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

n=int(input())

A=[]
for _ in range(n):
  x,y=map(int,input().split())
  A.append(x+y*1j)

flag=0
for i in range(n-1):
  for j in range(i+1,n):
    if cross(A[i]-A[i-1],A[j]-A[i-1])<0 or cross(A[i+1]-A[i],A[j]-A[i])<0:
      print("0")
      flag=1
      break
  if(flag==1):
    break

if(flag==0):
  print("1")

