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
def cross(ux, uy, vx, vy):
    return ux*vy - uy*vx


n = int(input())
points = [tuple(map(int, input().split())) for _ in range(n)]
points.append(points[0])
points.append(points[1])

is_convex = True
for i in range(n):
    x1, y1 = points[i]
    x2, y2 = points[i + 1]
    x3, y3 = points[i + 2]
    if cross(x2 - x1, y2 - y1, x3 - x1, y3 - y1) < 0:
        is_convex = False
        break

print(1 if is_convex else 0)

