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 sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

def main():
    h, w, n = MI()
    points = []
    cnt = 0
    # 2点とも周上にある組のみ残す
    # 原点（左上）から反時計回りに移動した距離と点の通し番号を記録
    for _ in range(n):
        i0, j0, i1, j1 = MI()
        if (0 < i0 < h and 0 < j0 < w) or (0 < i1 < h and 0 < j1 < w): continue
        for i, j in [(i0, j0), (i1, j1)]:
            if j == 0 or i == h:
                d = i + j
            else:
                d = 2 * (h + w) - i - j
            points.append([d, cnt])
        cnt += 1
    points.sort()
    first = [True] * cnt
    visited = []
    # ABABのように２つの区間がずれて重なっていたらNO
    # ABBAのように完全に含まれるのはセーフ
    for d, pi in points:
        if first[pi]:
            visited.append(pi)
            first[pi] = False
        else:
            last_pi = visited.pop()
            if pi != last_pi:
                print("NO")
                exit()
    print("YES")

main()
