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
#!/usr/bin/env python3
# CGL_3_B: Polygon - Is-Convex


def run():
    n = int(input())
    ps = []

    for _ in range(n):
        x, y = [int(i) for i in input().split()]
        ps.append((x, y))

    if convex(ps):
        print(1)
    else:
        print(0)


def dot(v1, v2):
    x1, y1 = v1
    x2, y2 = v2
    return x1 * x2 + y1 * y2


def orthogonal(v):
    x, y = v
    return -y, x


def convex(ps0):
    p0, *ps1 = ps0
    ps1.append(p0)
    p1, *ps2 = ps1
    ps2.append(p1)
    ret = []
    for pa, pb, pc in zip(ps0, ps1, ps2):
        xa, ya = pa
        xb, yb = pb
        xc, yc = pc
        v1 = (xb - xa, yb - ya)
        v2 = (xc - xb, yc - yb)
        ret.append(dot(orthogonal(v1), v2))

    return all([d >= 0 for d in ret]) or all([d <= 0 for d in ret])


if __name__ == '__main__':
    run()

