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
# Aizu Problem CGL_3_B: Is-Convex
#
import sys, math, os

# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
    sys.stdin = open("sample-input.txt", "rt")


def is_convex(P):
    # check whether polygon P is convex or not
    # see: https://stackoverflow.com/questions/471962/how-do-determine-if-a-polygon-is-complex-convex-nonconvex
    N = len(P)
    prods = []
    for k in range(N):
        x0, y0 = P[k]
        x1, y1 = P[(k + 1) % N]
        x2, y2 = P[(k + 2) % N]
        dx1 = x1 - x0
        dy1 = y1 - y0
        dx2 = x2 - x1
        dy2 = y2 - y1
        cross = dx1 * dy2 - dy1 * dx2
        prods.append(cross)
    prods = sorted(prods)
    return prods[0] * prods[-1] > 0


N = int(input())
P = [[int(_) for _ in input().split()] for __ in range(N)]
print(1 if is_convex(P) else 0)