Problem:
Is-Convex

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.

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.

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.

Sample Input 1

4
0 0
3 1
2 3
0 3

Sample Output 1

1

Sample Input 2

5
0 0
2 0
1 1
2 2
0 2

Sample Output 2

0

Solution in Ruby (judge verdict: Accepted)

ps = gets.to_i.times.map { Complex(*gets.split.map(&:to_i)) }
p ps.size.times.all? {|i|
  u, v = ps[(i+1)%ps.size] - ps[i], ps[i-1] - ps[i]
  (v / u).arg >= 0
} ? 1 : 0