Polygon Game

A convex polygon has $N$ vertices. Every interior angle is smaller than $180^\circ$, and the vertices are numbered $1$ through $N$ in clockwise order.

Seonggwan and Hongjun play a game on this polygon. Seonggwan moves first, and the two players alternate turns.

On a turn the player picks two vertices and draws the segment that joins them. The segment is allowed to lie on a side of the polygon. The new segment must not meet any segment drawn earlier. Two segments that touch at an endpoint count as meeting.

The player who cannot draw a segment loses. Given $N$, write a program that decides who wins when both players play optimally.

The first line contains $N$ ($3 \le N \le 1000$).

Print $1$ if Seonggwan wins, or $2$ if Hongjun wins.