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.List;
import java.io.IOException;
import java.util.Comparator;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

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

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

            List<Segment> a = new ArrayList<>();
            for (int i = 0; i < n; ++i) {
                int x1 = in.nextInt(), y1 = in.nextInt();
                int x2 = in.nextInt(), y2 = in.nextInt();

                int left = calcPos(r, c, x1, y1);
                int right = calcPos(r, c, x2, y2);
                if (left != -1 && right != -1) {
                    if (left > right) {
                        int aux = left;
                        left = right;
                        right = aux;
                    }
                    a.add(new Segment(left, right));
                }
            }
            Collections.sort(a, Comparator.comparingInt(o -> o.right));
            List<Segment> stk = new ArrayList<>();
            for (Segment e : a) {
                while (!stk.isEmpty() && e.left < stk.get(stk.size() - 1).right) {
                    Segment s = stk.get(stk.size() - 1);
                    stk.remove(stk.size() - 1);
                    if (s.left < e.left) {
                        out.println("NO");
                        return;
                    }
                }
                stk.add(e);
            }
            out.println("YES");
        }

        private int calcPos(int r, int c, int x, int y) {
            if (y == 0) {
                return x;
            } else if (x == r) {
                return r + y;
            } else if (y == c) {
                return r + c + (r - x);
            } else if (x == 0) {
                return r + c + r + (c - y);
            } else {
                return -1;
            }
        }

        private class Segment {
            int left;
            int right;

            Segment(int left, int right) {
                this.left = left;
                this.right = right;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

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

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

