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 <vector>
using namespace std;

template <class T> void readPoint(vector< vector<T> >& vec, int idx) {
    T x, y;
    vector<T> point(2);
    std::cin >> x >> y;
    point[0] = x;
    point[1] = y;
    vec[idx] = point;
}
int main()
{
    int size;
    cin >> size;
    vector< vector<int> > points(size);
    //vector<int> y(size);
    for (int i = 0; i < size; i++) {
        readPoint(points, i);
        //readVal(y, i);
    }
    int ans(1), dir(0), vecx(0), vecy(0), new_vecx(0), new_vecy(0);
    for (int i = 0; i <= size; i++) {
        new_vecx = points[(i + 1) % size][0] - points[i % size][0];
        new_vecy = points[(i + 1) % size][1] - points[i % size][1];
        int cross_prod = (vecx * new_vecy - vecy * new_vecx);
        if (cross_prod != 0) {
            if (cross_prod * dir >= 0) {
                dir = cross_prod > 0 ? 1 : -1;
            }
            else {
                ans = 0;
                break;
            }
        }
        vecx = new_vecx;
        vecy = new_vecy;
    }
    cout << ans << "\n";
    return 0;
}

