Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTwo players play the following game. Initially, the players have a knife and a rectangular sheet of paper, divided into equal square grid cells of unit size. The players make moves in turn, the player who can't make a move loses. In one move, a player can take the knife and cut the paper along any segment of the grid line (not necessarily from border to border). The part of the paper, that touches the knife at least once, is considered cut. There is one limit not to turn the game into an infinite cycle: each move has to cut the paper, that is the knife has to touch the part of the paper that is not cut before.

Obviously, the game ends when the entire sheet is cut into 1 × 1 blocks. During the game, the pieces of the sheet are not allowed to move. It is also prohibited to cut along the border. The coordinates of the ends of each cut must be integers.

You are given an *n* × *m* piece of paper, somebody has already made *k* cuts there. Your task is to determine who will win if the players start to play on this sheet. You can consider that both players play optimally well. If the first player wins, you also need to find the winning first move.

Input

The first line contains three integers *n*, *m*, *k* (1 ≤ *n*, *m* ≤ 10^{9}, 0 ≤ *k* ≤ 10^{5}) — the sizes of the piece of paper and the number of cuts. Then follow *k* lines, each containing 4 integers *xb*_{i}, *yb*_{i}, *xe*_{i}, *ye*_{i} (0 ≤ *xb*_{i}, *xe*_{i} ≤ *n*, 0 ≤ *yb*_{i}, *ye*_{i} ≤ *m*) — the coordinates of the ends of the existing cuts.

It is guaranteed that each cut has a non-zero length, is either vertical or horizontal and doesn't go along the sheet border.

The cuts may intersect, overlap and even be the same. That is, it is not guaranteed that the cuts were obtained during any correct game.

Output

If the second player wins, print "SECOND". Otherwise, in the first line print "FIRST", and in the second line print any winning move of the first player (the coordinates of the cut ends, follow input format to print them).

Examples

Input

2 1 0

Output

FIRST

1 0 1 1

Input

2 2 4

0 1 2 1

0 1 2 1

1 2 1 0

1 1 1 2

Output

SECOND

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/12/2021 05:16:43 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|