The hobbits Frodo and Sam are carrying the One Ring to Mordor. In order not to be spotted by orcs, they decided to go through the mountains.

The mountain relief can be represented as a polyline with n points (x_i, y_i), numbered from 1 to n (x_i < x_{i + 1} for 1 ≤ i ≤ n - 1). Hobbits start their journey at the point (x_1, y_1) and should reach the point (x_n, y_n) to complete their mission.

The problem is that there is a tower with the Eye of Sauron, which watches them. The tower is located at the point (x_n, y_n) and has the height H, so the Eye is located at the point (x_n, y_n + H). In order to complete the mission successfully, the hobbits have to wear cloaks all the time when the Sauron Eye can see them, i. e. when there is a direct line from the Eye to the hobbits which is not intersected by the relief.

The hobbits are low, so their height can be considered negligibly small, but still positive, so when a direct line from the Sauron Eye to the hobbits only touches the relief, the Eye can see them.

<image> The Sauron Eye can't see hobbits when they are in the left position, but can see them when they are in the right position.

The hobbits do not like to wear cloaks, so they wear them only when they can be spotted by the Eye. Your task is to calculate the total distance the hobbits have to walk while wearing cloaks.

Input

The first line of the input contains two integers n and H (2 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ H ≤ 10^4) — the number of vertices in polyline and the tower height.

The next n lines contain two integers x_i, y_i each (0 ≤ x_i ≤ 4 ⋅ 10^5; 0 ≤ y_i ≤ 10^4) — the coordinates of the polyline vertices. It is guaranteed that x_i < x_{i + 1} for 1 ≤ i ≤ n - 1.

Output

Print one real number — the total distance the hobbits have to walk while wearing cloaks. Your answer will be considered correct if its absolute or relative error does not exceed 10^{-6} — formally, if your answer is a, and the jury's answer is b, your answer will be accepted if (|a - b|)/(max(1, b)) ≤ 10^{-6}.

