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<cstdio>
#define MAX 100
struct Point{double x, y;};
Point T[MAX];

double cross(double x1, double y1, double x2, double y2){
    return x1*y2 - x2*y1;
}

double ccw(Point p1, Point p2, Point p3){
    return cross(p2.x-p1.x, p2.y-p1.y, p3.x-p2.x, p3.y-p2.y);
}

int main(int argc, char const *argv[])
{
    int n;
    scanf("%d", &n);
    for(int i =0; i<n; i++) scanf("%lf %lf", &T[i].x, &T[i].y);

    double result;
    bool flag = true;
    for(int i=0; i<n; i++){
        if(i==0){
            result = ccw(T[n-1], T[i], T[i+1]);
        }
        else if(i == n-1){
            result = ccw(T[i-1], T[i], T[0]);
        }else{
            result = ccw(T[i-1], T[i], T[i+1]);
        }
        if(result <0){
            flag = false;
            break;
        }
    }

    if(flag) printf("1\n");
    else printf("0\n");
    return 0;
}   

