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<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;

typedef long long ll;

bool debug = false;
const int NIL = -1;
const int INF = 1000000000;
const int NUM = 100010;
const double eps = 1e-10;
clock_t START, END;

//basic defitition
struct Point {
	double x, y;
	Point(double x = 0, double y = 0) :x(x), y(y) {}
};
typedef Point Vector;
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Point A, Point B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x * p, A.y * p); }
Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); }
bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
int dcmp(double x) { if (fabs(x) < eps)return 0; else return x < 0 ? -1 : 1; }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; }
// basic operator
double Dot(Vector A, Vector B) { return A.x * B.x + A.y * B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
//point and line
Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
	Vector u = P - Q;
	double t = Cross(w, u) / Cross(v, w);
	return P + v * t;
}//two lines only have one intersection and Cross(v,w) is not zero
double ConvexPolygonArea(vector<Point>& p, int n) {
	double area = 0;
	for (int i = 1; i < n; i++) {
		area += Cross(p[i] - p[0], p[i + 1] - p[0]);
	}
	return area / 2;
}

int main(void)
{
	if (debug) {
		START = clock();
		freopen("in29.txt", "r", stdin);
		freopen("out.txt", "w", stdout);
	};
	bool ok = true;
	int n;
	double x, y;
	vector<Point> p;
	cin >> n;
	for (int i = 0; i < n; i++) {
		scanf("%lf%lf", &x, &y);
		p.push_back(Point(x, y));
	}
	p.push_back(p[0]);
	p.push_back(p[1]);
	for (int i = 1; i <= n; i++) {
		if (dcmp(Cross(p[i + 1] - p[i], p[i - 1] - p[i])) < 0) {
			ok = false;
			break;
		}
	}
	printf("%d\n", ok);
	if (debug) {
		END = clock();
		double endtime = (double)(END - START) / 1000;
		printf("total time = %lf s", endtime);
	}
	return 0;
}
