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 {
	static int R, C;
	public static class Terminal {
		int d;
		int idx;
		public Terminal(int d, int idx) {
			this.d = d;
			this.idx = idx;
		}
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		R = sc.nextInt();
		C = sc.nextInt();
		int N = sc.nextInt();
		ArrayList<Terminal> list = new ArrayList<>();
		
		for(int i=0; i<N; i++) {
			int x1 = sc.nextInt();
			int y1 = sc.nextInt();
			int x2 = sc.nextInt();
			int y2 = sc.nextInt();
			
			if(isOnEdge(x1, y1) && isOnEdge(x2, y2)) {
				list.add(new Terminal(convert(x1, y1), i));
				list.add(new Terminal(convert(x2, y2), i));
			}
		}
		Collections.sort(list, new Comparator<Terminal>() {
			public int compare(Terminal t1, Terminal t2) {
				return t1.d - t2.d;
			}
		});
		
		LinkedList<Terminal> stack = new LinkedList<>();
		
		for(Terminal t : list) {
			if(!stack.isEmpty() && stack.peek().idx == t.idx)
				stack.pop();
			else
				stack.push(t);
		}
		
		System.out.println(stack.isEmpty() ? "YES" : "NO");
		
		sc.close();
	}
	
	static boolean isOnEdge(int x, int y) {
		return x==0 || x==R || y==0 || y==C;
	}
	
	static int convert(int x, int y) {
		if(x==0)
			return y;
		else if(y==C)
			return C + x;
		else if(x==R)
			return C + R + (C-y);
		else
			return C + R + C + (R-x);
	}
}
