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 vc(p,q):
    return[p[0]-q[0],p[1]-q[1]]

def cross(u,v):
    return(u[0]*v[1]-u[1]*v[0])

n = int(input())
v = []
for _ in range(n):
    x0,y0 = map(int,input().split())
    v.append([x0,y0])
flag = True
for i in range(n-2):
    e_i = vc(v[i+1],v[i])
    e_nxt = vc(v[i+2],v[i+1])
    if cross(e_i,e_nxt)<0:
        flag = False
e_i = vc(v[-1],v[-2])
e_nxt = vc(v[0],v[-1])
if cross(e_i,e_nxt)<0:
    flag = False
e_i = vc(v[0],v[-1])
e_nxt = vc(v[1],v[0])
if cross(e_i,e_nxt)<0:
    flag = False
if flag:
    print(1)
else:
    print(0)
        
    

