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
# coding: utf-8

import heapq


def coord_on_edge(x, y, R, C):
    if y == 0:
        return x
    if x == R:
        return R + y
    if y == C:
        return R + C + R - x
    if x == 0:
        return 2 * (R + C) - y
    return None


def on_edge(x1, y1, x2, y2, R, C, i, edge_points):
    c1 = coord_on_edge(x1, y1, R, C)
    c2 = coord_on_edge(x2, y2, R, C)
    if c1 is not None and c2 is not None:
        heapq.heappush(edge_points, (c1, i))
        heapq.heappush(edge_points, (c2, i))


def solve():
    R, C, N = map(int, input().split())
    edge_points = []            # (coord, point#)
    for i in range(N):
        x1, y1, x2, y2 = map(int, input().split())
        on_edge(x1, y1, x2, y2, R, C, i, edge_points)
    q = []
    while edge_points:
        c, i = heapq.heappop(edge_points)
        # print((c, i))           # dbg
        if len(q) and q[-1] == i:
            q.pop()
        else:
            q.append(i)
    if len(q):
        return "NO"
    return "YES"


print(solve())
