re(T& t, U&... u) {
  re(t);
  re(u...);
}
template <class T>
void re(complex<T>& c) {
  T a, b;
  re(a, b);
  c = {a, b};
}
template <class T, class U>
void re(pair<T, U>& p) {
  re(p.first, p.second);
}
template <class T>
void re(vector<T>& x) {
  for (auto& a : x) re(a);
}
template <class T, size_t SZ>
void re(AR<T, SZ>& x) {
  for (auto& a : x) re(a);
}
str to_string(char c) { return str(1, c); }
str to_string(const char* second) { return (str)second; }
str to_string(str second) { return second; }
str to_string(bool b) { return to_string((int)b); }
template <class T>
str to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
str to_string(vector<bool> v) {
  str res = "{";
  for (int i = (0); i < ((int)(v).size()); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
str to_string(bitset<SZ> b) {
  str res = "";
  for (int i = (0); i < (SZ); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
str to_string(pair<T, U> p);
template <class T>
str to_string(T v) {
  bool fst = 1;
  str res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
str to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
void setIn(str second) { freopen(second.c_str(), "r", stdin); }
void setOut(str second) { freopen(second.c_str(), "w", stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str second = "") {
  unsyncIO();
  if ((int)(second).size()) {
    setIn(second + ".in"), setOut(second + ".out");
  }
}
using T = ld;
int sgn(T a) { return (a > 0) - (a < 0); }
T sq(T a) { return a * a; }
T norm(const pair<T, T>& p) { return sq(p.first) + sq(p.second); }
T abs(const pair<T, T>& p) { return sqrt(norm(p)); }
T arg(const pair<T, T>& p) { return atan2(p.second, p.first); }
pair<T, T> conj(const pair<T, T>& p) { return pair<T, T>(p.first, -p.second); }
pair<T, T> perp(const pair<T, T>& p) { return pair<T, T>(-p.second, p.first); }
pair<T, T> dir(T ang) { return pair<T, T>(cos(ang), sin(ang)); }
pair<T, T> operator-(const pair<T, T>& l) {
  return pair<T, T>(-l.first, -l.second);
}
pair<T, T> operator+(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(l.first + r.first, l.second + r.second);
}
pair<T, T> operator-(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(l.first - r.first, l.second - r.second);
}
pair<T, T> operator*(const pair<T, T>& l, const T& r) {
  return pair<T, T>(l.first * r, l.second * r);
}
pair<T, T> operator*(const T& l, const pair<T, T>& r) { return r * l; }
pair<T, T> operator/(const pair<T, T>& l, const T& r) {
  return pair<T, T>(l.first / r, l.second / r);
}
pair<T, T> operator*(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(l.first * r.first - l.second * r.second,
                    l.second * r.first + l.first * r.second);
}
pair<T, T> operator/(const pair<T, T>& l, const pair<T, T>& r) {
  return l * conj(r) / norm(r);
}
pair<T, T>& operator+=(pair<T, T>& l, const pair<T, T>& r) { return l = l + r; }
pair<T, T>& operator-=(pair<T, T>& l, const pair<T, T>& r) { return l = l - r; }
pair<T, T>& operator*=(pair<T, T>& l, const T& r) { return l = l * r; }
pair<T, T>& operator/=(pair<T, T>& l, const T& r) { return l = l / r; }
pair<T, T>& operator*=(pair<T, T>& l, const pair<T, T>& r) { return l = l * r; }
pair<T, T>& operator/=(pair<T, T>& l, const pair<T, T>& r) { return l = l / r; }
pair<T, T> unit(const pair<T, T>& p) { return p / abs(p); }
T dot(const pair<T, T>& a, const pair<T, T>& b) {
  return a.first * b.first + a.second * b.second;
}
T cross(const pair<T, T>& a, const pair<T, T>& b) {
  return a.first * b.second - a.second * b.first;
}
T cross(const pair<T, T>& p, const pair<T, T>& a, const pair<T, T>& b) {
  return cross(a - p, b - p);
}
pair<T, T> reflect(const pair<T, T>& p, const pair<T, T>& a,
                   const pair<T, T>& b) {
  return a + conj((p - a) / (b - a)) * (b - a);
}
pair<T, T> foot(const pair<T, T>& p, const pair<T, T>& a, const pair<T, T>& b) {
  return (p + reflect(p, a, b)) / (T)2;
}
bool onSeg(const pair<T, T>& p, const pair<T, T>& a, const pair<T, T>& b) {
  return cross(a, b, p) == 0 && dot(p - a, p - b) <= 0;
