#891 X Clash

Statement

Statement language

You are given a simple polygon $G$ with vertices $P_1, P_2, \cdots, P_N$ in boundary order. The polygon includes its interior and boundary.

Let $\ell$ be the line through $P_1$ and $P_2$ . The entire polygon lies on one side of $\ell$ . Let be the closed half-plane on that side. The wall occupies .

Initially, $G$ fits exactly into the opening in the wall. Determine whether $G$ can be moved by a continuous sequence of translations, without rotation, until every point of $G$ is outside $H$ .

Throughout the motion, the area of the intersection between the moving polygon and the wall must be $0$ . Touching boundaries and sliding along them are allowed. The direction of translation may change during the motion. The wall and $H$ remain fixed.

Input

The input is given in the following format:

$N$ $x_1\ y_1$ $x_2\ y_2$

Output

Print YES if the polygon can be removed completely, and NO otherwise.

Constraints

$3 \leq N \leq 1000$ .
$-10\,000 \leq x_i,y_i \leq 10\,000$ ().

Subtasks

#	Score	Constraints
1	12	$N=3$ .
2	88	No additional constraints.

Samples

Sample 1

Input

Output

YES

Sample 2

Input

Output

NO

Sample 3

Input

Output

YES