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.util.*;

public class Main {

	public static void main (String[] args)  {
		Scanner sc = new Scanner(System.in);
		int r = sc.nextInt();
		int c = sc.nextInt();
		int n = sc.nextInt();
		ArrayList<Point> list = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			int r1 = sc.nextInt();
			int c1 = sc.nextInt();
			int r2 = sc.nextInt();
			int c2 = sc.nextInt();
			if (((r1 == 0 || r1 == r) || (c1 == 0 || c1 == c)) && ((r2 == 0 || r2 == r) || (c2 == 0 || c2 == c))) {
				list.add(new Point(r1, c1, i));
				list.add(new Point(r2, c2, i));
			}
		}
		Collections.sort(list, new Comparator<Point>() {
		public int compare(Point p1, Point p2) {
			if (p1.row == 0 || p1.col == c) {
				if (p2.row == 0 || p2.col == c) {
					return p1.row + p1.col - p2.row - p2.col;
				} else {
					return -1;
				}
			} else {
				if (p2.row == 0 || p2.col == c) {
					return 1;
				} else {
					return p2.row + p2.col - p1.row - p1.col;
				}
			}
		}
		});
		ArrayDeque<Point> deq = new ArrayDeque<>();
		for (Point p : list) {
			if (deq.size() > 0 && deq.getLast().idx == p.idx) {
				deq.pollLast();
			} else {
				deq.addLast(p);
			}
		}
		if (deq.size() == 0) {
			System.out.println("YES");
		} else {
			System.out.println("NO");
		}
	}
	
	static class Point {
		int row;
		int col;
		int idx;
		public Point(int row, int col, int idx) {
			this.row = row;
			this.col = col;
			this.idx = idx;
		}
		public String toString() {
			return "row:" + row + " col:" + col + " idx:" + idx;
		}
	}
}