}
pair<T, T> lineIsect(pair<T, T> a, pair<T, T> b, pair<T, T> c, pair<T, T> d) {
  T x = cross(a, b, c), y = cross(a, b, d);
  T X = cross(c, d, a), Y = cross(c, d, b);
  return {(d * x - c * y) / (x - y)};
}
pair<pair<T, T>, T> cenArea(const vector<pair<T, T> >& v) {
  pair<T, T> cen(0, 0);
  T area = 0;
  for (int i = (0); i < ((int)(v).size()); ++i) {
    int j = (i + 1) % (int)(v).size();
    T a = cross(v[i], v[j]);
    cen += a * (v[i] + v[j]);
    area += a;
  }
  return {cen / area / (T)3, area / 2};
}
int n, m;
int main() {
  setIO();
  re(n, m);
  vector<pair<T, T> > v(n);
  re(v);
  if (cenArea(v).second < 0) reverse(begin(v), end(v));
  for (int _ = (0); _ < (m); ++_) {
    pair<T, T> a, b;
    re(a, b);
    vi side;
    for (auto& t : v) side.push_back(sgn(cross(a, b, t)) >= 0);
    0;
    db ans = 0;
    for (int i = (0); i < (n); ++i) {
      int j = (i + 1) % (int)(side).size();
      if (side[i] != side[j]) {
        int whoops = sgn(cross(v[i] - v[j], b - a));
        ans += whoops * dot(b - a, lineIsect(a, b, v[i], v[j]));
      }
      if (cross(a, b, v[i]) == 0 && cross(a, b, v[j]) == 0 &&
          dot(b - a, v[j] - v[i]) > 0) {
        ans += dot(b - a, v[j] - v[i]);
      }
    }
    cout << fixed << setprecision(9) << ans / abs(b - a) << "\n";
  }
}

### Prompt

Please create a solution in CPP 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;
using ll = long long;
using ld = long double;
using db = double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
const int MOD = 1e9 + 7;
const int MX = 2e5 + 5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1, 0, -1, 0}, yd[4] = {0, 1, 0, -1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
template <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class U>
T fstTrue(T lo, T hi, U first) {
  hi++;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo) / 2;
    first(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U first) {
  lo--;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo + 1) / 2;
    first(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <class T>
void remDup(vector<T>& v) {
  sort(begin(v), end(v));
  v.erase(unique(begin(v), end(v)), end(v));
}
template <class T, class U>
void erase(T& t, const U& u) {
  auto it = t.find(u);
  assert(it != end(t));
  t.erase(u);
}
template <class T>
void re(complex<T>& c);
template <class T, class U>
void re(pair<T, U>& p);
template <class T>
void re(vector<T>& v);
template <class T, size_t SZ>
void re(AR<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(db& d) {
  str t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  str t;
  re(t);
  d = stold(t);
}
template <class T, class... U>
void re(T& t, U&... u) {
  re(t);
  re(u...);
}
template <class T>
void re(complex<T>& c) {
  T a, b;
  re(a, b);
  c = {a, b};
}
template <class T, class U>
void re(pair<T, U>& p) {
  re(p.first, p.second);
}
template <class T>
void re(vector<T>& x) {
  for (auto& a : x) re(a);
}
template <class T, size_t SZ>
void re(AR<T, SZ>& x) {
  for (auto& a : x) re(a);
}
str to_string(char c) { return str(1, c); }
str to_string(const char* second) { return (str)second; }
str to_string(str second) { return second; }
str to_string(bool b) { return to_string((int)b); }
template <class T>
str to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
str to_string(vector<bool> v) {
  str res = "{";
  for (int i = (0); i < ((int)(v).size()); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
str to_string(bitset<SZ> b) {
  str res = "";
  for (int i = (0); i < (SZ); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
str to_string(pair<T, U> p);
template <class T>
str to_string(T v) {
  bool fst = 1;
  str res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
str to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
void setIn(str second) { freopen(second.c_str(), "r", stdin); }
void setOut(str second) { freopen(second.c_str(), "w", stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str second = "") {
