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
#ifndef ___Geometry_Library
#define ___Geometry_Library

// ------ Includes ------ //
#include <cmath>
#include <vector>
#include <complex>
#include <utility>
#include <algorithm>

// ------ Defines ------ //
typedef long double GType;
typedef std::complex<GType> Point;
typedef std::pair<Point, Point> Segment;

// ------ Constants ------ //
const GType EPS = 1.0e-10L;

// ------ Functions Level 1 ------ //
GType dot(const Point& p1, const Point& p2) {
	return (std::conj(p1) * p2).real();
}
GType cross(const Point& p1, const Point& p2) {
	return (std::conj(p1) * p2).imag();
}
int ccw(const Point& p1, const Point& p2, const Point& p3) {
	Point v1 = p2 - p1, v2 = p3 - p1;
	if (cross(v1, v2) > EPS) return +1;
	if (cross(v1, v2) < -EPS) return -1;
	if (dot(v1, v2) < -EPS) return +2;
	if (std::norm(v1) < std::norm(v2)) return -2;
	return 0;
}

// ------ Functions Level 3 ------ //
bool is_convex(std::vector<Point> v) {
	if (v.size() < 3) return false;
	int s = -3;
	for (int i = 0; i < v.size(); i++) {
		int r = ccw(v[i], v[(i != 0 ? i - 1 : v.size() - 1)], v[(i + 1 != v.size() ? i + 1 : 0)]);
		if (abs(r) == 1 && s == -3) s = r;
		if (s * r == -1) return false;
	}
	return true;
}

#endif

#include <iostream>
using namespace std;
int n, x, y; vector<Point> v;
int main() {
	cin >> n; v.resize(n);
	for (int i = 0; i < n; i++) {
		cin >> x >> y;
		v[i] = Point(x, y);
	}
	cout << (int)(is_convex(v)) << endl;
	return 0;
}