Snuke is playing a puzzle game. In this game, you are given a rectangular board of dimensions R × C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i,1},y_{i,1}) and (x_{i,2},y_{i,2}).

The objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N. Here, the curves may not go outside the board or cross each other.

Determine whether this is possible.

Constraints

* 1 ≤ R,C ≤ 10^8
* 1 ≤ N ≤ 10^5
* 0 ≤ x_{i,1},x_{i,2} ≤ R(1 ≤ i ≤ N)
* 0 ≤ y_{i,1},y_{i,2} ≤ C(1 ≤ i ≤ N)
* All given points are distinct.
* All input values are integers.

Input

Input is given from Standard Input in the following format:


R C N
x_{1,1} y_{1,1} x_{1,2} y_{1,2}
:
x_{N,1} y_{N,1} x_{N,2} y_{N,2}


Output

Print `YES` if the objective is achievable; print `NO` otherwise.

Examples

Input

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2


Output

YES


Input

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1


Output

NO


Input

5 5 7
0 0 2 4
2 3 4 5
3 5 5 2
5 5 5 4
0 3 5 1
2 2 4 4
0 5 4 1


Output

YES


Input

1 1 2
0 0 1 1
1 0 0 1


Output

NO
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Collection;
import java.io.IOException;
import java.util.Deque;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
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);
        EConnected solver = new EConnected();
        solver.solve(1, in, out);
        out.close();
    }

    static class EConnected {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int r = in.nextInt();
            int c = in.nextInt();
            int n = in.nextInt();

            List<EConnected.P> l = new ArrayList<>();

            for (int i = 0; i < n; i++) {
                int x1 = in.nextInt();
                int y1 = in.nextInt();
                int x2 = in.nextInt();
                int y2 = in.nextInt();
                long t1 = transform(r, c, x1, y1);
                long t2 = transform(r, c, x2, y2);
                if (t1 == -1 || t2 == -1)
                    continue;
                l.add(new EConnected.P(i, t1));
                l.add(new EConnected.P(i, t2));
            }

            l.sort(Comparator.comparingLong(p -> p.t));

            Deque<Integer> stack = new ArrayDeque<>();
            for (EConnected.P p : l) {
                int label = p.label;
                if (!stack.isEmpty() && stack.peekLast() == label) {
                    stack.pollLast();
                } else {
                    stack.addLast(label);
                }
            }

            boolean answer = stack.isEmpty();
            out.println(answer ? "YES" : "NO");
        }

        long transform(int r, int c, int x, int y) {
            int L = Math.max(r, c) + 10;
            if (x == 0) {
                return y;
            }
            if (y == c) {
                return 3 * L + x;
            }
            if (x == r) {
                return 6 * L + L - y;
            }
            if (y == 0) {
                return 9 * L + L - x;
            }

            return -1;
        }

        static class P {
            final int label;
            final long t;

            P(int label, long t) {
                this.label = label;
                this.t = t;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

