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 Scala (judge verdict: Accepted)

import scala.io.StdIn._

import Math._
object Main extends App {
  val eps0 = 1e-12

  val q = readLine.toInt

  val xs = new Array[Int](q+2)
  val ys = new Array[Int](q+2)
  for (i <- 0 until q) {
    val Seq(x, y) = readLine.split(' ').map(_.toInt).toList
    xs(i) = x
    ys(i) = y
  }

  xs(q) = xs(0); xs(q+1) = xs(1)
  ys(q) = ys(0); ys(q+1) = ys(1)

  val subarea = for (i <- 0 until q) yield {
    val xs1 = xs(i+1) - xs(i)
    val ys1 = ys(i+1) - ys(i)
    val xs2 = xs(i+2) - xs(i)
    val ys2 = ys(i+2) - ys(i)

    xs1 * ys2 - ys1 * xs2
  }

  println(if (subarea.forall(_ >= 0)) "1" else "0")
}