Field Boundary Convexity Survey

A precision-agriculture crew is planning to install a straight-line irrigation boom across a field, and the boom can only pivot correctly if the field's outer boundary is convex, with no inward notches. A drone has already logged the coordinates of every boundary stake, in the exact order they are visited while walking once around the perimeter (either clockwise or counterclockwise).

You are given the n stake coordinates in that walking order. The boundary is convex only if, at every stake, the walker turns the same rotational direction (always toward the left, or always toward the right) before reaching the next stake — never straight through a stake, and never the opposite turning direction at any stake.

Input format

• Line 1: a single integer n, the number of boundary stakes.
• Next n lines: two integers x y, the coordinates of the i-th stake, listed in the order the boundary is walked.

Output format

Print YES if the boundary traced by the stakes (in the given order, wrapping from the last stake back to the first) is a convex polygon, otherwise print NO.

Constraints

• 3 <= n <= 10^4
• -10^4 <= x, y <= 10^4
• All n stakes have distinct coordinates.
• Connecting the stakes in the given order (including the closing edge from the last stake back to the first) always traces a simple polygon boundary — no two edges cross.
• If any three consecutive stakes (wrap-around included) are exactly collinear, the boundary must be judged NOT convex.

3
0 0
4 0
0 4

YES

5
0 0
4 0
4 4
2 2
0 4

NO