Problem: Two 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 ≤ 109, 0 ≤ k ≤ 105) — the sizes of the piece of paper and the number of cuts. Then follow k lines, each containing 4 integers xbi, ybi, xei, yei (0 ≤ xbi, xei ≤ n, 0 ≤ ybi, yei ≤ 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

Solution (in JAVA):

Solution:
import java.util.List;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Set;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author AlexFetisov
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC_CuttingPaper solver = new TaskC_CuttingPaper();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC_CuttingPaper {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();

        verticalCuts = new HashMap<Integer, List<Cut>>();
        horizontalCuts = new HashMap<Integer, List<Cut>>();

        for (int i = 0; i < k; ++i) {
            int x1 = in.nextInt();
            int y1 = in.nextInt();
            int x2 = in.nextInt();
            int y2 = in.nextInt();
            if (x1 == x2) {
                addCut(horizontalCuts, x1, y1, y2);
            } else {
                addCut(verticalCuts, y1, x1, x2);
            }
        }
        verticalSize = new HashMap<Integer, Integer>();
        horizontalSize = new HashMap<Integer, Integer>();
        unify(verticalCuts, verticalSize, n);
        unify(horizontalCuts, horizontalSize, m);

        int nim = 0;
        if (n % 2 == 0) {
            nim ^= m;
        }
        if (m % 2 == 0) {
            nim ^= n;
        }
        nim ^= updateNim(verticalSize, n);
        nim ^= updateNim(horizontalSize, m);
        if (nim == 0) {
            out.println("SECOND");
            return;
        }

        if (verticalCuts.size() < m-1) {
            if (tryFull(0, verticalCuts, n, nim, out)) {
                return;
            }
        }
        if (horizontalCuts.size() < n-1) {
            if (tryFull(1, horizontalCuts, m, nim, out)) {
                return;
            }
        }

        if (tryNotFull(0, verticalCuts, verticalSize, n, nim, out)) {
            return;
        }
        if (tryNotFull(1, horizontalCuts, horizontalSize, m, nim, out)) {
            return;
        }
        throw new AssertionError("!");
    }

    private boolean tryNotFull(int hor, HashMap<Integer, List<Cut>> cuts, HashMap<Integer, Integer> sizes, int n, int nim, PrintWriter out) {
        for (int id : cuts.keySet()) {
            int pileSize = sizes.get(id);
            if (pileSize == 0) continue;
            int need = (nim ^ pileSize);
            if (need < pileSize) {
                need = pileSize - need;
                outputNotFull(hor, need, id, cuts.get(id), n, out);
                return true;
            }
        }
        return false;
    }

    private void outputNotFull(int hor, int need, int id, List<Cut> cuts, int n, PrintWriter out) {
        out.println("FIRST");
        int left = 1, right = n, res = -1, middle;
        while (left <= right) {
            middle = (left + right) / 2;
            int total = getTotal(cuts, middle);
            if (total == need) {
                res = middle;
                break;
            }
            if (total < need) {
                left = middle + 1;
            } else {
                right = middle - 1;
            }
        }

        if (res == -1) throw new AssertionError("!");
        if (hor == 0) {
            // vertical
            out.println("0 " + id + " " + res + " " + id);
        } else {
            // horizontal
            out.println(id + " 0 " + id + " " + res);
        }
    }

    private int getTotal(List<Cut> cuts, int middle) {
        if (cuts.size() == 0) return middle;
        int id = -1;
        for (int i = 0; i < cuts.size(); ++i) {
            if (cuts.get(i).start > middle) {
                id = i;
                break;
            }
        }
        if (id == 0) {
            return middle;
        }
        if (id == -1) {
            id = cuts.size()-1;
        } else {
            --id;
        }
        int sum = 0;

        for (int i = 0; i < id; ++i) {
            sum += cuts.get(i).finish - cuts.get(i).start;
        }
        if (cuts.get(id).finish > middle) {
            sum += middle - cuts.get(id).start;
        } else {
            sum += cuts.get(id).finish - cuts.get(id).start;
        }
        return middle - sum;
    }

    private boolean tryFull(int hor, HashMap<Integer, List<Cut>> cuts, int n, int nim, PrintWriter out) {
        int pileSize = n;
        int need = (nim ^ pileSize);
        if (need < pileSize) {
            need = pileSize - need;
            int id = 1;
            while (cuts.containsKey(id)) {
                ++id;
            }
            outputFull(hor, need, id, out);
            return true;
        }
        return false;
    }

    private void outputFull(int hor, int need, int id, PrintWriter out) {
        out.println("FIRST");
        if (hor == 0) {
            // vertical
            out.println("0 " + id + " " + need + " " + id);
        } else {
            // horizontal
            out.println(id + " 0 " + id + " " + need);
        }
    }

    private long updateNim(HashMap<Integer, Integer> sizes, int n) {
        int res = 0;
        for (int id : sizes.keySet()) {
            int curSize = sizes.get(id);
            res ^= n;
            res ^= curSize;
        }
        return res;
    }

    private void unify(HashMap<Integer, List<Cut>> cuts, HashMap<Integer, Integer> sizes, int n) {
        for (int id : cuts.keySet()) {
            List<Cut> list = cuts.get(id);
            Collections.sort(list);
            Cut cur = null;
            List<Cut> newList = new ArrayList<Cut>();
            for (Cut c : list) {
                if (cur == null) {
                    cur = c;
                } else if (cur.finish < c.start) {
                    newList.add(cur);
                    cur = c;
                } else if (c.finish > cur.finish) {
                    cur.finish = c.finish;
                }
            }
            if (cur != null) {
                newList.add(cur);
            }

            cuts.put(id, newList);
            int totalSize = 0;
            for (Cut c : newList) {
                totalSize += c.finish - c.start;
            }
            sizes.put(id, n - totalSize);
        }
    }

    private void addCut(HashMap<Integer, List<Cut>> dict, int row, int x1, int x2) {
        if (x2 < x1) {
            int t = x1;
            x1 = x2;
            x2 = t;
        }
        List<Cut> list;
        if (dict.containsKey(row)) {
            list = dict.get(row);
        } else {
            list = new ArrayList<Cut>();
        }
        list.add(new Cut(x1, x2));
        dict.put(row, list);
    }

    HashMap<Integer, Integer> verticalSize;
    HashMap<Integer, Integer> horizontalSize;
    HashMap<Integer, List<Cut>> verticalCuts;
    HashMap<Integer, List<Cut>> horizontalCuts;

    class Cut implements Comparable<Cut> {
        int start, finish;

        public Cut(int start, int finish) {
            this.start = start;
            this.finish = finish;
        }

        public int compareTo(Cut cut) {
            if (start != cut.start) return start - cut.start;
            return finish - cut.finish;
        }
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer stt;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
    }

    public String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    public String nextString() {
        while (stt == null || !stt.hasMoreTokens()) {
            stt = new StringTokenizer(nextLine());
        }
        return stt.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(nextString());
    }

}