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
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    def check(x,y):
        return (x == 0)|(x == w)|(y == 0)|(y == h)

    w,h,n = LI()
    px0 = []
    pxw = []
    py0 = []
    pyh = []
    for i in range(1,n+1):
        x,y,s,t = LI()
        if check(x,y)&check(s,t):
            if x == 0:
                px0.append((y,i))
            elif x == w:
                pxw.append((-y,i))
            elif y == 0:
                py0.append((-x,i))
            else:
                pyh.append((x,i))
            if s == 0:
                px0.append((t,i))
            elif s == w:
                pxw.append((-t,i))
            elif t == 0:
                py0.append((-s,i))
            else:
                pyh.append((s,i))
    px0.sort()
    pxw.sort()
    py0.sort()
    pyh.sort()
    p = px0+pyh+pxw+py0
    q = deque()
    for x, i in p:
        if q:
            qi = q.pop()
            if qi != i:
                q.append(qi)
                q.append(i)
        else:
            q.append(i)
    if q:
        print("NO")
    else:
        print("YES")
    return

#Solve
if __name__ == "__main__":
    solve()
