Game#8506
Two players play a graph coloring game. They make moves in turn, first player moves first. Initially they take some undirected graph. At each move, a player can color an uncolored vertex with either white or black color (each player can use any color, possibly different at different turns). It's not allowed to color two adjacent vertices with the same color. A player that can't move loses.
After playing this game for some time, they decided to study it. For a start, they've decided to study very simple kind of graph - a chain. A chain consists of vertices, v_1, v_2, ... , v_n, and n - 1 edges, connecting v_1 with v_2, v_2 with v_3, ..., v_{n-1} with v_n.
Given a position in this game, and assuming both players play optimally, who will win?
The first line contains the integer (1 \leq n \leq 10^5).
The second line describes the current position. It contains digits without spaces. -th digit describesthe color of vertex v_i: - uncolored, - black, - white. No two vertices of the same color are adjacent.
On the only line print FIRST if the player moving first in that position wins the game, and SECOND otherwise.
Example 1
Example 2