For a given polygon g, print "1" if g is a convex polygon, "0" otherwise. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of the polygon. The line segment connecting pn and p1 is also a side of the polygon.

Constraints

* 3 ≤ n ≤ 100
* -10000 ≤ xi, yi ≤ 10000
* No point of the polygon will occur more than once.
* Two sides of the polygon can intersect only at a common endpoint.

Input

g is given by coordinates of the points p1,..., pn in the following format:


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them.

Output

Print "1" or "0" in a line.

Examples

Input

4
0 0
3 1
2 3
0 3


Output

1


Input

5
0 0
2 0
1 1
2 2
0 2


Output

0
#include <algorithm>
#include <bitset>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <tuple>
#include <vector>

using namespace std;

#define rep(i, n) for (int64_t i = 0; i < (n); i++)
#define irep(i, n) for (int64_t i = 0; i <= (n); i++)
#define rrep(i, n) for (int64_t i = (n)-1; i >= 0; i--)
#define rirep(i, n) for (int64_t i = n; i >= 0; i--)

class Vec;
Vec operator/(const Vec& v, const double& divisor);
Vec operator*(const double& scale, const Vec& v);

class Vec {
  using F = double;
  vector<F> container;

 public:
  Vec(size_t size) : container(size) {}
  Vec(initializer_list<F> elements)
      : container(elements.begin(), elements.end()) {}
  size_t dim() const { return container.size(); }
  F& operator[](const size_t size) { return container.at(size); }
  const F& operator[](const size_t size) const { return container.at(size); }
  Vec operator+(const Vec& other) const {
    Vec ret(*this);
    for (size_t i = 0; i < dim(); i++) ret[i] += other[i];
    return ret;
  }
  Vec operator-(const Vec& other) const { return (*this) + (-other); }
  Vec operator-() const { return -1.0 * (*this); }
  F inner(const Vec& other) const {
    F acc = 0;
    for (size_t i = 0; i < dim(); i++) {
      acc += (*this)[i] * other[i];
    }
    return acc;
  }
  F norm() const { return sqrt(inner(*this)); }
  Vec unit() const { return (*this) / this->norm(); }
  F ccw(const Vec& other) const {
    return (*this)[0] * other[1] - other[0] * (*this)[1];
  }
  Vec normal() const { return Vec({-(*this)[1], (*this)[0]}); }
};
Vec operator/(const Vec& v, const double& divisor) { return 1.0 / divisor * v; }
Vec operator*(const double& scale, const Vec& v) {
  Vec ret(v);
  for (size_t i = 0; i < ret.dim(); i++) ret[i] *= scale;
  return ret;
}

class Polygon {
  const vector<Vec>& vert;

 public:
  Polygon(const vector<Vec>& vert) : vert(vert) {}
  double area() const {
    const size_t n = vert.size();
    double acc = 0;
    for (size_t i = 0; i < n; i++) {
      acc += vert[i].ccw(vert[(i + 1) % n]);
    }
    return acc / 2.0;
  }
  bool isConvex(double eps) const {
    const size_t n = vert.size();
    for (size_t i = 0; i < n; i++) {
      const Vec a = vert[(i + 1) % n] - vert[i],
                b = vert[(i + 2) % n] - vert[i];
      const double c = a.ccw(b);
      if (c < -eps) {
        return false;
      }
    }
    return true;
  }
};

int main() {
  int n;
  cin >> n;

  vector<Vec> v;
  rep(i, n) {
    double x, y;
    cin >> x >> y;
    v.push_back(Vec({x, y}));
  }

  const double EPS = 1e-9;
  cout << (Polygon(v).isConvex(EPS) ? 1 : 0) << endl;
  return 0;
}

