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
n = int(input())
vec = []
for i in range(n):
    vec += [list(map(int, input().split()))]
vec += [vec[0]]
vec += [vec[1]]
Sum = 0
def cross(a, b):
    return a[0]*b[1]-a[1]*b[0]
def ab(a, b):
    c = (b[0]-a[0],b[1]-a[1])
    return c
def check(a, b, c):
    if cross(ab(a, b),ab(a, c)) >= 0:
        return 1
    else:
        return 0
    
for a, b, c in zip(vec[0:-2],vec[1:-1],vec[2:]):
    cnt = check(a,b,c)
    if cnt == 0:
        break
print(cnt)
