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
from sys import stdin
readline = stdin.readline


def cross(a, b):
    return a.real * b.imag - a.imag * b.real


def is_convex(p):
    for i in range(len(p)):
        j, k = i - 1, i - 2
        if 0 > cross(p[j] - p[k], p[i] - p[k]):
            return False
    return True

n = int(readline())
p = [map(int, readline().split()) for _ in range(n)]
p = [x + y * 1j for x, y in p]
print(1 if is_convex(p) else 0)