8554: CGL_3_B : Is-Convex
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Description
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 $p_1, p_2,..., p_n$ 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 $p_1$ is also a side of the polygon.
$g$ is represented by a sequence of points $p_1, p_2,..., p_n$ 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 $p_1$ is also a side of the polygon.
Input
$g$ is given by coordinates of the points $p_1,..., p_n$ in the following format:
$n$
$x_1\ y_1$
$x_2\ y_2$
$\vdots$
$x_n\ y_n$
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.
$n$
$x_1\ y_1$
$x_2\ y_2$
$\vdots$
$x_n\ y_n$
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.
$-10000 ≤ x_i, y_i ≤ 10000$
No point of the polygon will occur more than once.
Two sides of the polygon can intersect only at a common endpoint.
Sample 1 Input
4
0 0
3 1
2 3
0 3
Sample 1 Output
1
Sample 2 Input
5
0 0
2 0
1 1
2 2
0 2
Sample 2 Output
0