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,..., p_n where line segments connecting p_i and p_i+1 (1 ≤ i ≤ n-1) are sides of the polygon. The line segment connecting p_n and p₁ is also a side of the polygon.

Input

g is given by coordinates of the points p₁,..., p_n 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 p_i is given by two integers x_i and y_i. 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 ≤ x_i, y_i ≤ 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

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