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 <cassert>
#include <iomanip>
#include <vector>
#include <cmath>

using namespace std;

template<class T>
ostream& operator<<(ostream& os, const vector<T>& vs) {
    if (vs.empty()) return os << "[]";
    os << "[" << vs[0];
    for (int i = 1; i < vs.size(); i++) os << " " << vs[i];
    return os << "]";
}
 
const double EPS = 1e-7;

struct Point {
    double x, y;
    Point() {}
    Point(double x, double y) : x(x), y(y) {}
    Point operator+(const Point& p) const { return Point(x + p.x, y + p.y); }
    Point operator-(const Point& p) const { return Point(x - p.x, y - p.y); }
    Point operator*(double k) const { return Point(k * x, k * y); }
    Point operator/(double k) const { return Point(x / k, y / k); }
};
double dot(const Point& a, const Point& b) { return a.x * b.x + a.y * b.y; }
double cross(const Point& a, const Point& b) { return a.x * b.y - a.y * b.x; }
double norm(const Point& a) { return sqrt(dot(a, a)); }
Point rot90(const Point& p) { return Point(p.y, -p.x); } // 時計回りに90度回転 
ostream& operator<<(ostream& os, const Point& p) { return os << "(" << p.x << "," << p.y << ")"; }
istream& operator>>(istream& is, Point& p) { return is >> p.x >> p.y; }

int ccw(Point a, Point b, Point c){
    b = b - a; c = c - a;
    if (cross(b, c) > EPS) return +1;      // a,b,cの順に反時計周り
    if (cross(b, c) < -EPS) return -1;     // a,b,cの順に時計周り
    if (dot(b, c) < 0) return +2;          // c--a--b 直線
    if (norm(b) < norm(c)) return -2;      // a--b--c 直線
    return 0;                              // a--c--b 直線
}

// 頂点は反時計回りで与えられると仮定. 
typedef vector<Point> Polygon;
bool convex(const Polygon& vs) {
    int N = vs.size();
    for (int i = 0; i < N; i++) {
        Point a = vs[(i + N - 1) % N];
        Point b = vs[i];
        Point c = vs[(i + 1) % N];
        if (ccw(a, b, c) == -1) return false;
    }
    return true;
}

int main() {
    int N; cin >> N;
    Polygon P(N);
    for (int i = 0; i < N; i++) cin >> P[i];
    cout << convex(P) << endl;
    return 0;
}