  unsyncIO();
  if ((int)(second).size()) {
    setIn(second + ".in"), setOut(second + ".out");
  }
}
using T = ld;
int sgn(T a) { return (a > 0) - (a < 0); }
T sq(T a) { return a * a; }
T norm(const pair<T, T>& p) { return sq(p.first) + sq(p.second); }
T abs(const pair<T, T>& p) { return sqrt(norm(p)); }
T arg(const pair<T, T>& p) { return atan2(p.second, p.first); }
pair<T, T> conj(const pair<T, T>& p) { return pair<T, T>(p.first, -p.second); }
pair<T, T> perp(const pair<T, T>& p) { return pair<T, T>(-p.second, p.first); }
pair<T, T> dir(T ang) { return pair<T, T>(cos(ang), sin(ang)); }
pair<T, T> operator-(const pair<T, T>& l) {
  return pair<T, T>(-l.first, -l.second);
}
pair<T, T> operator+(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(l.first + r.first, l.second + r.second);
}
pair<T, T> operator-(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(l.first - r.first, l.second - r.second);
}
pair<T, T> operator*(const pair<T, T>& l, const T& r) {
  return pair<T, T>(l.first * r, l.second * r);
}
pair<T, T> operator*(const T& l, const pair<T, T>& r) { return r * l; }
pair<T, T> operator/(const pair<T, T>& l, const T& r) {
  return pair<T, T>(l.first / r, l.second / r);
}
pair<T, T> operator*(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(l.first * r.first - l.second * r.second,
                    l.second * r.first + l.first * r.second);
}
pair<T, T> operator/(const pair<T, T>& l, const pair<T, T>& r) {
  return l * conj(r) / norm(r);
}
pair<T, T>& operator+=(pair<T, T>& l, const pair<T, T>& r) { return l = l + r; }
pair<T, T>& operator-=(pair<T, T>& l, const pair<T, T>& r) { return l = l - r; }
pair<T, T>& operator*=(pair<T, T>& l, const T& r) { return l = l * r; }
pair<T, T>& operator/=(pair<T, T>& l, const T& r) { return l = l / r; }
pair<T, T>& operator*=(pair<T, T>& l, const pair<T, T>& r) { return l = l * r; }
pair<T, T>& operator/=(pair<T, T>& l, const pair<T, T>& r) { return l = l / r; }
pair<T, T> unit(const pair<T, T>& p) { return p / abs(p); }
T dot(const pair<T, T>& a, const pair<T, T>& b) {
  return a.first * b.first + a.second * b.second;
}
T cross(const pair<T, T>& a, const pair<T, T>& b) {
  return a.first * b.second - a.second * b.first;
}
T cross(const pair<T, T>& p, const pair<T, T>& a, const pair<T, T>& b) {
  return cross(a - p, b - p);
}
pair<T, T> reflect(const pair<T, T>& p, const pair<T, T>& a,
                   const pair<T, T>& b) {
  return a + conj((p - a) / (b - a)) * (b - a);
}
pair<T, T> foot(const pair<T, T>& p, const pair<T, T>& a, const pair<T, T>& b) {
  return (p + reflect(p, a, b)) / (T)2;
}
bool onSeg(const pair<T, T>& p, const pair<T, T>& a, const pair<T, T>& b) {
  return cross(a, b, p) == 0 && dot(p - a, p - b) <= 0;
}
pair<T, T> lineIsect(pair<T, T> a, pair<T, T> b, pair<T, T> c, pair<T, T> d) {
  T x = cross(a, b, c), y = cross(a, b, d);
  T X = cross(c, d, a), Y = cross(c, d, b);
  return {(d * x - c * y) / (x - y)};
}
pair<pair<T, T>, T> cenArea(const vector<pair<T, T> >& v) {
  pair<T, T> cen(0, 0);
  T area = 0;
  for (int i = (0); i < ((int)(v).size()); ++i) {
    int j = (i + 1) % (int)(v).size();
    T a = cross(v[i], v[j]);
    cen += a * (v[i] + v[j]);
    area += a;
  }
  return {cen / area / (T)3, area / 2};
}
int n, m;
int main() {
  setIO();
  re(n, m);
  vector<pair<T, T> > v(n);
  re(v);
  if (cenArea(v).second < 0) reverse(begin(v), end(v));
  for (int _ = (0); _ < (m); ++_) {
    pair<T, T> a, b;
    re(a, b);
    vi side;
    for (auto& t : v) side.push_back(sgn(cross(a, b, t)) >= 0);
    0;
    db ans = 0;
    for (int i = (0); i < (n); ++i) {
      int j = (i + 1) % (int)(side).size();
      if (side[i] != side[j]) {
        int whoops = sgn(cross(v[i] - v[j], b - a));
        ans += whoops * dot(b - a, lineIsect(a, b, v[i], v[j]));
      }
      if (cross(a, b, v[i]) == 0 && cross(a, b, v[j]) == 0 &&
          dot(b - a, v[j] - v[i]) > 0) {
        ans += dot(b - a, v[j] - v[i]);
      }
    }
    cout << fixed << setprecision(9) << ans / abs(b - a) << "\n";
  }
}

```