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.

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

inputFormat

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.

outputFormat

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

样例

5
0 0
2 0
1 1
2 2
0 2

0