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 array, bisect, collections, copy, heapq, itertools, math, random, re, string, sys, time
sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7


def II(): return int(input())
def ILI(): return list(map(int, input().split()))
def IAI(LINE): return [ILI() for __ in range(LINE)]
def IDI(): return {key: value for key, value in ILI()}


def read():
    R, C, N = ILI()
    num_point = []
    for __ in range(N):
        x_1, y_1, x_2, y_2 = ILI()
        num_point.append([(x_1, y_1), (x_2, y_2)])
    return R, C, N, num_point


# 周上を (0, 0) を原点として反時計回りに 1 本の数直線とした時の point の座標を返す．
# 周上にあるかの判定も行う．
def change_edge_point(R, C, point):
    x, y = point
    if x == 0:
        return R * 2 + C + (C - y)
    if x == R:
        return R + y
    if y == 0:
        return x
    if y == C:
        return R + C + (R - x)


def solve(R, C, N, num_point):
    point_double = []
    for ind, point in enumerate(num_point):
        p_1, p_2 = point
        if ((p_1[0] == 0 or p_1[0] == R) or (p_1[1] == 0 or p_1[1] == C)) and ((p_2[0] == 0 or p_2[0] == R) or (p_2[1] == 0 or p_2[1] == C)):
            point_double.append((ind + 1, change_edge_point(R, C, p_1)))
            point_double.append((ind + 1, change_edge_point(R, C, p_2)))
    point_double.sort(key=lambda  x: x[1])
    stack = []
    for point in point_double:
        if len(stack) == 0:
            stack.append(point[0])
            continue
        if point[0] == stack[-1]:
            stack.pop()
        else:
            stack.append(point[0])
    
    if len(stack) == 0:
        return "YES"
    else:
        return "NO"
    

def main():
    params = read()
    print(solve(*params))


if __name__ == "__main__":
    main()