Examples

Input


6 10
10 40
20 10
25 30
30 15
50 15
65 30


Output


70.4034587602


Input


9 5
0 0
5 10
15 10
20 0
25 11
30 0
35 10
50 10
60 5


Output


27.2787986124


Input


2 10000
0 10000
400000 0


Output


400124.9804748512
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
template <class T>
struct TPoint {
  T x, y;
  int index;
  static constexpr T eps = static_cast<T>(1e-9);
  explicit TPoint(T x = 0, T y = 0, int idx = -1) : x(x), y(y), index(idx) {}
  TPoint(const TPoint& p) {
    x = p.x;
    y = p.y;
    index = p.index;
  }
  TPoint& operator=(const TPoint& other) {
    x = other.x;
    y = other.y;
    index = other.index;
    return *this;
  }
  bool operator<(TPoint p) const { return tie(x, y) < tie(p.x, p.y); }
  bool operator==(TPoint p) const {
    return abs(x - p.x) <= eps && abs(y - p.y) <= eps;
  }
  TPoint operator+(TPoint p) const { return TPoint(x + p.x, y + p.y, index); }
  TPoint operator-(TPoint p) const { return TPoint(x - p.x, y - p.y, index); }
  TPoint operator*(T d) const { return TPoint(x * d, y * d, index); }
  TPoint operator/(T d) const { return TPoint(x / d, y / d, index); }
  T dot(TPoint p) const { return x * p.x + y * p.y; }
  T cross(TPoint p) const { return x * p.y - y * p.x; }
  T cross(TPoint a, TPoint b) const { return (a - *this).cross(b - *this); }
  T norm() const { return x * x + y * y; }
  T dist2(TPoint& b) const {
    return (x - b.x) * (x - b.x) + (y - b.y) * (y - b.y);
  }
  double dist(TPoint& b) const { return sqrt((double)dist2(b)); }
  double angle() const { return atan2(y, x); }
  TPoint unit() const { return *this / dist(); }
  TPoint perp() const { return TPoint(-y, x); }
  TPoint normal() const { return perp().unit(); }
  TPoint rotate(double a) const {
    return TPoint(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));
  }
};
template <class T>
struct TLine {
  static constexpr T eps = static_cast<T>(1e-9);
  TPoint<T> a, b, ab;
  TLine() : a(), b(), ab() {}
  TLine(const TPoint<T>& a, const TPoint<T>& b, bool twoPoints = true)
      : a(a), b(b), ab(twoPoints ? b - a : b) {}
  TLine(const T& xa, const T& ya, const T& xb, const T& yb)
      : a(xa, ya), b(xb, yb), ab(xb - xa, yb - ya) {}
  bool onLine(const TPoint<T>& p) {
    if (a == b) return p == a;
    return abs((p - a).cross(ab)) <= eps;
  }
  bool onSeg(const TPoint<T>& p) {
    if (a == b) return p == a;
    auto veca = a - p, vecb = b - p;
    return abs(veca.cross(vecb)) <= eps && veca.dot(vecb) <= eps;
  }
  T distLine(const TPoint<T>& p) {
    if (a == b) return a.dist(p);
    return abs((p - a).cross(ab)) / ab.norm();
  }
  T distSeg(const TPoint<T>& p) {
    if ((p - a).dot(ab) <= 0) return dist(p, a);
    if ((p - b).dot(ab) >= 0) return dist(p, b);
    return distLine(p);
  }
  TPoint<T> projection(const TPoint<T>& p) {
    TPoint<T> res = a;
    if (a == b) return a;
    res += ab * distLine(p);
    return res;
  }
  TPoint<T> reflection(const TPoint<T>& p) {
    TPoint<T> res = projection(p);
    res = 2 * res - p;
  }
  int intersect(const TLine& l, TPoint<T>& res) {
    if (abs(ab.cross(l.ab)) > eps) {
      res = l.a - (l.ab) * ab.cross(l.a - a) / (ab).cross(l.ab);
      return 1;
    } else
      return -(abs(ab.cross(l.a - a)) <= eps || l.a == l.b);
  }
  int intersectSeg(const TLine& l, TPoint<T>& r1, TPoint<T>& r2) {
    if (a == b) {
      if (l.a == l.b) {
        if (b == l.b) {
          r1 = b;
          return 1;
        } else
          return 0;
      } else
        return l.intersect(*this, r1, r2);
    }
    TPoint<T> d = l.a - a;
    auto s = ab.cross(l.ab), s1 = ab.cross(d), s2 = l.ab.cross(d);
    if (s == 0) {
      auto b1 = a.dot(ab), c1 = b.dot(ab), b2 = l.a.dot(ab), c2 = l.b.dot(ab);
      if (s1 || s2 || max(b1, min(b2, c2)) > min(c1, max(b2, c2))) return 0;
      r1 = min(b2, c2) < b1 ? a : (b2 < c2 ? l.a : l.b);
      r2 = max(b2, c2) > c1 ? b : (b2 > c2 ? l.a : l.b);
      return 2 - (r1 == r2);
    }
    if (s < 0) {
      s = -s;
      s1 = -s1;
      s2 = -s2;
    }
    if (0 < s1 || s <= s1 || 0 < s2 || s <= s2) return 0;
    r1 = a - ab * s2 / s;
    return 1;
  }
};
using Point = TPoint<double>;
using Line = TLine<double>;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int N, H;
  cin >> N >> H;
  vector<Point> points(N);
  for (int i = 0; i < N; i++) {
    int x, y;
    cin >> x >> y;
    points[i].x = x;
    points[i].y = y;
    points[i].index = i;
  }
  Point eye = points.back() + Point(0, H);
  vector<Point> orig = points;
  for (int i = 0; i < N; i++) points[i] = points[i] - eye;
  sort(points.begin(), points.end(), [](Point a, Point b) {
    const Point origin(0, 0);
    bool ba = a < origin, bb = b < origin;
    if (ba != bb) return ba < bb;
    return a.cross(b) > 0;
  });
  vector<int> ints;
  for (int i = 0; i < N; i++) {
    if (!ints.empty() && points[i].index < ints.back()) continue;
    ints.push_back(points[i].index);
  }
  double ans = 0;
  for (int i = 1; i < (int)ints.size(); i++) {
    Point p1 = orig[ints[i - 1]];
    Point p2 = orig[ints[i - 1] + 1];
    Point p3 = orig[ints[i]];
    Point res;
    Line l1(p1, p2);
    Line l2(p3, eye);
    int x = l1.intersect(l2, res);
    if (x == 0) continue;
    if (x == -1) {
      ans += p3.dist(p1);
      continue;
    }
    ans += p1.dist(res);
  }
  cout << fixed << setprecision(10) << ans << '\n';
}
